anÁlise numÉrica do escoamento turbulento no interior de secadores

8182019 ANAacuteLISE NUMEacuteRICA DO ESCOAMENTO TURBULENTO NO INTERIOR DE SECADORES

httpslidepdfcomreaderfullanalise-numerica-do-escoamento-turbulento-no-interior-de-secadores 174

DANIEL GIOVANI POSSAMAI

ANAacuteLISE NUMEacuteRICA DO ESCOAMENTO TURBULENTO NO INTERIOR DESECADORES

Dissertaccedilatildeo apresentada para a obtenccedilatildeo do tiacutetulo demestre em Engenharia Mecacircnica da Universidade do

Estado de Santa Catarina Centro de CiecircnciasTecnoloacutegicas ndash CCT

Orientador prof Dr Paulo Seacutergio Berving Zdanski

Coorientador prof Dr Miguel Vaz Junior

JOINVILLE SC2013



P856aPossamaiDaniel Giovani

Anaacutelise numeacuterica do escoamento turbulento no interior

de secadores Daniel Giovani Possamai ndash 2013

75 p il 21 cm

Orientador Paulo Sergio Berving Zdanski

Coorientador Miguel Vaz Junior

Bibliografia p 73-75

Dissertaccedilatildeo (mestrado) ndash Universidade do Estado de

Santa Catarina Centro de Ciecircncias Teacutecnicas Programa de

Poacutes-Graduaccedilatildeo em Engenharia MecacircnicaJoinville 2013

1 Escoamento turbulento 2 Anaacutelise numeacuterica I

Zdanski Paulo Sergio Berving II Vaz Junior Miguel

III Universidade do Estado de Santa Catarina Programa

de Poacutes-Graduaccedilatildeo em Engenharia Mecacircnica IV Tiacutetulo

CDD 6201 - 20ed



Dedico este trabalho agrave minha famiacutelia em especial ameus pais Nelson e Dolores e a minha namoradaDanielli



AGRADECIMENTOS

Agradeccedilo principalmente a meus pais o Sr Nelson Possamai e a Sra Dolores pelo apoio

e incentivo que durante este tempo foi de grande importacircncia para mim dando me forccedilas e

motivaccedilatildeo

Agradeccedilo tambeacutem a Danielli que esteve sempre ao meu lado durante esta etapa me

apoiando e incentivando

Agradeccedilo ao meu orientador Prof Dr Paulo Sergio Berving Zdanski e ao meu

coorientador Prof Dr Miguel Vaz Junior pela orientaccedilatildeo e paciecircncia que dispunham em retirar

duacutevidas corrigir erros e dividir os conhecimentos

Agradeccedilo agrave UDESC e ao Programa de Poacutes-Graduaccedilatildeo em Engenharia Mecacircnica pela

oportunidade de ingresso e financiamento deste estudo



O que vocecirc sabe natildeo tem valor o valor estaacute no quevocecirc faz com o que sabe

Bruce Lee





RESUMO

O presente trabalho teve por objetivo principal a anaacutelise de um escoamento turbulentoincompressiacutevel e isoteacutermico no interior de um secador de madeira utilizando uma metodologianumeacuterica baseada no programa comercial ANSYS CFXreg O estudo fiacutesico realizado consistiu emavaliar a aerodinacircmica do secador a saber determinar a distribuiccedilatildeo de velocidades no interiordo dispositivo em diferentes condiccedilotildees de operaccedilatildeo No estudo da topologia do escoamento nointerior do secador de madeira a anaacutelise foi focada principalmente na avaliaccedilatildeo da influecircnciados seguintes paracircmetros (i) largura do canal vertical de entrada lsquo plenumrsquo e (ii) velocidade doescoamento na entrada De acordo com os resultados obtidos a largura do lsquo plenumrsquo teminfluecircncia direta na distribuiccedilatildeo de velocidades no interior do secador Este paracircmetro estaacutediretamente relacionado agrave localizaccedilatildeo e tamanho do voacutertice gerado apoacutes a quina de entrada Por

outro lado a variaccedilatildeo da velocidade de entrada natildeo apresentou diferenccedilas significativas natopologia do escoamento no interior do secador Por fim vale salientar que para se obter ganhossignificativos na uniformidade do escoamento nos canais faz-se necessaacuterio encontrar alternativasque minimizem o voacutertice gerado na quina de entrada do secador

Palavras-chave Escoamento turbulento Beneficiamento de madeira Anaacutelise numeacuterica



ABSTRACT

The main objective of the present work is the numerical simulation of an incompressibleisothermal turbulent flow inside a timber dry kiln using the commercial software ANSYS CFXregThe physical study aims at assessing the dry kiln aerodynamics by determining the velocitydistribution inside the kiln for different operating conditions In the study of the flow topologyinside the dry kiln the analysis is focused mainly on the evaluation of the influence of the (i)width of the inlet ldquo plenumrdquo and (ii) flow velocity at its entrance The simulations show that theldquo plenumrdquo width has a direct influence on the velocity distribution in the kiln This parameterdirectly affects the location and size of the vortex generated just after the ldquo plenumrdquo entrancecorner Moreover the variation of the inlet velocity imposes no significant differences in theflow topology inside the kiln Finally it is worth to emphasize that to significantly improve flow

uniformity in the channels across the stack height it is necessary to find alternatives able toreduce or eliminate the vortex generated at the entrance of the inlet ldquo plenumrdquo

Keywords Turbulence flow Wood processing Numerical analysis



LISTA DE ILUSTRACcedilOtildeES

Figura 21 - Representaccedilatildeo de um secador de madeira convencional 22

Figura 22- Objeto submetido ao processo de secagem 23

Figura 23 - Diferentes arranjos para um processo de secagem 24

Figura 24 minus Distribuiccedilatildeo de um escoamento de ar em um secador de madeira industrial 25

Figura 25 minus Padrotildees de escoamento para um secador sem a seccedilatildeo semicircular (a) e com a seccedilatildeo

semicircular (b) 26

Figura 26 minus Linhas de corrente durante o tratamento teacutermico 27

Figura 27 minus Representaccedilatildeo esquemaacutetica da geometria analisada 27

Figura 28 minus Linhas de corrente na geometria e moacutedulo da velocidade para A = 01[m] 28

Figura 31 minus Discretizaccedilatildeo mostrando o elemento 34

Figura 32 minus O elemento 1234 e o volume de controle centrado em 1 35

Figura 41 - Representaccedilatildeo esquemaacutetica do escoamento em um canal bidimensional 41

Figura 42 minus Perfis de energia cineacutetica turbulenta 42

Figura 43 minus Perfis de velocidade normalizada em funccedilatildeo da coordenada adimensional

na seccedilatildeo de saiacuteda do canal 43

Figura 44minus Representaccedilatildeo esquemaacutetica da geometria de um secador de madeira 44

Figura 45 ndash Aspectos da malha na regiatildeo de entrada dos canais superiores 45

Figura 46 ndash Linhas de corrente no interior da geometria do secador de madeira (a) Resultados

obtidos por Nijdam e Keey (2002) e (b) Resultados obtidos no presente trabalho 46

Figura 47 ndash Perfis de velocidade relativa nos canais do secador de madeira 47

Figura 48 ndash Perfil das velocidades relativas nos canais utilizando as malhas MU (malha

uniforme) e MB ( Malha com estiramento) ndash estudo de refinamento da malha 48

Figura 49 minus Linhas de corrente no interior da geometria modificada do secador de madeira 49


Figura 411 minus Perfis de pressatildeo estaacutetica meacutedia nas seccedilotildees de entrada dos canais do secador de

madeira 51

Figura 51 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria de referecircncia

para um lsquoplenumrsquo igual a 015 m 55



Figura 52 ndash Vista em detalhe da topologia do escoamento nas regiotildees de entrada e saiacuteda da

geometria de referecircncia para um lsquoplenumrsquo igual a 015 m 55

Figura 53 ndash Distribuiccedilatildeo da componente da velocidade no interior da geometria de referecircncia

56

Figura 54 - Vista em detalhe da distribuiccedilatildeo da componente da velocidade nas regiotildees de

entrada e saiacuteda da geometria de referecircncia 56


57



Figura 57 - Distribuiccedilatildeo da pressatildeo estaacutetica relativa no interior da geometria de referecircncia 58

Figura 58 - Vista em detalhe da distribuiccedilatildeo da pressatildeo estaacutetica relativa nas regiotildees de entrada

e saiacuteda da geometria de referecircncia 59

Figura 59 - Distribuiccedilatildeo da energia cineacutetica turbulenta no interior da geometria de referecircncia

60

Figura 510 - Vista em detalhe da distribuiccedilatildeo da energia cineacutetica turbulenta nas regiotildees de


Figura 511 - Velocidade meacutedia nos canais formados pelas placas de madeiras na geometria

de referecircncia 62

Figura 512 - Variaccedilatildeo de pressatildeo estaacutetica meacutedia nos canais do secador de madeira 62

Figura 513 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria para o

lsquoplenumrsquo de 01 m 63



Figura 515 ndash Velocidade meacutedia nos canais formados pelas placas de madeiras nas

geometrias testadas 65

Figura 516 - Variaccedilatildeo de pressatildeo estaacutetica nos canais do secador de madeira para as trecircs


Figura 517 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria de

referecircncia lsquoplenumrsquo de 015 m com = 3 ms 66



Figura 519 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria dereferecircncia lsquoplenumrsquo de 015 m com = 9 ms 67



Figura 520 - Velocidade meacutedia nos canais no interior do secador de madeira para as quatro

velocidades 68

Figura 521 ndash Variaccedilatildeo de pressatildeo no canais no interior do secador de madeira para as quatro

velocidades 68

Figura 522 - Perda de carga global entre a entrada e saiacuteda do secador 70



LISTA DE SIacuteMBOLOS

A Largura do lsquoplenumrsquo

Aacuterea normal ao escoamento

B Espessura da madeira

C Altura do canal formado pelas madeiras

Constantes de fechamento do modelo de turbulecircncia

D Comprimento da madeira

E Distacircncia entre o canal de entrada e o primeiro canal de escoamento

F Altura do canal de entrada do secador

G Lado direito (RHS ndash Right Hand Side)H Altura total do secador de madeira

Altura do canal

Energia cineacutetica turbulenta - 1

2 i jk u u=

Energia cineacutetica turbulenta na entrada

L Comprimento total do secador de madeira

l Largura do secador de madeira M Matriz dos Coeficientes

Fluxo de massa

n Nuacutemero da iteraccedilatildeo

Direccedilatildeo normal a parede

Pressatildeo instantacircnea

Pressatildeo meacutedia

Taxa de produccedilatildeo de turbulecircncia

Pressatildeo efetiva -2

3e p p k ρ = +

Pressatildeo meacutedia na entrada do canal

Pressatildeo meacutedia na entrada do secador

Pressatildeo meacutedia na saiacuteda do canal

Pressatildeo meacutedia na saiacuteda do secador

Vazatildeo

Resiacuteduo

Nuacutemero de Reynolds baseado na altura do canal - R e h

uh ν =



Aacuterea da entrada do secador

Taxa de deformaccedilatildeo do escoamento

Termos de fonte do modelo de turbulecircncia

Componente da velocidade instantacircnea

Velocidade do escoamento na entrada

Componente de velocidade instantacircnea

Velocidade normal ao plano de simetria

Velocidade na parede

Velocidade de atrito (lei da parede)

Velocidade adimensional (lei da parede)

Componente de velocidade com valor especificado

Componente da velocidade instantacircnea Coordenadas dos eixos cartesianos

Componente dos eixos cartesianos

Distacircncia adimensional da parede (lei da parede)

