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Study of heat and mass transfer of water evaporation in a gypsum board subjected to natural convection

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Abstract

The present paper reports a numerical study to investigate the drying of rectangular gypsum sample based on a diffusive model. Both vertical and low sides of the porous media are treated as adiabatic and impermeable surfaces plate. The upper face of the plate represents the permeable interface. The energy equation model is based on the local thermal equilibrium assumption between the fluid and the solid phases. The lattice Boltzmann method (LBM) is used for solving the governing differential equations system. The obtained numerical results concerning the moisture content and the temperature within a gypsum sample were discussed. A comprehensive analysis of the influence of the mass transfer coefficient, the convective heat transfer coefficient, the external temperature, the relative humidity and the diffusion coefficient on macroscopic fields are also investigated. They all presented results in this paper and obtained in the stable regime correspond to time superior than 4000 s. Therefore the numerical error is inferior to 2%. The experimental data and the descriptive information of the approach indicate an excellent agreement between the results of our developed numerical code based on the LBM and the published ones.

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Abbreviations

C p :

Specific heat (Jkg−1 K−1)

u :

Displacement vector (ms−1)

L :

Length (m)

\(h_{m}\) :

Mass transfer coefficient (ms−1)

\(h_{conv}\) :

Convective heat transfer coefficient (Wm−2 K−1)

t :

Time (s)

\(K_{r}\) :

Relative permeability (kgs−1 m−2 Pa−1)

\(dx, \;dy\) :

Space steps

\(f_{k}\) :

Dynamic distribution function

\(g_{k}\) :

Temperature distribution function

\(HR\) :

Relative humidity of the ambient air (%)

\(R_{u}\) :

Universal gas constant (JK−1 mol−1)

\(P_{cap}\) :

Capillary pressure (Pa)

\(P_{v,a}\) :

Vapor pressure in the ambient medium (Pa)

\(P_{v,surf}\) :

Vapor pressure at the product surface (Pa)

\(R_{e}\) :

Reynolds number

\(R_{k}\) :

Thermal conductivity ratio

c s :

Sound speed (ms−1)

e :

Thickness (m)

\(T\) :

Temperature (K)

\(X\) :

Moisture content (kg kg−1)

X eq :

Equilibrium moisture content (kg kg−1)

K :

Intrinsic permeability (m2)

D :

Diffusion coefficient (m2 s−1)

c k :

Microscopic velocity (ms−1)

\(f_{k}^{eq}\) :

Equilibrium distribution function

\(g_{k}^{eq}\) :

Equilibrium distribution function

I :

Unitary matrix

L v :

Latent heat of water evaporation (Jkg−1)

M v :

Molar mass of the pure water (gmol−1)

F k :

External force (N)

\(\dot{m}\) :

Mass evaporation rate per unit area (kgs−1 m−2)

P r :

Prandtl number

R c :

Thermal capacity ratio

\(\vec{\nabla }\) :

Gradient

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

Divergence

\(\Delta t\) :

Time step

\(\tau\) :

Relaxation time

\(\mu\) :

Dynamic viscosity (kgm−1 s−1)

\(\rho\) :

Macroscopic density (kgm−3)

\(\varepsilon\) :

Volumetric fraction

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

Spatial step

\(\Omega\) :

Collision operator

\(\omega_{k}\) :

Weight coefficient

\(\lambda_{eff}\) :

Effective thermal conductivity (Wm−1 K−1)

l :

Liquid

g :

Gas

k :

Velocity discretized direction

v :

Vapor

w :

Water

s :

Solid

a :

Air

i :

Space direction

0:

Initial

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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

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

Authors
  1. K. Zannouni
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  2. H. El Abrach
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  3. H. Dhahri
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  4. A. Mhimid
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Correspondence to K. Zannouni.

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Zannouni, K., El Abrach, H., Dhahri, H. et al. Study of heat and mass transfer of water evaporation in a gypsum board subjected to natural convection. Heat Mass Transfer 53, 1911–1921 (2017). https://doi.org/10.1007/s00231-016-1950-y

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  • DOI: https://doi.org/10.1007/s00231-016-1950-y

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