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Effects of Anisotropy and Drying Air Parameters on Drying of Deformable Porous Media Hydro-Dynamically and Thermally Anisotropic

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Abstract

The purpose of this work was to investigate numerically the drying of saturated deformable porous media. The considered sample is a rectangular porous plate which assumed to be both hydro-dynamically and thermally anisotropic, while the mechanical behavior of the sample is supposed to be isotropic. All walls of the plate are subjected to a convective heat flux. Moreover, the top and bottom walls are allowed the mass transfer. The Darcy–Brinkman extended model was used as the momentum balance equation for the liquid and solid phases. The energy balance equation is based on the local thermodynamic equilibrium assumption between the both phases. The lattice Boltzmann method is used to solve the governing differential equation system. A comprehensive analysis of the effect of anisotropy and the drying air parameters on macroscopic fields is investigated throughout this work.

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Abbreviations

\(\vec {c}_k \) :

Microscopic velocity

\(\hbox {C}_{\mathrm{p}}\) :

Specific heat

\(\hbox {c}_{\mathrm{s}}\) :

Sound speed

e:

Thickness

\(E\) :

Young’s modulus

\(\hbox {f}_{\mathrm{k}}, \hbox {d}_{\mathrm{k}}\) :

Dynamic distributions functions

\(\hbox {f}_{\mathrm{k}}^{\mathrm{eq}}, \hbox {d}_{\mathrm{k}}^{\mathrm{eq}}\) :

Dynamic equilibrium distributions functions

\(\hbox {F}_{\mathrm{k}}, \hbox {D}_{\mathrm{k}}\) :

External forces

\(F_m\) :

Mass flux

\(\hbox {g}_{\mathrm{k}}\) :

Temperature distribution function

\(\hbox {g}_{\mathrm{k}}^{\mathrm{eq}}\) :

Temperature equilibrium distribution function

\(h_k\) :

Intermediate distribution function

\(h_k^{eq}\) :

Intermediate equilibrium distribution function

\(\overline{h_k}\) :

Pressure distribution function

\(h_m\) :

Mass exchange coefficient

\(k_s^*\) :

Conductivity ratio

\(k_{s x}, k_{s y}\) :

Conductivities along principal axes

\(\overline{\overline{k}}\) :

Thermal conductivity tensor

\(K^{*}\) :

Permeability ratio

\(K_x, K_y\) :

Permeabilities along principal axes

\(\overline{\overline{K}}\) :

Second-order permeability tensor

L:

Length

\(\vec {n}\) :

Unit vector

P:

Pressure

\(P_l^{*}=\frac{\prec p_l^l \succ -p_{atm}}{E}\) :

Dimensionless liquid pressure

HR:

Air moisture

t:

Time

\(Time=\frac{tU}{e}\) :

Dimensionless time

T:

Temperature

\(T^{*}=\frac{\prec T\succ -T_0}{T_\infty -T_0}\) :

Dimensionless temperature

\(\hbox {U} = \hbox {V}_{\mathrm{a}}\) :

Reference velocity

\(\vec {u}\) :

Displacement vector

\(\vec {V}_l^*=\frac{\prec \vec {v}_l^l \succ }{U}\) :

Dimensionless solid deformation velocity

\(\vec {V}_s^*=\frac{\prec \vec {v}_s^s \succ }{U}\) :

Dimensionless liquid velocity

W:

Vapor concentration

\(X=\frac{x}{e}, Y=\frac{y}{e}\) :

Dimensionless space coordinates (orthonormal system)

\(\Delta H_v\) :

Vaporization enthalpy

\(\varepsilon \) :

Volumetric fraction

\(\mu \) :

Dynamic viscosity

\(\tau _s\) :

Solid stress tensors

\(\overline{e} \) :

Solid deformation tensor

\(\upsilon \) :

Poisson’s coefficient

\({\lambda }', {\mu }'\) :

Lamé constants

\(\Omega \) :

collision operator

\(\omega _k \) :

Weight coefficient

\(\tau \) :

Relaxation time

\(\rho \) :

Macroscopic density

\(\Delta x, \Delta y\) :

Spatial step

\(\Delta t\) :

Time step

\(\vec {\nabla }\) :

Gradient

\(\vec {\nabla }.\) :

Divergence

\(\theta \) :

Orientation angle

a:

Air

cap:

Capillary

i:

Space direction

k:

Velocity discretized direction

l:

Liquid

s:

Solid

surf:

Surface

\(\infty \) :

Ambient

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Authors and Affiliations

  1. Laboratory of thermal and energy systems studies, National School of Engineers, Monastir University, Ibn Eljazzar Street, 5019 , Monastir, Tunisia

    H. El Abrach, H. Dhahri & A. Mhimid

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  1. H. El Abrach
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  2. H. Dhahri
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  3. A. Mhimid
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Correspondence to H. Dhahri.

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El Abrach, H., Dhahri, H. & Mhimid, A. Effects of Anisotropy and Drying Air Parameters on Drying of Deformable Porous Media Hydro-Dynamically and Thermally Anisotropic. Transp Porous Med 104, 181–203 (2014). https://doi.org/10.1007/s11242-014-0327-2

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