Coeficiente de difusatildeo nas equaccedilotildees do modelo de turbulecircncia

Operador de Kronecker

Variaccedilatildeo de pressatildeo no interior dos canais

Perda de carga global Avanccedilo no tempo

Taxa de dissipaccedilatildeo da energia cineacutetica turbulenta

Taxa de dissipaccedilatildeo da energia cineacutetica turbulenta na entrada

Vetor soluccedilatildeo

Viscosidade dinacircmica molecular

Viscosidade efetiva - e T micro micro micro = +

Viscosidade turbulenta -2

T

k C micro micro ρ

ε =

Viscosidade cinemaacutetica molecular - ν micro ρ =

Densidade do fluido


Tensotildees de Reynolds -

ij i juuτ ρ = minus

Tensatildeo de cisalhamento na parede

Funccedilatildeo de dissipaccedilatildeo viscosa

Variaacutevel instantacircnea do escoamento



Flutuaccedilatildeo da variaacutevel instantacircnea

Variaacutevel meacutedia do escoamento



SUMAacuteRIO

1 INTRODUCcedilAtildeO 19

11 OBJETIVO DO TRABALHO 20

12 ORGANIZACcedilAtildeO DO TRABALHO 20

2 REVISAtildeO BIBLIOGRAacuteFICA 21

21 PROCESSO DE SECAGEM 21

22 AERODINAcircMICA DO SECADOR 22

3 FORMULACcedilAtildeO TEOacuteRICA 29

31 EQUACcedilOtildeES DE GOVERNO 29

32 EQUACcedilOtildeES DE NAVIER-STOKES COM MEacuteDIA DE REYNOLDS 30

33 MODELAGEM DE TURBULEcircNCIA 31

331 Modelo de duas equaccedilotildees 32

34 MEacuteTODO NUMEacuteRICO 34

341 Discretizaccedilatildeo das equaccedilotildees 35

342 Soluccedilatildeo do sistema linear 37

343 Acoplamento pressatildeo ndash velocidade 38

35 CONDICcedilOtildeES DE CONTORNO 38

351 Entrada 39

352 Saiacuteda 39

353 Plano de Simetria 39

354 Paredes soacutelidas 40

4 VERIFICACcedilAtildeO E VALIDACcedilAtildeO 41

41 ESCOAMENTO TURBULENTO EM UM CANAL PLANO BIDIMENSIONAL 41

42 GEOMETRIA SIMPLIFICADA PARA UM SECADOR 43

421 Proposta de alteraccedilatildeo na geometria do secador 48

5 RESULTADOS E DISCUSSOtildeES 53

51 ESTUDO DA GEOMETRIA DE REFEREcircNCIA 53



52 INFLUEcircNCIA DA LARGURA DOS CANAIS DE ENTRADA E SAIacuteDA (LARGURA

DO lsquoPLENUMrsquo) 62

53 INFLUEcircNCIA DA VELOCIDADE DE ENTRADA 65

6 CONCLUSOtildeES E SUGESTOtildeES 71

61 SUGESTOtildeES 72

REFEREcircNCIAS 73





19

1 INTRODUCcedilAtildeO

O conhecimento da aerodinacircmica (estudo da distribuiccedilatildeo de velocidades do ar) no

interior de secadores em processos de secagem de madeira tem impacto direto na qualidade do

produto final (PERREacute KEEY 2006) De acordo com estudos realizados por Perreacute e Keey

(2006) uma distribuiccedilatildeo natildeo-uniforme de velocidades no interior dos canais de um secador

resulta em taxas de secagem distintas para cada uma das regiotildees da pilha de madeira Estas

diferenccedilas nas taxas de secagem satildeo indesejaacuteveis pois levam agrave geraccedilatildeo de tensotildees internas na

madeira resultando em flexatildeo e torccedilatildeo o que pode ocasionar trincas e empenamentos (PERREacute

KEEY 2006) Um segundo aspecto importante a se destacar segundo Nijdam e Keey (2000)

satildeo os principais fatores que conduzem a uma distribuiccedilatildeo natildeo-uniforme de velocidades a saber

(i) a geometria do secador bem como a (ii) disposiccedilatildeo das pilhas de madeira no interior do

mesmo

No contexto do presente trabalho que aborda o estudo da distribuiccedilatildeo de velocidades

(anaacutelise do escoamento) no interior de secadores de madeira eacute de extrema importacircncia o

conhecimento dos principais fatores que influenciam um processo de secagem Segundo Kaya et

al (2008) um problema de secagem eacute compreendido por mecanismos acoplados de difusatildeo de

calor e massa em regime transiente os quais satildeo influenciados por diversos de fatores externos

(temperatura velocidade umidade relativa do ar insuflado) bem como fatores internos (massa

especiacutefica permeabilidade porosidade e caracteriacutesticas fiacutesicas de cada tipo de madeira)

(PERREacute KEEY 2006) Ainda segundo Perreacute e Keey (2006) este processo pode ocorrer ao ar

livre ou de maneira artificial controlada atraveacutes de estufassecadores sendo o processo

controlado mais vantajoso em decorrecircncia do menor tempo de secagem controle do conteuacutedo

final de umidade e independecircncia das condiccedilotildees climaacuteticas da regiatildeo Desta maneira o

entendimento e a modelagem deste tipo de problema satildeo importantes do ponto de vista

tecnoloacutegico e tambeacutem cientiacutefico uma vez que o assunto tem sido escopo de trabalhos tanto na

aacuterea de anaacutelise experimental quanto numeacuterica

Finalmente vale salientar que vaacuterios trabalhos recentes da literatura envolvendo a anaacutelise

numeacuterica de processos de secagem (difusatildeo acoplada de calor e massa em um soacutelido) utilizam

uma formulaccedilatildeo simplificada para incorporarem os efeitos das condiccedilotildees do escoamento a

saber o problema do escoamento do gaacutes eacute resolvido de forma desacoplada sendo asinformaccedilotildees transferidas na forma de condiccedilotildees de contorno na interface com o soacutelido Esta

abordagem eacute utilizada nos trabalhos de Kaya et al (2006 2008) Mohan e Talukdar (2010) Lu e



20

Shen (2007) Zdanski et al (2012) dentre outros Desta forma conclui-se que melhorias nos

processos de secagem podem ser facilitadas se primeiramente forem conhecidos os fatores que

influenciam a distribuiccedilatildeo de velocidades no interior dos canais do dispositivo estimulando o

processo criativo na busca de soluccedilotildees Em virtude do grande custo envolvido na anaacutelise

experimental a simulaccedilatildeo computacional vem ocupando uma posiccedilatildeo de destaque na anaacutelise

deste tipo de processo Dentro deste contexto neste trabalho as simulaccedilotildees foram realizadas

utilizando o programa comercial ANSYS CFXreg

11 OBJETIVO DO TRABALHO

O presente trabalho tem por objetivo principal a anaacutelise de um escoamento turbulentoisoteacutermico no interior de um secador de madeira utilizando uma metodologia numeacuterica baseada

no programa comercial ANSYS CFXreg O estudo fiacutesico a ser realizado consiste em avaliar a

aerodinacircmica do secador a saber determinar a distribuiccedilatildeo de velocidades no interior do

dispositivo em diferentes condiccedilotildees de operaccedilatildeo

12 ORGANIZACcedilAtildeO DO TRABALHO

Este trabalho estaacute dividido em cinco capiacutetulos O primeiro corresponde agrave introduccedilatildeo

onde eacute relacionado o estudo da aerodinacircmica com os problemas de secagem sendo tambeacutem

apresentado o objetivo do trabalho O segundo capiacutetulo compreende uma revisatildeo bibliograacutefica

sobre processos de secagem e aerodinacircmica do secador O terceiro capiacutetulo apresenta a

formulaccedilatildeo teoacuterica onde satildeo apresentadas as equaccedilotildees governantes os modelos utilizados para a

modelagem da turbulecircncia e as condiccedilotildees de contorno No quarto capiacutetulo satildeo apresentadas averificaccedilatildeo e a validaccedilatildeo do programa ANSYS CFXreg

onde os resultados numeacutericos obtidos nas

simulaccedilotildees satildeo confrontados com dados da literatura Finalizando no quinto capiacutetulo satildeo

apresentados os resultados da anaacutelise fiacutesica do escoamento em secadores onde alguns

paracircmetros importantes satildeo analisados Neste capiacutetulo final tambeacutem satildeo apresentadas as

conclusotildees e sugestotildees para trabalhos futuros



21

2 REVISAtildeO BIBLIOGRAacuteFICA

21 PROCESSO DE SECAGEM

Um processo de secagem de madeira tem como objetivo a reduccedilatildeo do conteuacutedo de

umidade ateacute um valor adequado conforme o uso final do produto Os objetivos da secagem satildeo

inibir ataque de fungos reduzir a deformaccedilatildeo dimensional melhorar a resistecircncia mecacircnica

aumentar a trabalhabilidade e facilitar o seu transporte (PERREacute KEEY 2006)

Os processos de secagem podem ser divididos entre secagem ao ar livre e secagem

artificial onde a umidade e a temperatura satildeo controladas sendo este uacuteltimo mais utilizado em

madeiras destinadas a produtos de maior qualidade (PERREacute KEEY 2006) No processo de

secagem ao ar livre as madeiras satildeo dispostas em locais abertos e empilhadas de modo que seja

possiacutevel o ar escoar entre as mesmas retirando a umidade Devem ser tomadas algumas

precauccedilotildees em relaccedilatildeo ao isolamento com o solo alinhamento das madeiras e cobertura sendo

este processo comumente utilizado como um processo preacute-estufa Dentre os processos de

secagem artificiais os mais conhecidos satildeo secador a vaacutecuo secador convencional secador de

alta temperatura e secador solar (PERREacute KEEY 2006)

Para um melhor entendimento do processo de secagem satildeo apresentadas a seguir as trecircs

fases distintas para a secagem de madeira em estufa (ver Figura 21) (i) Na primeira fase ocorre

a elevaccedilatildeo gradativa da temperatura no interior da estufa em condiccedilotildees de elevada umidade do

ar (ii) Apoacutes este processo ter sido concluiacutedo daacute-se iniacutecio agrave segunda fase ndash secagem ndash sendo

caracterizada pela elevaccedilatildeo lenta da temperatura e a diminuiccedilatildeo gradativa da umidade do ar no

interior da estufa neste ponto faz-se necessaacuterio o monitoramento da umidade para cada tipo de

madeira seguindo um programa previamente estabelecido (iii) Por uacuteltimo ocorre a

uniformizaccedilatildeo sendo que nessa fase o objetivo eacute homogeneizar a umidade dentro da estufa para

que natildeo ocorram falhas nas madeiras como empenamento e rachaduras (PERREacute KEEY 2006)

No processo de secagem devem-se considerar alguns fatores importantes tais como

espeacutecie da madeira tipo de corte espessura tempo de secagem teor de umidade relativa

desejada e velocidade do escoamento do ar no interior do secador dentre outros A secagem

artificial apresenta como principais vantagens menor tempo do processo maior controle e

obtenccedilatildeo de teores de umidade mais baixos poreacutem destaca-se como desvantagem um maior

custo de implementaccedilatildeo do sistema e de operaccedilatildeo do equipamento (PERREacute KEEY 2006)



22

Figura 21 - Representaccedilatildeo de um sec

Fonte Perreacute e Keey (2006)

Neste sentido o entendi

desenvolvimento da induacutestria d

conhecimento teacutecnico sobre o tem

22 AERODINAcircMICA DO SECA

A madeira ocupa uma pos

grande quantidade de produtos

Visando assegurar a qualidade do

pelo processo de secagem Confortem influecircncia direta no tempo e n

satildeo apresentados alguns trabalhos

satildeo discutidos

Um trabalho recente envol

secagem foi desenvolvido por M

geometria analisada por estes au

empregado para estudar o comport

retangular submetido a diferentes

dor de madeira convencional

ento desta praacutetica faz-se necessaacuterio natilde

e produtos madeireiros mas para o en

DOR

iccedilatildeo de destaque sendo a principal mateacuteria

eja na induacutestria civil ou moveleira (KAD

produto final grande parte da umidade da

me discutido no capiacutetulo anterior a aerodinqualidade do processo de secagem Desta f

da literatura onde os aspectos da aerodinacircm

endo a anaacutelise numeacuterica do escoamento em

ohan e Talukdar (2010) Na Figura 22 es

tores para o qual um modelo numeacuterico t

amento transiente da temperatura e da umid

condiccedilotildees de escoamento Como variaacutevei

apenas para o

riquecimento do

prima para uma

EM et al2011)

adeira eacute retirada

mica do secadorrma nesta seccedilatildeo

ica em secadores

um problema de

aacute representada a

idimensional foi

de em um objeto

do processo de



secagem foram analisados

os resultados obtidos por e

para as velocidades e temp

promissores a saber (i) di

na velocidade do escoamen

do escoamento passa de 313

Figura 22- Objeto submetido

Fonte Mohan e Talukdar (201

Outros estudos sobr

avaliam variaacuteveis como a i

uma cavidade retangular ndash

No interior da cavidade re

conhecida o qual foi subme

conhecer a distribuiccedilatildeo d

favoraacutevel agrave troca de calor

superfiacutecie caso (e)

s efeitos da velocidade e temperatura do esc

stes autores natildeo foi possiacutevel obter uma tax

eraturas utilizadas Entretanto foram encon

inuiccedilatildeo de 43 no tempo de secagem para

o e (ii) reduccedilatildeo de 40 no tempo de secage

K para 353 K

o processo de secagem

0)

e a aerodinacircmica como os desenvolvidos

fluecircncia da posiccedilatildeo da entrada e saiacuteda do es

geometria utilizada como modelo para um s

tangular foi posicionado um objeto soacutelido

ido a um processo de secagem Apoacutes a reali

velocidades e temperatura verificou-se

e massa eacute aquela onde o escoamento te

23

oamento de ar Segundo

a de secagem constante

rados alguns resultados

m incremento de 300

m quando a temperatura

por Kaya et al (2008)

coamento no interior de

ecador (ver Figura 23)

uadrado com umidade

accedilatildeo da simulaccedilatildeo para

ue a disposiccedilatildeo mais

m incidecircncia normal a



24

Figura 23 - Diferentes arranjos para u

Fonte Kaya et al (2008)

