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Conduction-radiation effect on natural convection flow in fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

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Abstract

The combined effect of conduction-convection-radiation on natural convection flow of an optically thick Newtonian fluid with gray radiant properties, confined in a porous media square cavity with Darcy-Brinkman-Forchheimer drag is studied numerically. For a gray fluid, Rosseland diffusion approximation is considered. It is assumed that (i) the temperature of the left vertical wall varies linearly with height, (ii) the right vertical and top walls are at a lower temperature, and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the alternate direct implicit method together with the successive over relaxation technique. The investigation of the effect of governing parameters, namely, the Forschheimer resistance (Γ), the temperature difference (Δ), and the Plank number (Rd), on the flow pattern and heat transfer characteristics is carried out. It can be seen that the reduction of flow and heat transfer occur as the Forschheimer resistance is increased. On the other hand, both the flow strength and heat transfer increase as the temperature ratio Δ is increased.

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Abbreviations

a R :

the mean absorption coefficient

V :

velocity vector in two dimension

Da :

Darcy drag parameter

x,y :

dimensional Cartesian coordinates

F :

Forschheimer constant

X,Y :

dimensionless Cartesian coordinates

K :

permeability of the porous media

k :

thermal conductivity

k r :

radiative conductivity

g :

acceleration due to gravity

Pr :

Prandtl number

q w :

dimensionless heat transfer rate

q r :

radiative flux vector

Ra :

Rayleigh number for thermal diffusion

Rd :

Plank number

T :

temperature of the fluid in the boundary layer

T H :

temperature at the heated surface

T 0 :

temperature of the cold surface

U, V :

dimensionless fluid velocities in the X- and Y-directions, respectively

t :

time

c p :

Molar specific heat at constant pressure

u, v :

dimensional fluid velocities in the x- and y-directions, respectively

α :

thermal diffusivity

β :

coefficient of thermal expansion

Γ :

Forschheimer resistance

Δ :

temperature ratio

ρ :

density of the fluid

gv :

kinematic viscosity

σ :

Stefan-Boltzman constant

τ :

dimensionless time

ψ :

stream function

Ψ:

dimensionless stream function

ω :

vorticity function

θ :

dimensionless temperature

γ :

porosity parameter

Ω :

dimensionless vorticity function

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Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, 44000, Pakistan

    M. A. Hossain & M. Saleem

  2. School of Chemistry, Physics & Mechanical Engineering, Queensland University of Technology, Brisbane, 4000, Australia

    S. C. Saha

  3. Department of Mechanical Engineering, Shizuoka University, Hamamatsu, 422-8529, Japan

    A. Nakayama

Authors
  1. M. A. Hossain
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  2. M. Saleem
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  3. S. C. Saha
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  4. A. Nakayama
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Correspondence to M. A. Hossain.

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Hossain, M.A., Saleem, M., Saha, S.C. et al. Conduction-radiation effect on natural convection flow in fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls. Appl. Math. Mech.-Engl. Ed. 34, 687–702 (2013). https://doi.org/10.1007/s10483-013-1700-7

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  • DOI: https://doi.org/10.1007/s10483-013-1700-7

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