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Irreversibility Analysis for Double Diffusive Convection Flow of a Gas Mixture in a Chamfered Corners Square Enclosure Filled with a Porous Medium

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Abstract

An analysis of thermodynamic irreversible principle (TPI), through determination of entropy generation rate, during double-diffusive convection in an octagonal shape, filled with saturated fluid in a porous enclosure, is numerically investigated in this work, by studying the influence of thermodiffusion effect on entropy generation variations. According to the fluid flow evolution under consideration, the influence of mass flux due to temperature gradient is incorporated into the governing equations of the problem, which are solved numerically, using the COMSOL software. Appropriated thermal and solutal Dirichlet boundary conditions are used under the Boussinesq approximation. For the porous medium, the Darcy–Brinkman model is assumed in coupling with energy and mass transfer balance equations. The flow model is described in terms of mass flux due to temperature gradient, buoyancy ratio, thermal Rayleigh number and porosity of the medium. Results of the variations of heat transfer and entropy generation in the studied enclosure are graphically illustrated and are basically discussed, through various physical aspects of the problem. The numerical computations are presented for various values of thermal Rayleigh number (RaT), thermal diffusion parameter (Kt), Darcy number (Da), buoyancy ratio (N) and porosity of the medium (ε). In addition, the total entropy generation due to thermal, species and mixed diffusion gradients; Darcy–Brinkman dissipation; and fluid friction are studied and discussed. It is found that the entropy generation increases strongly when passing from the cooperative case of buoyancy forces to the opposite case. A similar behaviour is obtained with increasing the thermal diffusion ratio, at a constant buoyancy ratio. Also, an accentuated increase in entropy generation is observed when the Darcy number exceeds the value 10−6. Moreover, the results show that the augmentation of the thermodiffusion effect induces an increase in total entropy generation, at fixed value of the porosity.

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Abbreviations

C :

Concentration (mol m−3)

Da:

Darcy number

D CT :

Thermal diffusion coefficient (mol m−1 s−1 K−1)

D e :

Molecular diffusivity (m2 s−1)

g :

Gravitational acceleration (m s−2)

H :

Cavity height (m)

k :

Thermal conductivity (W m−1 K−1)

K :

Permeability (m2)

Le:

Lewis number

N :

Buoyancy ratio (GrS/GrT)

Nu:

Average Nusselt number

p :

Pressure (kg m−1 s−2)

P :

Dimensionless pressure

Pr:

Prandtl number

R k :

Thermal conductivity ratio (km/kf)

Ra:

Rayleigh number

RaT :

Thermal porous Rayleigh number

Kt :

Soret parameter

S gen :

Total dimensionless entropy generation

T′:

Temperature (K)

T :

Dimensionless temperature T0 = (Th′ + Tc′)/2

t, τ :

Dimensional and dimensionless time

u, v :

Velocity components in x and y directions (m s−1)

U, V :

Dimensionless velocity components

x, y :

Cartesian coordinates (m)

X, Y :

Dimensionless Cartesian coordinates

α e :

Effective thermal diffusivity (m2 s−1)

ε :

Medium porosity

μ :

Kinematic (m2 s−1)

μ eff :

Viscosity (kg m−1 S−1)

\( \varLambda \) :

Viscosity ratio (μeff/μ)

ρ :

Density (kg m−3)

σ :

Specific heat ratio [(ρc)m/(ρc)f]

Ω :

Temperature ratio ∆T/T0

Ω′:

Concentration ratio ∆C/C0

0:

Reference

c:

Cold wall

d:

Dimensional

e:

Effective

f:

Fluid

h:

Hot wall

m:

Porous

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Acknowledgements

Authors are grateful to thank all reviewers and editors for their great suggestions and valuable comments which greatly improved the quality of the paper.

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Authors and Affiliations

  1. Applied Thermodynamics Research Unit, Chemical Engineering Process Department, Engineers National School of Gabes, Gabes University, Omar Ibn El Khattab Street, 6029, Gabès, Tunisia

    Mounir Bouabid, Naoufal Ghoudi & Rahma Bouabda

  2. Industrial Chemistry and Chemical Engineering Process Department, High Institute of Applied Sciences and Technology, Gabes University, Omar Ibn El Khattab Street, 6072, Gabès, Tunisia

    Mourad Magherbi

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  1. Mounir Bouabid
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  2. Naoufal Ghoudi
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  4. Mourad Magherbi
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Correspondence to Mounir Bouabid.

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Bouabid, M., Ghoudi, N., Bouabda, R. et al. Irreversibility Analysis for Double Diffusive Convection Flow of a Gas Mixture in a Chamfered Corners Square Enclosure Filled with a Porous Medium. Arab J Sci Eng 45, 7499–7510 (2020). https://doi.org/10.1007/s13369-020-04613-4

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  • DOI: https://doi.org/10.1007/s13369-020-04613-4

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