Ledig et al (2001) tambeacute

de secagem ocorra corretamente

madeiras Segundo Ledig et al (2

devido a vaacuterios fatores a saber

incorreto das madeiras no interior

principais pontos de destaque n

descolamento da camada limite

bloqueando grande parte do escoa

Estudos numeacutericos sobre

(1999) indicam que a qualidade

secagem mas tambeacutem da unifor

Estes autores ressaltam a import

diferentes situaccedilotildees seja em canai

material suficiente para que sejam

projetar um secador Utilizand

escoamento Riepen e Paarhuis

m processo de secagem

salientam que um importante requisito par

a uniformidade do escoamento nos canai

001) uma natildeo-uniformidade do escoament

(i) um sistema de ventiladores deficiente

do secador e principalmente (iii) geometr

geometria satildeo a quina de entrada onde

como consequecircncia uma regiatildeo de recir

ento nas pilhas (com grande perda de carga

erodinacircmica de secadores realizados por R

a secagem da madeira depende natildeo apen

idade das condiccedilotildees do escoamento no int

ncia de se conhecer o comportamento d

s paralelos ou quinas sendo este o papel da

desenvolvidas regras e identificar maneiras

-se das simulaccedilotildees para verificar o co

(1999) propuseram uma soluccedilatildeo para

a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o

ulaccedilatildeo eacute gerada

nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em

imulaccedilatildeo ndash gerar

ais eficientes de

mportamento do

o problema de



25

descolamento de camada limite na quina de entrada a qual consiste no uso de pequenas

ldquobarreirasrdquo impedindo que a regiatildeo de recirculaccedilatildeo influencie o escoamento nos canais

superiores (ver resultados da Figura 24)

Figura 24 minus Distribuiccedilatildeo de um escoamento de ar em um secador de madeira industrial

Fonte Riepen e Paarhuis (1999)

Na mesma linha de trabalho de Riepen e Paarhuis (1999) estudos experimentais de

Nijdam e Keey (1999 2000 2002) mostram a influecircncia da geometria do secador na

distribuiccedilatildeo de velocidades em uma pilha de madeiras Segundo Nijdam e Keey (2000) existem

dois grandes fatores que induzem uma distribuiccedilatildeo natildeo-uniforme do escoamento no interior do

secador (i) o primeiro aspecto corresponde agraves forccedilas de atrito que causam as variaccedilotildees de

pressatildeo em relaccedilatildeo agrave altura do secador Estas forccedilas de atrito induzem a perda de carga no

sentido do escoamento fazendo com que grande parte do escoamento percorra

preferencialmente os canais superiores do secador Esta perda de carga diminui quando a largura

do lsquo plenumrsquo (regiatildeo com comprimento A ndash ver Figura 27) aumenta apresentando melhorias na

uniformidade do escoamento em toda a altura do secador segundo resultados encontrados por

Nijdam e Keey (2000) (ii) O segundo fator importante de contribuiccedilatildeo para uma distribuiccedilatildeo

natildeo-uniforme eacute a quina localizada na regiatildeo de entrada do secador (NIJDAM KEEY 2002) O

voacutertice gerado nesta regiatildeo tem seu centro localizado proacuteximo agrave entrada dos canais superiores da

pilha bloqueando consideravelmente a passagem do fluido (ver Figura 25 (a)) Segundo Nijdam

e Keey (2002) uma soluccedilatildeo viaacutevel para impedir a formaccedilatildeo deste voacutertice em decorrecircncia do



26

descolamento da camada limite na seccedilatildeo de entrada do secador seria a utilizaccedilatildeo de uma seccedilatildeo

semicircular com um raio em funccedilatildeo da altura do canal de entrada (ver Figura 25 (b)) Esta

seccedilatildeo semicircular evita o descolamento da camada limite na quina de entrada minimizando os

efeitos do voacutertice localizado na entrada dos canais superiores

Figura 25 minus Padrotildees de escoamento para um secador sem a seccedilatildeo semicircular (a) e com a seccedilatildeosemicircular (b)

Fonte Nijdam e Keey (2002)

Um trabalho recente abordando a aerodinacircmica em secadores e utilizando modelagem

numeacuterica eacute apresentado em Younsi et al (2010) Os autores abordaram o processo de tratamento

teacutermico da madeira em secadores onde o escoamento turbulento no interior da geometria foi

simulado com o programa comercial ANSYS FLUENTreg (ver Figura 26) Os principais

resultados apresentados por estes autores compreendem uma comparaccedilatildeo entre as curvas

numeacuterica e experimental para a distribuiccedilatildeo de temperatura na madeira



27

Figura 26 minus Linhas de corrente durante o tratamento teacutermico

Fonte Younsi et al (2010)

Outro estudo da aerodinacircmica de um secador satildeo as anaacutelises numeacutericas realizadas por

Possamai et al (2013) no estudo de uma geometria semelhante a um secador de madeira (ver

Figura 27) que visaram a anaacutelise dos efeitos do arranjo do secador sobre as caracteriacutesticas do

escoamento do ar

Figura 27 minus Representaccedilatildeo esquemaacutetica da geometria analisada

Fonte Possamai et al (2013)



28

Em funccedilatildeo das anaacutelises realizadas em Possamai et al (2013) demonstrou-se que (i) a

distribuiccedilatildeo de velocidades no interior do secador em especial de seus canais estaacute diretamente

ligada ao modo como o escoamento se comporta na regiatildeo vertical de entrada (regiatildeo com

comprimento A ndash ver Figura 27) chamada de largura do lsquo plenumrsquo (ii) a quina da seccedilatildeo de

entrada do escoamento tem influecircncia direta na geraccedilatildeo de voacutertices na entrada dos canais e

como consequecircncia na distribuiccedilatildeo natildeo-uniforme de velocidades no interior dos mesmos

conforme observa-se na Figura 28

Figura 28 minus Linhas de corrente na geometria e moacutedulo da velocidade para A = 01[m]


Como conclusatildeo desta seccedilatildeo destaca-se que o problema de aerodinacircmica em secadores

de madeira tem sido atualmente o foco de estudo de muitos pesquisadores Desta forma conclui-

se que para um entendimento completo da aerodinacircmica de um secador de madeira todas as

possibilidades e arranjos devem ser testados e avaliados a fim de se encontrar soluccedilotildees

plausiacuteveis



29

3 FORMULACcedilAtildeO TEOacuteRICA

31 EQUACcedilOtildeES DE GOVERNO

Na abordagem claacutessica da mecacircnica dos fluidos considera-se o meio como sendo

contiacutenuo Considerando o fluido de trabalho como Newtoniano as equaccedilotildees de conservaccedilatildeo da

quantidade de movimento que modelam este tipo de problema fiacutesico satildeo conhecidas como

equaccedilotildees de Navier-Stokes Sendo assim tem-se para o caso do escoamento incompressiacutevel

( )( ) j i ji i

j i j j i

u u uu u pt x x x x x

ρ ρ micro part partpart partpart part

+ = minus + + part part part part part part (31)

Para a soluccedilatildeo do problema considera-se tambeacutem a equaccedilatildeo de conservaccedilatildeo de massa

que eacute dada por

0i

i

u

x

part =part

(32)

As variaacuteveis a serem calculadas nas equaccedilotildees acima satildeo as componentes instantacircneas do

vetor velocidade e a pressatildeo Em decorrecircncia do fato de o escoamento ser

incompressiacutevel natildeo existe uma equaccedilatildeo expliacutecita para determinar a pressatildeo como ocorre para

um escoamento compressiacutevel para o qual a pressatildeo eacute obtida via equaccedilatildeo de estado Este impasse

eacute conhecido como problema de acoplamento pressatildeo-velocidade Desta forma para solucionar

este problema obteacutem-se uma equaccedilatildeo de Poisson para a pressatildeo a partir das equaccedilotildees de

quantidade de movimento e conservaccedilatildeo da massa Na sequecircncia deste documento seratildeo

apresentados mais detalhes sobre o esquema de correccedilatildeo de pressatildeo adotado



30

32 EQUACcedilOtildeES DE NAVIER-STOKES COM MEacuteDIA DE REYNOLDS

A soluccedilatildeo numeacuterica de escoamentos turbulentos sem qualquer tipo de aproximaccedilatildeo aleacutem

daquelas inerentes aos meacutetodos numeacutericos eacute chamada de simulaccedilatildeo direta DNS (WILCOX

1998) Entretanto mesmo para escoamentos com baixo nuacutemero de Reynolds este procedimento

exige um tempo de processamento extremamente alto e uma enorme capacidade de

armazenamento de dados (WILCOX 1998) Em decorrecircncia da simulaccedilatildeo direta em geometrias

complexas a altos nuacutemeros de Reynolds ainda natildeo ser viaacutevel a alternativa encontrada foi a

utilizaccedilatildeo das equaccedilotildees de Navier-Stokes com meacutedia de Reynolds Neste procedimento uma

variaacutevel instantacircnea do escoamento ϕ eacute decomposta como

ϕ ϕ ϕ = + (33)

onde ϕ representa a meacutedia da variaacutevel e ϕ a flutuaccedilatildeo em torno deste valor Aplicando-se a

decomposiccedilatildeo de Reynolds agraves equaccedilotildees de Navier-Stokes e tomando-se a meacutedia no tempo tem-

se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ

partpart part part + = minus + minus part part part part

(34)

onde a taxa de deformaccedilatildeo do escoamento meacutedio eacute definida como

1

2 ji

ij

j i

uus

x x

partpart= + part part

(35)

Os componentes do tensor de Reynolds ij i ju uτ ρ = minus representam o efeito das

flutuaccedilotildees turbulentas sobre o escoamento meacutedio Por outro lado a equaccedilatildeo meacutedia da

continuidade fica similar agrave equaccedilatildeo instantacircnea ou seja



31

0i

i

u

x

part=

part (36)

33 MODELAGEM DE TURBULEcircNCIA

O problema fundamental do caacutelculo de escoamentos turbulentos estaacute na determinaccedilatildeo

dos termos do tensor de Reynolds (WILCOX 1998) As expressotildees que envolvem as flutuaccedilotildees

de velocidade resultantes do processo de meacutedia representam novas incoacutegnitas para o problema

Como o nuacutemero de equaccedilotildees continua o mesmo o problema natildeo eacute fechado Desta forma a

funccedilatildeo da modelagem da turbulecircncia eacute elaborar aproximaccedilotildees para estas correlaccedilotildees

desconhecidas Os diversos modelos para o tratamento de escoamentos turbulentos existentes

diferem-se apenas pela forma com a qual estas relaccedilotildees satildeo tratadas (WILCOX 1998)

O presente trabalho utiliza um modelo do tipo viscosidade turbulenta que se apoia na

hipoacutetese de Boussinesq Desta forma para um escoamento incompressiacutevel o tensor de Reynolds

relaciona-se com o tensor taxa de deformaccedilatildeo meacutedio pela expressatildeo

23

jiij i j T ij

j i

uuu u k

x xτ ρ micro δ ρ partpart

= minus = + minus part part (37)

onde e satildeo respectivamente a viscosidade aparente ou viscosidade turbulenta e a energia

cineacutetica turbulenta por unidade de massa que eacute dada pela equaccedilatildeo

1

2 i ik u u= (38)

Fazendo a substituiccedilatildeo da Equaccedilatildeo (37) na Equaccedilatildeo (34) e sabendo que

2 2

3 3ij

j i

k k x xδ ρ ρ part part

minus = minus part part (39)



32

obteacutem-se a forma final

( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro

partpart part part + = minus +

part part part part

(310)

sendo o coeficiente de difusatildeo efetivo definido como a soma do coeficiente de difusatildeo

molecular e do coeficiente de difusatildeo turbulento

e T micro micro micro = +

(311)

Por outro lado o termo e p eacute definido como uma pressatildeo efetiva sendo dado por

2

3e p p k ρ = + (312)

331 Modelo de duas equaccedilotildees

O modelo utilizado neste trabalho alto Reynolds desenvolvido por Lauder e

Spalding (1974) eacute muito difundido na comunidade cientiacutefica e utiliza duas equaccedilotildees diferenciais

parciais para a obtenccedilatildeo da viscosidade turbulenta Nesta abordagem as variaacuteveis dependentes

satildeo a energia cineacutetica turbulenta (Eq 38) e a taxa de dissipaccedilatildeo da energia cineacutetica turbulenta

por unidade de massa definida como

i i

k k

u u

x xε ν

part part=

part part (313)

onde eacute a viscosidade cinemaacutetica molecular do fluido Desta forma as equaccedilotildees de transporte

para a obtenccedilatildeo de e satildeo dadas por (LAUDER SPALDING 1974)



33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ

partpart part part+ = +

part part part part (314)

e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ



onde os termos fonte k S

eS

ε satildeo determinados por

k d S P ρ ρε = minus (316)

2

1 2d S C P C

k k ε ε ε

ε ε ρ ρ = minus (317)

Nas expressotildees anteriores o termo de produccedilatildeo de turbulecircncia d P eacute definido por

ji iT d

j i j

uu uP

x x x

micro

ρ

partpart part= + part part part

(318)

sendo a viscosidade turbulenta calculada pela expressatildeo

2

T

k C micro micro ρ

ε = (319)

Nas equaccedilotildees anteriores surgem constantes que satildeo determinadas empiricamente

