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Heat and Mass Transfer in Porous Materials with Complex Geometry: Fundamentals and Applications

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Heat and Mass Transfer in Porous Media

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 13))

Abstract

This chapter provides information related to simultaneous heat and mass transfer and dimension variations in unsaturated porous bodies of arbitrary shape during transient problems. Two mathematical approaches are presented and discussed: lumped and distributed-parameters models. Here, applications have been given to some engineering processes (cooling, heating and drying). A two-dimensional distributed model written in a orthogonal curvilinear coordinate system and which assumes the pure diffusion as the sole mechanism of heat and moisture transport within the solid is applied to ellipsoidal porous bodies (prolate spheroid). A lumped-parameter model written in any coordinate system which includes effects such as shape of the body, heat and mass generation, evaporation and convection is presented, and analytical solution of the governing equations, limitations of the modeling and general theoretical results are discussed.

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Abbreviations

Bih :

Heat transfer Biot number

Bim :

Mass transfer Biot number

c:

Specific heat, J/kg/K

D:

Diffusion coefficient, m2/s

Foc :

Heat transfer Fourier number

Fom :

Mass transfer Fourier number

hc :

Heat transfer coefficient, W/m2/K

hfg :

Latent heat of vaporization of the moist solid, J/kg

hm :

Mass transfer coefficient, m/s

J:

Jacobian

\( {\text{k}},\,{\bar{\text{k}}} \) :

Local and average thermal conductivity, W/m/K

L:

Focal length, m

L′ :

Characteristic dimension, m

Lc :

Characteristic length, m

L1, L2 :

Minor and major axis of the solid, m

M, \( \overline{\text{M}} \) :

Local and average moisture content, kg/kg (d.b.)

\( {\dot{\text{M}}} \) :

Mass generation per unit time, (kg/kg)/s

n:

Number of experimental points

\( {\hat{\text{n}}} \) :

Parameters number fitted

\( {\dot{\text{q}}} \) :

Heat generation per volume unit, W/m3

\( {\bar{\text{S}}}^{2} \) :

Variance

S:

Area, m2

\( {\text{S}}^{{{\Upphi}}} \) :

Source term

T:

Air temperature, °C

t:

Time, s

\( \hat{\text{U}},\;\hat{\text{V}},\;\hat{\text{W}} \) :

Metric coefficients

UR:

Air relative humidity

v:

Air velocity, m/s

V:

Volume, m3

x, y, z:

Cartesian coordinates, m

Exp:

Experimental

fn:

Final

0:

Initial

Num:

Numerical

p:

Product

s:

Dry solid

t:

Time

v:

Vapor

\( \infty \) :

Equilibrium

\( {{\upalpha}} \) :

Thermal diffusivity, m2/s

\( \overline{{{\upbeta}}}_{1} ,\,\overline{{{\upbeta}}}_{2} \) :

Shrinkage coefficient

\( {{\Updelta}} \) :

Variation

\( {{\Upphi}} \) :

Function

\({ {\Upphi}^{\prime\prime}}\) :

Potential \( {{\Upphi}} \) per area unit

\({ {\Upphi}^{\prime\prime\prime}}\) :

Potential \( \Upphi \) per volume unit

\( \Upgamma^{\Upphi } ,\;\Uppsi \) :

Transport property of material

μ, ϕ, ω:

Prolate spheroidal coordinates

η, ξ, ζ:

Orthogonal curvilinear coordinates

\( {{\theta}},\,\overline{{{\theta}}} \) :

Local and mean temperature of solid, °C

∇:

Del operator

ρ:

Density, kg/m3

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Acknowledgments

The authors would like to express their thanks to CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil) and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil) for supporting this work, and are also grateful to the authors of the references in this paper that helped in the improvement of quality.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Federal University of Campina Grande, Campina Grande, Brazil

    A. G. B. de Lima

  2. Department of Chemical Engineering, Federal University of Campina Grande, Campina Grande, Brazil

    S. R. Farias Neto

  3. Department of Physics, Federal University of Campina Grande, Campina Grande, Brazil

    W. P. Silva

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  1. A. G. B. de Lima
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  2. S. R. Farias Neto
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  3. W. P. Silva
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Correspondence to A. G. B. de Lima .

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Editors and Affiliations

  1. Universidade do Porto, Laboratorio de Fisica das, Faculdade de Engenharia, Rua Dr. Roberto Frias, Porto, 4200-465, Portugal

    J.M.P.Q. Delgado

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de Lima, A.G.B., Farias Neto, S.R., Silva, W.P. (2012). Heat and Mass Transfer in Porous Materials with Complex Geometry: Fundamentals and Applications. In: Delgado, J. (eds) Heat and Mass Transfer in Porous Media. Advanced Structured Materials, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21966-5_7

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