(LAUDER SPALDING 1974) a saber



34

10k σ = 13ε σ = 009C micro = 1 144C ε = e 2 192C ε = (320)

As equaccedilotildees do modelo alto Reynolds satildeo vaacutelidas em regiotildees onde o escoamento eacute

totalmente turbulento Em regiotildees proacuteximas a superfiacutecies soacutelidas onde a condiccedilatildeo de natildeo

deslizamento implica que os efeitos viscosos predominam eacute utilizada a lei da parede

(LAUDER SPALDING 1974) a qual estabelece uma conexatildeo entre as condiccedilotildees de contorno

na parede e as propriedades do escoamento na zona de validade do modelo

34 MEacuteTODO NUMEacuteRICO

O nuacutecleo numeacuterico do programa comercial ANSYS CFXreg eacute baseado no Meacutetodo deVolumes Finitos Baseado em Elementos (EbFVM) (MALISKA 2004) A malha computacional

eacute empregada na construccedilatildeo de volumes finitos que seratildeo utilizados para a integraccedilatildeo das

equaccedilotildees diferenciais A Figura 31 mostra uma malha 2D tipicamente utilizada pelo programa

Como o nome indica EbFVM eacute um meacutetodo de volumes finitos embora seja baseado em

elementos o meacutetodo utiliza um volume de controle para a integraccedilatildeo das equaccedilotildees diferenciais

A montagem de um volume de controle no programa comercial utiliza a formulaccedilatildeo centrada no

veacutertice (lsquocell vertexrsquo) sendo o mesmo formado pelo somatoacuterio dos sub-volumes de controleadjacentes que envolvem o noacute (Ver Figura 32) Aleacutem disto o centro dos volumes de controle eacute

posicionado sobre os noacutes que satildeo os veacutertices das ceacutelulas (elementos) O volume de controle eacute

construiacutedo envolvendo cada noacute da malha utilizando a teacutecnica de mediana Esta teacutecnica consiste

na uniatildeo das medianas dos veacutertices que compotildeem os elementos (MALISKA 2004) Todas as

variaacuteveis e as propriedades do fluido estatildeo armazenadas nos noacutes (veacutertices da malha) conforme

mostrado na Figura 32

Figura 31 minus Discretizaccedilatildeo mostrando o elemento

Fonte produccedilatildeo do proacuteprio autor baseado em Maliska (2004)



35

Figura 32 minus O elemento 1234 e o volume de controle centrado em 1


Esse meacutetodo pode ser considerado como uma associaccedilatildeo do meacutetodo claacutessico de volumes

finitos que eacute muito utilizado para soluccedilatildeo de escoamentos e transferecircncia de calor devido a sua

natureza conservativa e a versatilidade e liberdade geomeacutetrica comum do meacutetodo de elementos

finitos Assim sendo o EbFVM permite o tratamento de malhas natildeo estruturadas em

coordenadas cartesianas mantendo o caraacuteter conservativo do meacutetodo de volumes finitos

(MALISKA 2004)

341 Discretizaccedilatildeo das equaccedilotildees

O processo de discretizaccedilatildeo consiste na integraccedilatildeo das equaccedilotildees diferenciais em sua

forma conservativa sobre os volumes de controle Com base no Teorema de Gauss algumas

integrais de volume podem ser representadas como integrais de superfiacutecie no caso a superfiacuteciedo volume de controle (HIRSH 2009) Assim para a equaccedilatildeo da conservaccedilatildeo da massa

quantidade de movimento e um escalar passivo tem-se que

( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro

part partpart part partpart+ = minus + + part part part part part part

(322)

( )( ) j

e

j j j

uS

t x x x φ

ρ φ ρφ φ partpart part part+ = Γ + part part part part

(323)

Integrando sobre um volume de controle e considerando que a regiatildeo de integraccedilatildeo natildeo

sofre influecircncia do tempo tem-se

0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i

uuu dV u u dn p dn dn

t x x ρ ρ micro partpartpart

+ = minus + + part part part int int int int (325)

j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ

part part+ = Γ + part part

int int int int (326)

onde V representa o volume de integraccedilatildeo S a superfiacutecie de integraccedilatildeo e a componente

diferencial de superfiacutecie orientada de acordo com o vetor normal unitaacuterio apontando para fora

Estas integrais representam o somatoacuterio dos fluxos que atravessam cada uma das superfiacutecies dos

volumes de controle (MALISKA 2004)

Os termos volumeacutetricos (acuacutemulo e fontes) satildeo aproximados de forma discreta pelos seusvalores especiacuteficos em cada subvolume de controle enquanto os fluxos satildeo aproximados sobre

cada elemento diferencial de superfiacutecie sobre o ponto de integraccedilatildeo pi sendo este valor



37

considerado representativo da meacutedia dos fluxos que atravessam o elemento diferencial de

superfiacutecie Assim

( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o

ji i i pi i e i e j pi pi

pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro

part minus part+ = minus ∆ + + ∆ ∆ part part

sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ

minus part+ = Γ ∆ + ∆ part

sum sum (329)

sendo que

representa o fluxo de massa atraveacutes do elemento de superfiacutecie

discreto orientado e o sobrescrito ldquo ordm rdquo representa o tempo anterior Vale salientar que neste

trabalho o esquema de Euler impliacutecito eacute adotado na discretizaccedilatildeo temporal das Equaccedilotildees (327)

ndash (329)

342 Soluccedilatildeo do sistema linear

Apoacutes a discretizaccedilatildeo do sistema de equaccedilotildees diferenciais o mesmo eacute reduzido a um

sistema linear de equaccedilotildees algeacutebricas que pode ser escrito na forma matricial como sendo

[ ][ ] [ ] M Gθ = (330)

onde eacute o vetor soluccedilatildeo G eacute vetor lado direito (conhecido) M representa a matriz dos

coeficientes Este sistema eacute resolvido de forma iterativa

n 1 n θ θ θ += + (331)



38

sendo a soluccedilatildeo aproximada da iteraccedilatildeo n

n M r θ = (332)

Como natildeo eacute a soluccedilatildeo exata do sistema tem-se o resiacuteduo que eacute obtido por

n nr G M θ = minus (333)

Para a soluccedilatildeo do sistema de equaccedilotildees lineares o software ANSYS CFXreg utiliza um

meacutetodo do tipo lsquomultigridrsquo com decomposiccedilatildeo LU incompleta (ANSYS 2007)

343 Acoplamento pressatildeo ndash velocidade

O arranjo de malha deslocado (lsquostaggered gridrsquo) representa a soluccedilatildeo ideal enquanto

problemas 2D satildeo resolvidos (PERIC 1988) A necessidade de resolver problemas em

geometrias mais complexas com o uso de coordenadas generalizadas motivou os pesquisadores

a desenvolverem meacutetodos de acoplamento baseados em arranjos colocalizados (PERIC 1988)

O crescimento atual de meacutetodos usando malhas natildeo estruturadas (onde eacute ainda mais complicadousar o arranjo deslocado) e a busca da generalizaccedilatildeo dos meacutetodos atuais praticamente eliminou o

uso de arranjos deslocados (VASCONCELLOS MALISKA 2004)

O programa ANSYS CFXreg efetua o acoplamento pressatildeo-velocidade utilizando um

esquema do tipo correccedilatildeo de pressatildeo proposto por Rhie-Chow (RHIE CHOW 1983) para um

arranjo de malha colocalizado Este esquema utiliza funccedilotildees de interpolaccedilatildeo nas faces dos

volumes de controle baseadas nas equaccedilotildees de quantidade de movimento evitando assim o

problema do desacoplamento par-iacutempar (ZDANSKI 2003) Este eacute um problema tiacutepico quesurge no caacutelculo de escoamentos incompressiacuteveis com arranjo de variaacuteveis colocalizadas Como

exemplo um campo de pressatildeo oscilatoacuterio seria ldquovistordquo como constante na discretizaccedilatildeo da

equaccedilatildeo de quantidade de movimento em decorrecircncia de o gradiente de pressatildeo ser expresso em

funccedilatildeo de pontos alternados ao inveacutes de pontos adjacentes (ZDANSKI 2003)

35 CONDICcedilOtildeES DE CONTORNO



39

As condiccedilotildees de contorno tecircm grande importacircncia na soluccedilatildeo de qualquer problema pois

satildeo estas que definem os mesmos A seguir satildeo apresentadas as condiccedilotildees de contorno que

foram utilizadas neste trabalho

351 Entrada

Considera-se que a distribuiccedilatildeo de velocidades na entrada tem perfil uniforme e que o

sentido do escoamento do fluido estaacute entrando no domiacutenio Os valores de e satildeo especificados

na entrada do domiacutenio sendo assumidos perfis uniformes no plano de entrada

Desta forma em coordenadas cartesianas os componentes da velocidade especificada

podem ser descritos como

ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda

Para a fronteira de saiacuteda da geometria o programa comercial ANSYS CFXreg possibilita a

utilizaccedilatildeo de dois tipos distintos de condiccedilatildeo de contorno sendo elas lsquoOutlet rsquo e lsquoOpeningrsquo A

condiccedilatildeo lsquoOpeningrsquo permite simular situaccedilotildees onde o escoamento cruza a fronteira em ambas as

direccedilotildees sendo possiacutevel agrave localizaccedilatildeo de um voacutertice nesta regiatildeo distintamente da condiccedilatildeo

lsquoOutlet rsquo onde somente eacute permitido que o escoamento saia do domiacutenio sem a possibilidade de um

refluxo Em decorrecircncia da existecircncia de muacuteltiplos descolamentos de camada limite e voacutertices

na geometria estudada (secador) neste trabalho foi utilizada a condiccedilatildeo de contorno lsquoOpeningrsquona fronteira de saiacuteda (ANSYS 2007)

353 Plano de Simetria

O programa comercial ANSYS CFXreg eacute utilizado para simulaccedilotildees tridimensionais

entretanto para casos bidimensionais faz-se necessaacuterio a utilizaccedilatildeo de um plano de simetria Acondiccedilatildeo de simetria impotildee que o fluxo seja ldquoespelhadordquo em ambos os lados da geometria

Desta forma o componente da velocidade normal ao plano de simetria eacute zero



40

0nu = (335)

sendo os gradientes das variaacuteveis escalares normais ao plano simeacutetrico tambeacutem iguais a zero

0n

φ part=

part (336)

354 Paredes soacutelidas

Ao longo das paredes eacute aplicada agrave condiccedilatildeo de natildeo escorregamento para as velocidades

com acoplamento via lei da parede Desta forma a velocidade na parede eacute definida como

0wu = (337)



41

4 VERIFICACcedilAtildeO E VALIDACcedilAtildeO

Neste capiacutetulo satildeo apresentados os resultados obtidos atraveacutes das simulaccedilotildees numeacutericas

bem como as comparaccedilotildees com soluccedilotildees analiacuteticas numeacutericas e experimentais de outros

autores visando uma verificaccedilatildeo e validaccedilatildeo da soluccedilatildeo Para a execuccedilatildeo desta etapa foram

escolhidos dois casos de escoamento a saber (i) escoamento turbulento em um canal plano e

(ii) escoamento turbulento em um modelo simplificado para a geometria de um secador de

madeira Eacute importante mencionar que a verificaccedilatildeo eacute compreendida pela comparaccedilatildeo dos

resultados com soluccedilotildees numeacutericas ou analiacuteticas e a validaccedilatildeo eacute feita comparando-se os

resultados numeacutericos a valores experimentais (OBERKAMPF E TRUCANO 2002)

41 ESCOAMENTO TURBULENTO EM UM CANAL PLANO BIDIMENSIONAL

Objetivando verificar os resultados obtidos pelo programa comercial ANSYS CFXreg

realizou-se a simulaccedilatildeo de um escoamento turbulento em um canal plano bidimensional e

posterior comparaccedilatildeo dos resultados obtidos com dados disponiacuteveis na literatura Na Figura 41

eacute apresentado um esquema da geometria utilizada onde o domiacutenio computacional compreende

toda a altura do canal h = 0011 m e todo o seu comprimento L = 60h Utilizou-se uma malhaestruturada com 401x41 pontos nas direccedilotildees longitudinal e transversal respectivamente

Figura 41 - Representaccedilatildeo esquemaacutetica do escoamento em um canal bidimensional

Fonte produccedilatildeo do proacuteprio autor

As condiccedilotildees de contorno adotadas foram as seguintes distribuiccedilatildeo uniforme da velocidade

energia cineacutetica turbulenta e taxa de dissipaccedilatildeo na entrada condiccedilatildeo de natildeo escorregamento nas



42

paredes e pressatildeo estaacutetica de 1 atm na regiatildeo de saiacuteda do domiacutenio O criteacuterio de convergecircncia

adotado foi a raiz meacutedia quadraacutetica do resiacuteduo (RMS) lt 10-7 (ver definiccedilatildeo do resiacuteduo na

Equaccedilatildeo 333) Para esta simulaccedilatildeo foram utilizados os seguintes valores = 193 m s-1 =

13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)

A Figura 42 apresenta o perfil da energia cineacutetica turbulenta adimensional

onde eacute a velocidade de atrito em funccedilatildeo da coordenada adimensional

A distribuiccedilatildeo corresponde agrave seccedilatildeo de saiacuteda do canal onde o escoamento eacute totalmente

desenvolvido Observa-se que para grande parte do canal os resultados apresentam boa

concordacircncia com a literatura no entanto nas regiotildees proacuteximas a parede o pico de observado

pelos resultados de Mansour et al (1988) e Wilcox (1998) natildeo eacute capturado Este fato eacute explicado

devido agrave utilizaccedilatildeo de um modelo do tipo alto Reynolds o qual natildeo possui termos que permitam

a aproximaccedilatildeo de uma fronteira soacutelida

Figura 42 minus Perfis de energia cineacutetica turbulenta

0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))

Fonte produccedilatildeo do proacuteprio autor baseado em Zdanski (2003)

A Figura 43 apresenta os perfis normalizados de velocidade em funccedilatildeo da

coordenada adimensional na seccedilatildeo de saiacuteda do canal Conforme observado na

figura os resultados obtidos pelo programa ANSYS CFXreg para esta simulaccedilatildeo tem boa

concordacircncia apresentando comportamento semelhante aos resultados publicados na literatura



43

Figura 43 minus Perfis de velocidade normalizada em funccedilatildeo da coordenada adimensional na seccedilatildeode saiacuteda do canal

14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))


42 GEOMETRIA SIMPLIFICADA PARA UM SECADOR

Como forma de avaliar os resultados obtidos pelo programa comercial ANSYS CFXreg de

forma mais convicta realizou-se a simulaccedilatildeo de um escoamento turbulento em uma geometria

semelhante a um secador de madeira A decisatildeo em favor desta geometria ocorreu devido agrave

existecircncia de resultados experimentais na literatura (NIJDAM KEEY 2002) bem como a

semelhanccedila para com o problema principal foco de estudo deste trabalho Na Figura 44 eacute

apresentada a geometria utilizada onde o domiacutenio computacional compreende toda a altura H

=026 m e todo o comprimento L = 048005 m As geometrias que representam as madeiras nointerior do secador tecircm comprimento D = 03 m e espessura B = 0010 m sendo a altura dos

canais de escoamento C = 0005 m As demais cotas F = 0065 m A = 0090025 m e E = 0010

m correspondem respectivamente agrave altura do canal de entrada largura do lsquo plenumrsquo e distacircncia

entre o canal de entrada e o primeiro canal de escoamento (NIJDAM KEEY 2002)

Este problema foi simulado utilizando o modelo de turbulecircncia padratildeo alto

Reynolds As condiccedilotildees de contorno adotadas para a modelagem do escoamento turbulento no

secador foram as seguintes distribuiccedilatildeo uniforme da velocidade na entrada condiccedilatildeo de natildeo

escorregamento (velocidade nula) nas paredes e condiccedilatildeo lsquoopeningrsquo na regiatildeo de saiacuteda do



44

domiacutenio O criteacuterio de convergecircncia adotado foi a raiz meacutedia quadraacutetica do resiacuteduo (RMS) lt 10-

4 Para esta simulaccedilatildeo foram utilizados os seguintes valores de velocidade de entrada = 42 m

s-1 taxa de dissipaccedilatildeo da energia cineacutetica turbulenta = 392 J kg

-1s

-1 e energia cineacutetica

turbulenta = 004 sup22 m2 s

-2 Os valores para o nuacutemero de Reynolds baseiam-se no

diacircmetro hidraacuteulico dos canais formados pelas placas de madeiras De acordo com os

experimentos realizados por Nijdam e Keey (2002) estes valores encontram-se entre 3000 e

12000 caracterizando um escoamento turbulento e sendo condizentes com valores encontrados

em secadores industriais

Figura 44minus Representaccedilatildeo esquemaacutetica da geometria de um secador de madeira


O modelo geomeacutetrico foi executado no programa comercial ICEMreg sendo que para este

caso foi utilizada uma malha com fator de estiramento maacuteximo de 10 com concentraccedilatildeo de

pontos proacuteximo agraves paredes e quinas Para um melhor entendimento da malha utilizada na Figura

45 eacute apresentada uma vista detalhada da mesma na regiatildeo de entrada do escoamento no secador

A malha utilizada apresenta espaccedilamento uniforme de 00005 m na direccedilatildeo Y sendo que e na

direccedilatildeo X optou-se pela concentraccedilatildeo de pontos nas regiotildees proacuteximas as paredes entradas e

saiacutedas dos canais (ver Figura 45 (a)) com um fator de estiramento maacuteximo de 10 A malha



45

padratildeo utilizada conteacutem 143656 pontos poreacutem outras malhas foram utilizadas nas simulaccedilotildees

visando investigar a sua influecircncia nos resultados

Figura 45 ndash Aspectos da malha na regiatildeo de entrada dos canais superiores


O experimento conduzido por Nijdam e Keey (2002) consistiu em construir uma

geometria semelhante a um secador de madeiras em escala reduzida verificando a influecircncia de

certos paracircmetros nas velocidades relativas no interior dos canais do dispositivo Para a

visualizaccedilatildeo das linhas de corrente estes autores utilizaram o meacutetodo de bolhas de hidrogecircnio o

qual consiste em instalar um fio de platina por todo o comprimento da seccedilatildeo de entrada da

geometria e aplicar uma tensatildeo no mesmo Pode-se observar claramente o resultado para a

topologia do escoamento obtido por Nijdam e Keey (2002) na Figura 46 (a) Por outro lado os

resultados apresentados pela Figura 46 (b) revelam as linhas de corrente resultantes da

simulaccedilatildeo da geometria pelo programa ANSYS CFXreg sendo claramente perceptiacutevel a

semelhanccedila qualitativa entre os dois resultados

Em ambos os resultados apresentados na Figura 46 ocorre a formaccedilatildeo de uma regiatildeo de

recirculaccedilatildeo nas imediaccedilotildees da entrada dos canais superiores O centro do voacutertice estaacute localizado

nas proximidades da entrada do canal 2 sendo uma consequecircncia do descolamento da camada

limite na quina de entrada (regiatildeo de espessura E ndash ver Figura 44) Como consequecircncia deste

voacutertice eacute observado um estreitamento do canal vertical de entrada (regiatildeo do ldquo plenumrdquo com

largura A ndash ver Figura 44) tendo como impacto imediato um aumento da velocidade nesta

regiatildeo



46

Figura 46 ndash Linhas de corrente no interior da geometria do secador de madeira (a) Resultados obtidospor Nijdam e Keey (2002) e (b) Resultados obtidos no presente trabalho


A distribuiccedilatildeo de velocidade meacutedia no interior dos canais do secador em X = 0240025 m

eacute apresentada na Figura 47 Analisando detalhadamente esta figura observa-se que os pontos de

miacutenimo e maacuteximo das velocidades relativas encontram-se nos canais 2 e 4

respectivamente (segundo os resultados das simulaccedilotildees) O ponto de velocidade miacutenima no

canal 2 provavelmente ocorre devido agrave influecircncia da localizaccedilatildeo do voacutertice ndash o centro do voacutertice

(regiatildeo de baixa pressatildeo) estaacute perfeitamente alinhado com a entrada do canal 2 (ver Figura 46

(b)) sendo este voacutertice indesejaacutevel para aplicaccedilotildees praacuteticas Aleacutem disto percebe-se nos

resultados da Figura 47 que mesmo o centro do voacutertice estando localizado na entrada do canal

2 os canais 1 e 3 tambeacutem sofrem influecircncia apresentando valores baixos para a velocidade

relativa Por outro lado pode ser observado que a curva experimental segundo Nijdam e Keey

(2002) natildeo apresenta o ponto de miacutenima velocidade no canal 2 Um dado intrigante sobre estes

resultados experimentais diz respeito agrave ausecircncia das informaccedilotildees sobre as velocidades relativas

nos canais pares sendo somente apresentados os valores para os canais iacutempares (ver Figura 47)

Vale novamente salientar que justamente nos canais pares 2 e 4 ocorrem os valores miacutenimo emaacuteximo para as velocidades no interior do secador segundo as simulaccedilotildees do presente trabalho



47

O comportamento do escoamento a partir do canal 4 eacute semelhante a outros tipos de escoamento

em dutos com vaacuterias saiacutedas As velocidades relativas dos canais superiores satildeo maiores que nos

canais inferiores devido agrave perda de carga no (lsquo plenumrsquo) levando o escoamento a percorrer o

caminho com menor resistecircncia Todavia o aspecto principal a ser observado eacute a boa

concordacircncia entre os resultados numeacutericos e os dados experimentais obtidos por Nijdam e Keey

(2002) sendo que o erro meacutedio dos resultados encontrados no presente trabalho atinge um valor

em torno de 67 fato que confirma uma boa concordacircncia (este erro eacute definido como sendo a

diferenccedila entre os valores experimentais e numeacutericos para todos os canais)

Figura 47 ndash Perfis de velocidade relativa nos canais do secador de madeira

0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)


Com o intuito de avaliar o impacto do tipo de malha ndash uniforme ou estirada - nos resultados

foram geradas 6 (seis) malhas distintas no programa ICEMreg a saber trecircs malhas uniformes e

trecircs malhas com estiramento Na Figura 48 satildeo apresentados os resultados obtidos com cada

uma das malhas utilizadas A principal constataccedilatildeo eacute que os resultados apresentam pouca

variaccedilatildeo em relaccedilatildeo ao tipo de malha utilizada caracterizando uma independecircncia dos mesmos

em relaccedilatildeo ao refino da malha Em funccedilatildeo deste estudo foi possiacutevel utilizar uma malha mais

grosseira diminuindo o tempo de processamento e facilitando o tratamento dos resultados A

malha estirada 02 foi utilizada para as simulaccedilotildees apresentadas neste capiacutetulo sendo que a

mesma apresenta estiramento maacuteximo de 10 no eixo x e espaccedilamento uniforme de 00005 m

no eixo y



48

Figura 48 ndash Perfil das velocidades relativas nos canais utilizando as malhas MU (malha uniforme)e MB ( Malha com estiramento) ndash estudo de refinamento da malha

0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133


421 Proposta de alteraccedilatildeo na geometria do secador

Nas discussotildees sobre a topologia do escoamento (linhas de corrente) bem como nasdistribuiccedilotildees de velocidade relativa nos canais do secador foi destacado o efeito adverso do

voacutertice que se forma na entrada dos canais superiores (Figura 46 (b) e Figura 47) De forma a

avaliar o real impacto da posiccedilatildeo deste voacutertice nas velocidades dos primeiros canais o

paracircmetro E da geometria original foi alterado (ver Figura 44) Desta forma o objetivo foi

aumentar a distacircncia entre o canal de entrada do secador e o primeiro canal de escoamento da

pilha de madeiras ( E = 0010 m para E = 0075 m) de forma que o voacutertice gerado na quina natildeo

se posicione na regiatildeo frontal aos canais superiores Os resultados obtidos com esta nova

simulaccedilatildeo satildeo apresentados nas Figura 49 Figura 410 e Figura 411

Inicialmente na Figura 49 satildeo apresentadas as linhas de corrente no interior da

geometria modificada onde se observa claramente que a localizaccedilatildeo e o tamanho do voacutertice

foram alterados (ver Figura 46 (b) e Figura 49) Portanto o objetivo inicial de afastar o centro

do voacutertice da entrada do canal 2 foi atingido com sucesso



Figura 49 minus Linhas de corrent

Fonte produccedilatildeo do proacuteprio au

Na sequecircncia da anaacutelise de

de velocidade meacutedia no int

Nesta figura satildeo apresentad

46 (b)) e para a geometri

importantes estatildeo relaciona

claramente que para a geo

do escoamento ao longo d

canais 1 ao 3 e uma reduccedilatildeo

agraves discussotildees sobre o ponto

do secador original na se

ocorria no segundo canal d

(b)) em funccedilatildeo dos result

geometria do secador modi

no interior da geometria modificada do secador

or

te caso o principal aspecto a ser avaliado c

erior dos canais do secador em X = 02400

os os valores da velocidade meacutedia para a ge

a modificada (Figura 49) com fins comp

os agrave anaacutelise da Figura 410 (i) primeirament

etria modificada houve uma melhora signi

todos os canais do secador (houve um i

de fluxo nos canais 4 ao 13) (ii) o segundo

de velocidade miacutenima que ocorre no segund

atildeo 42 deste capiacutetulo foi argumentado qu

vido ao posicionamento frontal do centro d

ados apresentados na Figura 410 constata

ficada (ver Figura 49) o canal 2 apresenta

49

de madeira

nsiste nas distribuiccedilotildees

25 m (ver Figura 410)

ometria original (Figura

arativos Dois aspectos

e os resultados indicam

icativa na uniformidade

cremento de fluxo nos

aspecto estaacute relacionado

canal para a geometria

e a velocidade miacutenima

voacutertice (ver Figura 46

-se claramente que na

uma velocidade meacutedia



50

superior ao canal 1 Este resultado reforccedila a hipoacutetese de que o centro do voacutertice deve ser

afastado da regiatildeo de entrada dos canais para natildeo prejudicar as condiccedilotildees de fluxo nos mesmos


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137


Para reforccedilar as discussotildees do paraacutegrafo anterior na Figura 411 satildeo apresentados os

valores da pressatildeo estaacutetica meacutedia na entrada dos canais para as duas geometrias estudadas Estes

resultados confirmam claramente que a pressatildeo meacutedia na entrada dos canais 1 ao 3 aumenta

consideravelmente para a geometria do secador modificada O aumento de pressatildeo estaacutetica na

seccedilatildeo de entrada dos canais eacute devido ao afastamento do voacutertice desta regiatildeo e tem como

consequecircncia direta uma maior uniformidade do escoamento no interior do secador (um aspectodesejaacutevel em processos de secagem)



51

Figura 411 minus Perfis de pressatildeo estaacutetica meacutedia nas seccedilotildees de entrada dos canais do secador de madeira

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53

5 RESULTADOS E DISCUSSOtildeES

Este capiacutetulo estaacute dividido em duas partes (i) na primeira parte satildeo apresentados os

resultados obtidos na simulaccedilatildeo para uma geometria de referecircncia de um secador de madeira(ii) apoacutes os estudos de aspectos importantes do escoamento na geometria de referecircncia realizou-

se a segunda parte do trabalho que consistiu numa anaacutelise parameacutetrica do escoamento no interior

do secador

A geometria do secador analisada neste capiacutetulo assemelha-se agravequela utilizada para a

validaccedilatildeo (ver Figura 44) todavia as dimensotildees aqui empregadas representam um secador de

madeira compacto com geometria e condiccedilotildees operacionais reais Isso eacute a espessura e o

comprimento das madeiras dispostas no interior do dispositivo condizem com valores utilizadoscomercialmente

O escoamento turbulento no interior do secador foi analisado sistematicamente levando-

se em conta a largura do lsquo plenumrsquo e a velocidade de entrada do escoamento A variaccedilatildeo de

cada um desses paracircmetros foi realizada a partir do caso de referecircncia descrito na seccedilatildeo 51 a

seguir Os resultados obtidos para a geometria de referecircncia satildeo discutidos atraveacutes de graacuteficos

que mostram as linhas de corrente o moacutedulo do vetor velocidade as distribuiccedilotildees das

componentes e da velocidade pressatildeo estaacutetica relativa e energia cineacutetica turbulenta

no interior do dispositivo Aleacutem disto satildeo apresentados os perfis de velocidade meacutedia e

variaccedilatildeo de pressatildeo nos canais formados pelas madeiras do interior do secador Para

analisar a influecircncia da largura do lsquo plenumrsquo na topologia do escoamento foram utilizados os

seguintes valores para este paracircmetro 01 015 e 03 m (ver Figura 44) Por outro lado

para estudar os efeitos da velocidade de entrada do escoamento foram adotados os seguintes

valores 3 5 7 e 9 m s-1 Os valores das velocidades utilizados neste trabalho foram

definidos com base em dados tiacutepicos e usuais para secadores de madeira (PANG 1996)

51 ESTUDO DA GEOMETRIA DE REFEREcircNCIA

Conforme descrito anteriormente a geometria de referecircncia assemelha-se agravequela

utilizada para a validaccedilatildeo (ver Figura 44) poreacutem as dimensotildees do domiacutenio computacional satildeo

maiores apresentando altura H = 05875 m e comprimento L = 19 m As geometrias que

representam as placas de madeira no interior do secador assumem comprimento D = 16 m e



54

espessura B = 0025 m sendo a altura dos canais de escoamento igual a C = 00125 m As

demais cotas altura do canal de entrada largura do lsquo plenumrsquo e distacircncia entre o canal de entrada

e o primeiro canal de escoamento satildeo respectivamente F = 01 m A = 015 m e E = 00125 m

(ver Figura 44)

Este problema foi simulado utilizando-se o modelo de turbulecircncia de alto

Reynolds Para a modelagem do escoamento turbulento no secador as condiccedilotildees de contorno

adotadas foram as seguintes distribuiccedilatildeo uniforme da velocidade na entrada condiccedilatildeo de natildeo


domiacutenio O criteacuterio de convergecircncia adotado foi a raiz meacutedia quadraacutetica do resiacuteduo ( RMS) lt 10-

4 Para esta simulaccedilatildeo foram utilizados os seguintes valores de velocidade de entrada = 5 m s-

1 taxa de dissipaccedilatildeo da energia cineacutetica turbulenta

= 392 J kg-1

s-1 e energia cineacutetica

turbulenta = 004 sup22 m2 s-2 (ZDANSKI 2003)

O novo modelo geomeacutetrico foi feito no programa comercial ICEMreg sendo que para este

caso utilizou-se uma malha com fator de estiramento maacuteximo de 10 com concentraccedilatildeo de

pontos proacuteximo agraves paredes e quinas A malha utilizada apresenta espaccedilamento uniforme de

00005 m na direccedilatildeo Y e na direccedilatildeo X optou-se pela concentraccedilatildeo de pontos nas regiotildees

proacuteximas as paredes entradas e saiacutedas dos canais (ver Figura 45 (a)) Para estas simulaccedilotildees a

malha utilizada conteacutem 358876 pontos computacionais

Inicialmente as Figuras 51 e 52 mostram a topologia do escoamento nas regiotildees de

entrada e saiacuteda da geometria de referecircncia para um lsquoplenumrsquo igual a 015 m Satildeo apresentadas as

linhas de corrente e o moacutedulo da velocidade para a geometria de referecircncia Observa-se nas

figuras que a topologia do escoamento obtida assemelha-se agravequela da geometria utilizada para a

validaccedilatildeo (ver Figura 46) Desta forma ocorre a formaccedilatildeo de um voacutertice proacuteximo agrave entrada dos

canais superiores 1 a 4 decorrente do descolamento da camada limite na quina de entrada Como

consequecircncia deste voacutertice formado apoacutes a quina de entrada haacute um estreitamento da aacuterea de

passagem efetiva do canal vertical de entrada ndash lsquo plenumrsquo de entrada (ver Figura 52) com

consequente aumento do moacutedulo da velocidade nesta regiatildeo Por outro lado na regiatildeo de saiacuteda

dos canais formados pelas placas de madeira bem como na seccedilatildeo de saiacuteda do secador satildeo

encontrados vaacuterios voacutertices devido agraves muacuteltiplas quinas que a geometria apresenta nestas regiotildees

(ver Figura 52) Neste ponto eacute importante salientar que a condiccedilatildeo de contorno utilizada para a

seccedilatildeo de saiacuteda do secador permite a entrada e saiacuteda de fluxo a saber eacute possiacutevel obter um voacutertice

posicionado na seccedilatildeo de saiacuteda conforme pode ser observado na Figura 52



55

Figura 51 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria de referecircncia para umlsquoplenumrsquo igual a 015 m


Figura 52 ndash Vista em detalhe da topologia do escoamento nas regiotildees de entrada e saiacuteda da geometria dereferecircncia para um lsquoplenumrsquo igual a 015 m


Para auxiliar a interpretaccedilatildeo dos resultados apresentados nas Figura 51 e 52

apresentam-se nas Figura 53 a 56 as distribuiccedilotildees para as componentes e do vetor

velocidade no interior da geometria de referecircncia Inicialmente nas Figura 53 e 54 nota-se que



56

os valores para a componente da velocidade nos canais 1 ao 4 apresentam valores menores aos

encontrados nos canais inferiores (canais 5 a 13) Este comportamento estaacute relacionado agrave

influecircncia da posiccedilatildeo do voacutertice que estaacute localizado na regiatildeo de entrada dos canais 1 a 4 Outro

aspecto importante observado na Figura 54 eacute a presenccedila de uma regiatildeo de intensa mistura na

saiacuteda dos vaacuterios canais formados pelas placas de madeira (o escoamento na saiacuteda de cada canal

se assemelha a um jato livre que interage com os canais vizinhos)



Figura 54 - Vista em detalhe da distribuiccedilatildeo da componente da velocidade nas regiotildees de entrada esaiacuteda da geometria de referecircncia




57

Outra consequecircncia do voacutertice formado na regiatildeo de entrada dos canais 1 a 4 pode ser

visualizada com maior clareza nas Figura 55 e 56 onde satildeo apresentados os valores da

distribuiccedilatildeo da componente da velocidade no interior da geometria Desta forma na regiatildeo do

lsquoplenumrsquo de entrada eacute observado um aumento da componente da velocidade devido ao

estreitamento do canal (nesta regiatildeo ocorrem as maacuteximas velocidades no interior do secador)

Por outro lado na entrada dos canais superiores 1 a 4 notam-se valores positivos para a

componente da velocidade indicando um escoamento em sentido contraacuterio ao desejado

caracterizando uma regiatildeo de recirculaccedilatildeo





58



Figura 57 - Distribuiccedilatildeo da pressatildeo estaacutetica relativa

no interior da geometria de referecircncia




59

Figura 58 - Vista em detalhe da distribuiccedilatildeo da pressatildeo estaacutetica relativa nas regiotildees de entrada e saiacutedada geometria de referecircncia


Os resultados obtidos para a distribuiccedilatildeo da pressatildeo estaacutetica relativa no interior da

geometria satildeo apresentados nas Figura 57 e 58 O voacutertice formado na regiatildeo de entrada doscanais 1 a 4 gera uma regiatildeo de baixa pressatildeo no lsquo plenumrsquo de entrada Por outro lado o

lsquo plenumrsquo de saiacuteda apresenta valores de pressatildeo estaacutetica menores devido agrave elevada perda de carga

do escoamento no interior dos canais formados pelas placas de madeira Finalmente eacute

importante salientar que a pressatildeo estaacutetica meacutedia no plano de saiacuteda do secador foi fixada em

zero Desta forma todos os valores apresentados nas Figuras 57 e 58 representam a diferenccedila

entre a pressatildeo estaacutetica num dado local em relaccedilatildeo agrave saiacuteda

Como a anaacutelise apresentada neste trabalho considera um escoamento turbulento eacute de

extrema importacircncia o estudo de aspectos relacionados agraves grandezas turbulentas Dentro deste

contexto nas Figura 59 e 510 satildeo apresentadas as distribuiccedilotildees da energia cineacutetica turbulenta

no interior da geometria do secador O principal aspecto consiste em observar as regiotildees no

interior da geometria onde ocorre a maacutexima produccedilatildeo de energia cineacutetica turbulenta a saber (i)

a regiatildeo do voacutertice formado na quina do lsquo plenumrsquo de entrada (ii) as regiotildees de entrada de todos

os canais formados pelas placas de madeira e (iii) as regiotildees proacuteximas a descarga de todos os

canais onde ocorre um escoamento tipo jato com intensa mistura entre camadas cisalhantes

Estes resultados satildeo fisicamente consistentes (de forma qualitativa) uma vez que regiotildees onde



60

ocorrem quinas desenvolvimento de camadas limite ou mistura entre camadas de cisalhamento

satildeo locais que apresentam elevada atividade turbulenta



Figura 510 - Vista em detalhe da distribuiccedilatildeo da energia cineacutetica turbulenta nas regiotildees de entrada esaiacuteda da geometria de referecircncia




61

Finalmente como uma forma de avaliar a natildeo uniformidade do escoamento no interior

dos canais satildeo apresentados os valores das velocidades meacutedias na seccedilatildeo de entrada de cada

canal e a variaccedilatildeo de pressatildeo estaacutetica entre a entrada e a saiacuteda dos canais formados pelas

placas de madeira

c ec sc p p p∆ = minus (51)

onde

1n

n

p pdA A

= int (52)

Eacute importante salientar que a variaccedilatildeo de pressatildeo expressa pela Equaccedilatildeo 51 representa a

perda de carga no interior de cada canal Desta forma ao analisarem-se os resultados das Figuras

511 e 512 constata-se os seguintes aspectos relevantes (i) inicialmente destaca-se que a

distribuiccedilatildeo de velocidade meacutedia nos canais eacute similar ao caso analisado no capiacutetulo de validaccedilatildeo

Novamente constata-se que os canais com velocidades meacutedias menores (canais 1 a 4)

coincidem com a regiatildeo do voacutertice (na Figura 52 pode ser observado que o centro do voacutertice

estaacute localizado exatamente entre os canais 2 e 3) (ii) A variaccedilatildeo de pressatildeo no interior dos

canais segue a mesma tendecircncia da curva de velocidades a saber o gradiente de pressatildeo eacute a

forccedila motriz para o escoamento Desta forma quanto maior a velocidade meacutedia no interior de

um canal maior eacute a perda de carga



62

Figura 511 - Velocidade meacutedia nos canais formados pelas placas de madeiras na geometria dereferecircncia

0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148


Figura 512 - Variaccedilatildeo de pressatildeo estaacutetica meacutedia nos canais do secador de madeira


52 INFLUEcircNCIA DA LARGURA DOS CANAIS DE ENTRADA E SAIacuteDA (LARGURA DO

lsquoPLENUMrsquo)

Com o intuito de avaliar a influecircncia da largura do lsquoplenumrsquo na topologia do escoamento

realizaram-se novas simulaccedilotildees utilizando geometrias com valores do paracircmetro A iguais a 01 e

03 m (ver ilustraccedilatildeo da dimensatildeo A na Figura 44) As condiccedilotildees de contorno e os outros



63

valores dos paracircmetros geomeacutetricos foram mantidos iguais ao caso de referecircncia (onde A = 015

m) As malhas geradas obedeceram as mesmas diretrizes da geometria de referecircncia com

espaccedilamento uniforme na direccedilatildeo Y e estiramento de 10 na direccedilatildeo X (as malhas possuem

392196 e 462364 pontos respectivamente)

Na Figura 513 satildeo apresentadas as linhas de corrente e o moacutedulo da velocidade para a

geometria com largura de lsquoplenumrsquo A = 01 m Inicialmente observa-se que a topologia do

escoamento apesar de semelhante qualitativamente ao caso da geometria de referecircncia (ver

Figura 52) possui diferenccedilas importantes Em decorrecircncia do estreitamento do lsquo plenumrsquo de

entrada o voacutertice que se forma na quina possui o tamanho reduzido bem como sua localizaccedilatildeo

foi alterada a saber o centro do mesmo natildeo se encontra entre os canais 2 e 3 mas sim na

entrada do canal 2 Outra consequecircncia da reduccedilatildeo da largura do lsquo plenumrsquo estaacute relacionada agraves

velocidades maacuteximas encontradas no interior da geometria houve um incremento na velocidade

maacutexima em torno de 18 devido agrave reduccedilatildeo da aacuterea de passagem efetiva do escoamento Por

outro lado a topologia do escoamento na regiatildeo do lsquo plenumrsquo de saiacuteda da geometria natildeo sofreu

alteraccedilotildees significativas em relaccedilatildeo ao caso de referecircncia

Figura 513 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria para o lsquoplenumrsquo de

01 m




64

Na Figura 514 satildeo apresentadas as linhas de corrente e o moacutedulo da velocidade obtidos

para a geometria com largura de lsquo plenumrsquo A = 03 m Eacute possiacutevel notar que neste caso ocorre a

formaccedilatildeo de um grande voacutertice na regiatildeo do lsquoplenumrsquo de entrada poreacutem o centro do mesmo

encontra-se mais afastado da seccedilatildeo de entrada dos vaacuterios canais do secador

Figura 514 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria para o lsquoplenumrsquo de03 m


Finalmente visando analisar os efeitos da largura do lsquo plenumrsquo sobre a uniformidade do

escoamento no interior dos vaacuterios canais satildeo apresentados nas Figura 515 e 516 os resultados

para as velocidades meacutedias e para as variaccedilotildees de pressatildeo estaacutetica meacutedia (ver Equaccedilatildeo

51) De acordo com os resultados verifica-se claramente que quanto menor a largura dolsquoplenumrsquo maior seraacute a diferenccedila encontrada entre os pontos miacutenimo e maacuteximo tanto para as

velocidades meacutedias quanto para a variaccedilatildeo de pressatildeo no interior dos canais Desta forma

conclui-se que para uma geometria hipoteacutetica onde a largura do lsquoplenumrsquo fosse infinita ter-se-ia

um escoamento praticamente uniforme nos canais (variaccedilatildeo de velocidades meacutedias pequenas

entre os canais)



65

Figura 515 ndash Velocidade meacutedia nos canais formados pelas placas de madeiras nas geometriastestadas

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105


Figura 516 - Variaccedilatildeo de pressatildeo estaacutetica nos canais do secador de madeira para as trecircs geometriastestadas


53 INFLUEcircNCIA DA VELOCIDADE DE ENTRADA

A segunda variaacutevel analisada no estudo parameacutetrico consistiu em alterar o valor da

velocidade de entrada verificando os efeitos sobre a topologia do escoamento Desta forma

realizaram-se novas simulaccedilotildees para trecircs valores distintos de velocidade 3 7 e 9 m s-1



66

comparando posteriormente os resultados obtidos ao caso padratildeo 5 m s -1 para a geometria de

referecircncia Os principais resultados indicando a topologia do escoamento estatildeo representados

nas Figuras 517 a 519

Na Figura 517 apresentam-se as linhas de corrente e o moacutedulo da velocidade obtidospara uma velocidade de entrada = 3 m s-1 As velocidades de 7 e 9 m s -1 satildeo apresentadas nas

Figura 518 e 519 A partir da anaacutelise das figuras tem-se clara evidencia que natildeo existem

diferenccedilas significativas na topologia do escoamento para as velocidades simuladas

Figura 517 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria de referecircncialsquoplenumrsquo de 015 m com = 3 ms




67



Figura 519 ndash Linhas de corrente e o moacutedulo da velocidade no interior da geometria de referecircncialsquoplenumrsquo de 015 m com

= 9 ms




68

Por outro lado visando compreender melhor a influecircncia da velocidade de entrada na

uniformidade do escoamento no interior do secador satildeo apresentadas nas Figura 520 e 521 os

valores para as velocidades meacutedias e variaccedilatildeo de pressatildeo estaacutetica nos canais

respectivamente De acordo com os resultados apresentados na Figura 520 nota-se claramente

que as curvas apresentam semelhanccedila poreacutem para a velocidade de 3 m s -1 o escoamento

apresenta uma menor variaccedilatildeo entre os pontos de miacutenimo e maacuteximo (maior uniformidade) Um

comportamento similar pode ser observado na Figura 521 para a variaccedilatildeo de pressatildeo estaacutetica

isto eacute velocidades maiores nos canais satildeo consequecircncia direta de uma maior variaccedilatildeo de pressatildeo

entre a entrada e saiacuteda dos canais

Figura 520 - Velocidade meacutedia nos canais no interior do secador de madeira para as quatrovelocidades

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue


Figura 521 ndash Variaccedilatildeo de pressatildeo no canais no interior do secador de madeira para as quatrovelocidades




69

Finalmente como uma forma de avaliar todos os resultados obtidos para as variaacuteveis

estudadas largura do lsquoplenumrsquo e velocidade de entrada apresentam-se na Figura 522 as

curvas de perda de carga global no secador como funccedilatildeo da vazatildeo

es ssg

p p p ρ minus∆ = (53)

onde eacute a pressatildeo estaacutetica meacutedia (Equaccedilatildeo 52) avaliada entre a entrada e a saiacuteda do secador

Por outro lado a vazatildeo eacute calculada por

e eQ u S = (54)

sendo a aacuterea de entrada dada por

eS El= (55)

Na expressatildeo anterior E representa a altura do canal de entrada (ver Figura 44) sendo l a

profundidade do secador (neste trabalho foi assumido uma profundidade unitaacuteria)

Analisando os resultados da Figura 522 eacute possiacutevel extrair as seguintes conclusotildees (i) a

perda de carga global aumenta com o incremento da vazatildeo (velocidade) para os trecircs valores da

largura de lsquoplenumrsquo analisados (comportamento esperado) (ii) Analisando o efeito da largura do

lsquo plenumrsquo percebe-se claramente que a perda de carga global eacute maior para A = 01 m e

praticamente constante para as outras duas larguras investigadas Todavia vale destacar que

apesar da perda global do sistema para os valores do lsquo plenumrsquo A = 015 e 03 m serem

praticamente iguais observa-se que a topologia do escoamento (ver Figuras 52 e 514) bem

como a distribuiccedilatildeo de velocidades meacutedias nos canais (ver Figura 515) satildeo completamente

diferentes Este aspecto eacute de grande importacircncia no projeto de secadores visto que pode

conduzir a uma interpretaccedilatildeo errocircnea dos resultados se apenas for observada uma das

informaccedilotildees perda de carga global do sistema ou topologia do escoamento



70

Figura 522 - Perda de carga global entre a entrada e saiacuteda do secador




71

6 CONCLUSOtildeES E SUGESTOtildeES

Neste trabalho foi apresentada a simulaccedilatildeo numeacuterica de um escoamento turbulento no

interior de uma geometria que modela um secador de madeira As simulaccedilotildees foram realizadasutilizando o programa comercial ANSYSreg CFX onde o objetivo principal foi avaliar a

topologia do escoamento no interior da geometria e analisar a influecircncia da largura do lsquo plenumrsquo

e da velocidade de entrada As principais conclusotildees desta anaacutelise fiacutesica estatildeo apresentadas a

seguir

(i) Efeito da largura do lsquoplenumrsquo na topologia do escoamento observou-se que este paracircmetro

tem influecircncia direta no niacutevel de uniformidade do escoamento no interior dos canais formados

pelas placas de madeira Foi determinado que a largura do lsquo plenumrsquo eacute um dos fatores queestabelece o tamanho e a localizaccedilatildeo do voacutertice gerado apoacutes a quina de entrada Com base nos

resultados conclui-se que para valores da largura de lsquo plenumrsquo menores satildeo encontrados maiores

gradientes para a velocidade meacutedia ū e a variaccedilatildeo de pressatildeo c p∆ nos canais (conforme

resultados das Figuras 515 e 516) Outro aspecto importante relacionado com a largura do

lsquo plenumrsquo eacute a perda de carga global no sistema (resultados apresentados na Figura 522)

Observa-se claramente que a perda de carga eacute maior para o lsquo plenumrsquo de 01m enquanto que

para os valores de lsquo plenumrsquo de 015 e 03m a mesma natildeo apresenta diferenccedilas significativas

Vale destacar que apesar dos resultados encontrados para a perda de carga para as larguras de

lsquo plenumrsquo de 015 e 03m serem praticamente iguais deve-se ter em mente que se tratam de duas

topologias de escoamento diferentes

(ii) Efeito da velocidade de entrada percebeu-se que a topologia do escoamento natildeo apresenta

diferenccedilas significativas para as velocidades simuladas Destaca-se poreacutem que as velocidades

meacutedias ū e a variaccedilatildeo de pressatildeo c p∆

nos canais formados pelas placas de madeiraapresentam menores gradientes para a velocidade de 3 m s-1 em relaccedilatildeo agraves outras velocidades

simuladas (ver Figuras 520 e 521) o que indica uma maior uniformidade do escoamento Em

relaccedilatildeo agrave perda de carga global do secador os resultados obtidos indicaram o comportamento

esperado isto eacute maiores velocidades (vazotildees elevadas) apresentam maior perda de carga

independente da largura do lsquoplenumrsquo

(iii) Posiccedilatildeo do voacutertice apoacutes a quina da entrada conforme resultados encontrados uma das

principais causas para a natildeo uniformidade do escoamento no interior do secador eacute a posiccedilatildeo dovoacutertice gerado apoacutes a quina de entrada Neste trabalho foi demonstrado que a localizaccedilatildeo e

abrangecircncia do voacutertice dependem de fatores como a largura do lsquo plenumrsquo A e a distacircncia entre o



72

canal de entrada e o primeiro canal de escoamento E (ver Figuras 44 e 49) Conforme foi

discutido anteriormente constatou-se que este voacutertice tem influencia direta na distribuiccedilatildeo das

velocidades no interior do secador sendo seus efeitos mais perceptiacuteveis nas proximidades de sua

localizaccedilatildeo a saber nos canais superiores

61 SUGESTOtildeES

O presente trabalho teve como objetivo contribuir para o entendimento de escoamentos

turbulentos no interior de secadores de madeira Entretanto trata-se de uma primeira abordagem

que necessita ser continuada Na visatildeo do autor os principais pontos a serem investigados numa

proacutexima etapa da pesquisa satildeo

(i) Soluccedilotildees para o voacutertice apoacutes a quina da entrada em relaccedilatildeo ao voacutertice formado na regiatildeo da

quina de entrada faz-se necessaacuterio realizar estudos mais aprofundados com o objetivo de

minimizar os efeitos do mesmo sobre a distribuiccedilatildeo das velocidades no interior do secador

(ii) Estudo do processo de secagem faz-se necessaacuterio apoacutes esta primeira abordagem avaliar os

processos da difusatildeo de calor e massa no interior das placas de madeira de forma acoplada com

a anaacutelise do escoamento

(iii) Escoamento tridimensional para se verificar os reais efeitos das alteraccedilotildees propostas faz-se

necessaacuterio avaliar o escoamento tridimensional Estes resultados podem vir a contribuir para o

desenvolvimento de soluccedilotildees para o problema da natildeo uniformidade do escoamento no interior

do secador



73

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ANSYS ANSYS CFXreg Release 110 Manual 2007

CHANDRA MOHAN VP TALUKDAR P Three dimensional numerical modeling of simulations

heat and moisture transfer in a moist object subjected to convective drying International Journal of

Heat and Mass Transfer v 53 p 4638-4650 2010

HIRSCH CH Numerical computation of internal and external flows 2nd edMassachusetts EUA Elsevier 2009

KADEM S LACHEMET A YOUNSI R KOCAEFE D 3d ndash Transient modeling of

heat and mass transfer during heat treatment of wood International Communications inHeat and Mass Transfer v 38 p 717-722 2011

KAYA A AYDM O DINCER I Heat and mass transfer modeling of recirculating flows during

air drying of moist objects for various dryer configurations Numerical Heat Transfer v 53 n 1 p

18-34 2008

KAYA A AYDM O DINCER I Numerical modeling of heat and mass transfer duringforced convection drying of rectangular moist objects International Journal of Heat andMass Transfer v 49 p 3094-3103 2006

LAUNDER B E SPALDING D B The Numerical Computation of Turbulent Flows Computer

Methods in Applied Mechanics and Engineering v 3 p 269-289 1974

LEDIG S F NIJDAM J J KEEY R B Airflow distributions in the fillet spaces of a timber

stack Drying Technology v19 n 8 p1697-1710 2001

LU T SHEN SQ Numerical and Experimental Investigation of Paper Drying Heat and Mass

Transfer with Phase Change in Porous Media Applied Thermal Engineering v 27 p 1248-1258 2007

MALISKA C R Transferecircncia de Calor e Mecacircnica dos Fluidos Computacional 2ed Rio de

Janeiro LTC 2004

MANSOUR N M KIM J MOIN P Reynolds Stress and Dissipation Rate Budgets in Turbulent

Channel Flow Journal of Fluid Mechanics v 194 p 15-44 1988

NIJDAM JJ KEEY RB Airflow behavior in timber (lumber) kilns Drying Technologyv 17 p 1511-1522 1999

NIJDAM JJ KEEY RB An experimental study of airflow in lumber kilns Wood Science



74

and Technology v 36 n 1 p 19-26 2002

NIJDAM JJ KEEY RB The influence of kiln geometry on flow maldistribution acrosstimber stacks in kilns Drying Technology v 18 n 8 p 1865-1877 2000

OBERKAMPF L TRUCANO TG Verification and Validation in Computacional Fluid

Dynamics Progress inAerospace v38 p 209-272 2002

PANG S External heat and mass transfer coefficients for kiln drying of timber Drying

Technology v 14 n 3-4 p859-871 1996

PERIC M KESSLER R SCHEUERER G Comparison of finite Volume Numerical Methods

with Staggered and Colocated Grids Computers and Fluids v 16p 389-403 1988

PERREacute P KEEY RB Drying of Wood Principles and practices Handbook of Industrial Drying

3rd ed New York EUA CRC Press 2006

POSSAMAI DG ZDANSKI PSB VAZ JUNIOR M GARGIONI GT Simulaccedilatildeonumeacuterica do escoamento turbulento em secadores Aplicaccedilotildees no processo de beneficiamentode madeiraIn Congresso Brasileiro de Engenharia de Fabricaccedilatildeo 7 2013 Itatiaia RJ Anaisdo VII Congresso Brasileiro de Engenharia de Fabricaccedilatildeo Rio de Janeiro ABCM 2013

RHIE C M CHOW W L Numerical Study of the Flow Past an Airfoil with Trailing-Edge

Separation AIAA Journal v 21 n11 p 1525-1532 1983

RIEPEN M PAARHUIS B Analysis and optimization of the airflowdistribution in convection kilns In 1st COST Action E15 Wood DryingWorkshop 1999 Edinburg Proceedings of the COST-E15 Workshop Edinburg

VASCONCELLOS JFV MALISKACR A Finite-Volume Method based on Voronoi

discretization for fluid flow problems Numerical Heat Transfer v 45 n 4 p 319-342 2004

WILCOX D C Turbulence Modeling for CFD La Canatildeda EUA DCW Industries 1998

YOUNSI R KOCAEFE D PONCSAK S KOCAEFEY Computational andexperimental analysis of high temperature thermal treatment of Wood based onThermoWood Technology International Communications in Heat and Mass Transfer v 37 p21-28 2010

ZDANSKI P S B Desenvolvimento de um Meacutetodo Numeacuterico para Caacutelculo deEscoamentos Incompressiacuteveis Aplicaccedilatildeo na Anaacutelise da Troca de Calor em Cavidades Rasas2003 Tese de doutorado ITA Satildeo Joseacute dos Campos

ZDANSKI PSB VAZ JUNIOR M CERQUEIRA R F L GARGIONI G T



75

POSSAMAI D G AMARAL F R CAVALI D Simulaccedilatildeo numeacuterica do acoplamentoentre os processos de difusatildeo de calor e massa em regime transiente In Congresso Nacional deEngenharia Mecacircnica 7 2012 Satildeo Luiacutes MA Anais do VII Congresso Nacional deEngenharia Mecacircnica Rio de Janeiro ABCM 2012 P 1-10



P856aPossamaiDaniel Giovani

Anaacutelise numeacuterica do escoamento turbulento no interior

de secadores Daniel Giovani Possamai ndash 2013

75 p il 21 cm

Orientador Paulo Sergio Berving Zdanski

Coorientador Miguel Vaz Junior

Bibliografia p 73-75

Dissertaccedilatildeo (mestrado) ndash Universidade do Estado de

Santa Catarina Centro de Ciecircncias Teacutecnicas Programa de

Poacutes-Graduaccedilatildeo em Engenharia MecacircnicaJoinville 2013

1 Escoamento turbulento 2 Anaacutelise numeacuterica I

Zdanski Paulo Sergio Berving II Vaz Junior Miguel

III Universidade do Estado de Santa Catarina Programa

de Poacutes-Graduaccedilatildeo em Engenharia Mecacircnica IV Tiacutetulo

CDD 6201 - 20ed






AGRADECIMENTOS



motivaccedilatildeo











Bruce Lee





RESUMO






ABSTRACT












semicircular (b) 26




















madeira 51








56




57







60






















velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75







AGRADECIMENTOS



motivaccedilatildeo











Bruce Lee





RESUMO






ABSTRACT












semicircular (b) 26




















madeira 51








56




57







60






















velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75





Bruce Lee





RESUMO






ABSTRACT












semicircular (b) 26




















madeira 51








56




57







60






















velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75






RESUMO






ABSTRACT












semicircular (b) 26




















madeira 51








56




57







60






















velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




ABSTRACT












semicircular (b) 26




















madeira 51








56




57







60






















velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75










semicircular (b) 26




















madeira 51








56




57







60






















velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75







56




57







60






















velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75





velocidades 68


velocidades 68














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75














Altura do canal


2 i jk u u=




Fluxo de massa







3e p p k ρ = +





Vazatildeo

Resiacuteduo


uh ν =



























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




























T

k C micro micro ρ

ε =


Densidade do fluido













SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75








SUMAacuteRIO

















351 Entrada 39

352 Saiacuteda 39
















REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75









REFEREcircNCIAS 73





19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75






19












mesmo






















20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




20



























21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




21

































22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




22












satildeo discutidos









DOR











apenas para o

riquecimento do

prima para uma

EM et al2011)



ica em secadores

um problema de


idimensional foi

de em um objeto

do processo de











Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75












Outros estudos sobr













K para 353 K


0)








23




m incremento de 300





uadrado com umidade






24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




24




































a que o processo

s formados pelas

pode ser gerada

(ii) um arranjo

a do secador Os

pode ocorrer o


nesta regiatildeo)

iepen e Paarhuis

s das rotinas de

erior do secador

escoamento em


ais eficientes de

mportamento do

o problema de



25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




25























26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




26















27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




27






escoamento do ar





28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




28














plausiacuteveis



29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




29







( )( ) j i ji i

j i j j i





que eacute dada por

0i

i

u

x

part =part

(32)











30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




30










ϕ ϕ ϕ = + (33)



se

( )( )2 j ii

ij i j

j i j

u uu ps u u

t x x x

ρ ρ micro ρ


(34)


1

2 ji

ij

j i

uus

x x


(35)






31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




31

0i

i

u

x

part=

part (36)












23

jiij i j T ij

j i

uuu u k





1

2 i ik u u= (38)


2 2

3 3ij

j i





32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




32


( )( )

2

j ii e

e ij j i j

u uu p

st x x x

ρ ρ

micro


part part part part

(310)




(311)


2

3e p p k ρ = + (312)







i i

k k

u u

x xε ν

part part=

part part (313)





33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




33

( )( ) j T k

j j k j

u k k k S

t x x x

ρ micro ρ

σ



e

( )( ) j T

j j j

uS

t x x x ε

ε

ρ ε micro ρε ε

σ




eS



2

1 2d S C P C

k k ε ε ε



ji iT d

j i j

uu uP

x x x

micro

ρ


(318)


2

T

k C micro micro ρ

ε = (319)





34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




34
























35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




35








(MALISKA 2004)






( )0 j

j

u

t x

ρ ρ partpart+ =

part part (321)



36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




36

( )( ) j i ji e ie

j i j j i

u u uu p u

t x x x x x

ρ ρ micro


(322)

( )( ) j

e

j j j

uS

t x x x φ


(323)



0 j j

V S dV u dn

t ρ ρ

part+ =

part int int (324)

jii j i j e j e j

V S S S j i




j j e jV S S V

j

dV u dn dn S dV t x

φ

φ ρφ ρ φ











37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




37



( ) 0

o

j j pi pi

V u nt

ρ ρ

ρ

minus

+ ∆ = ∆ sum (327)

( ) ( )o o


pi pi pi j i pi

uu u uV m u p n n

t x x

ρ ρ micro


sum sum sum (328)

( )o o

pi i e j pi pi pi j

pi

V m n S V t x

φ

ρφ ρ φ φ φ


sum sum (329)

sendo que




ndash (329)




[ ][ ] [ ] M Gθ = (330)



n 1 n θ θ θ += + (331)



38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




38


n M r θ = (332)























39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




39




351 Entrada






ˆ ˆe esp esp

u u i v j= + (334)

352 Saiacuteda














40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




40

0nu = (335)


0n

φ part=

part (336)




0wu = (337)



41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




41






















42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




42




13740 = 392 J kg-1

s-1 e = 002 sup22 (ZDANSKI2003)










0

02

04

06

08

1

12

0 1 2 3 4 5

983161 983144

983147983157983134

983120983154983141983158983145983155983267983151 983156983145983152983151 983108983118983123 (983117983137983150983155983151983157983154

983141983156 983137983148 (1988))

983120983154983141983155983141983150983156983141 983124983154983137983138983137983148983144983151

983117983151983140983141983148983151 983147983085983159 (983127983145983148983139983151983160 (1998))








43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




43


14

16

18

20

22

1 10 100 1000

983157

983161

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983116983141983145 983148983151983143983137983154983145983156983149983137 (983117983137983150983155983151983157983154 983141983156

983137983148 (1988))



















44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




44




-1s



















45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




45





















regiatildeo



46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




46



















47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




47










0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137

ū 983087 983157 983141

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983120983154983141983155983141983150983156983141 983156983154983137983138983137983148983144983151

983126983137983148983151983154983141983155 983141983160983152983141983154983145983149983141983150983156983137983145983155 983118983145983146983140983137983149 983141

983115983141983141983161 (2002)











no eixo y



48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




48


0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983107983137983150983137983148

983117983137983148983144983137 983125983150983145 983142983151983154983149983141 01 9831311161724 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 02 983131775524 983152983151983150983156983151983155983133

983117983137983148983144983137 983125983150983145983142983151983154983149983141 03 983131621044 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 01 983131214376 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 02 983131143656 983152983151983150983156983151983155983133

983117983137983148983144983137 983109983155983156983145983154983137983140983137 03 983131121584 983152983151983150983156983151983155983133

































or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




















or














49

de madeira
















50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




50




0

02

04

06

08

1

12

14

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983154 983141 983148 983137 983156 983145 983158 983137 ū 983157

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983151983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137










51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




51


0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

983120 983154 983141 983155 983155 983267 983151 983141 983155 983156 983265 983156 983145 983139 983137 983149 983273 983140 983145 983137 983131 983120

983137 983133

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

983111983141983151983149983141983156983154983145983137 983119983154983145983143983145983150983137983148

983111983141983151983149983141983156983154983145983137 983149983151983140983145983142983145983139983137983140983137




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




52



53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




53





do secador

























54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




54




(ver Figura 44)








= 392 J kg-1

























55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




55










56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




56













57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




57













58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




58








59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




59





















60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




60









61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




61




placas de madeira


onde

1n

n

p pdA A

= int (52)













62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




62


0

05

1

15

2

25

335

4

45

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148





lsquoPLENUMrsquo)






63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




63

















01 m




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




64














entre os canais)



65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




65


0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

01 983149

015 983149

03 983149

983105










66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




66











67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




67




= 9 ms




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




68











0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

983126 983141 983148 983151 983139 983145 983140 983137 983140 983141 983149 983273 983140 983145 983137 ū

983118983290983149983141983154983151 983140983151 983139983137983150983137983148

3 983149983155

5 983149983155

7 983149983155

9 983149983155

ue






69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




69




es ssg




e eQ u S = (54)


eS El= (55)
















70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




70





71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




71






seguir


























72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




72





61 SUGESTOtildeES














do secador



73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




73

REFEREcircNCIAS










18-34 2008









Janeiro LTC 2004







74






Technology v 14 n 3-4 p859-871 1996

















75




74






Technology v 14 n 3-4 p859-871 1996

















75




75


anÁlise numÉrica do escoamento turbulento no interior de secadores

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