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Effects of thermal dispersion and stratification on combined convection on a vertical surface embedded in a porous medium

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Abstract

The effects of thermal dispersion and thermal stratification on mixed convection about a vertical surface in a porous medium are studied. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The resulting equations are solved on the basis of the local similarity approximation. The results indicate that both dispersion and stratification effects have considerable influence on the heat transfer rate.

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Abbreviations

B :

buoyancy parameter

d :

particle diameter (m)

f :

dimensionless stream function

g :

acceleration due to gravity (m/s2)

K :

permeability of the porous medium (m2)

k :

thermal conductivity (W/mK)

Nu:

local Nusselt number

q w :

heat flux at the surface (W/m2)

Pe:

local Péclet number

S :

Stratification parameter (Tt8 − T0)/(Tw − T0)

T :

temperature (K)

Ra:

local Rayleigh number

u, v :

velocity components in x and y directions (m/s)

x, y :

coordinates parallel and normal to the plate (m)

α:

equivalent thermal diffusivity (m2/s)

β:

coefficient of thermal expansion (1/K)

η:

dimensionless similarity variable

θ:

dimensionless temperature

ρ:

density of the fluid (Kg/m3)

μ:

dynamic viscosity (Ns/m2)

v:

kinematic viscosity of the convective fluid (m2/s)

Ψ:

stream function

λ:

wall temperature exponent

γ:

dispersion coefficient

∞:

condition at infinity

s :

saturated porous medium

w :

wall conditions

0:

reference conditions

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Author information

Authors and Affiliations

  1. Department Mechanical Engineering, Cleveland State University, 44115, Cleveland, OH, USA

    Rama Subba Reddy Gorla

  2. Department of Mathematics, Assiut University, Assiut, Egypt

    A. Y. Bakier

  3. FIBE Loads and Criteria Section, 45433-7552, Wright Patterson Air Force Base, OH, USA

    L. Byrd

Authors
  1. Rama Subba Reddy Gorla
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  2. A. Y. Bakier
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  3. L. Byrd
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Gorla, R.S.R., Bakier, A.Y. & Byrd, L. Effects of thermal dispersion and stratification on combined convection on a vertical surface embedded in a porous medium. Transp Porous Med 25, 275–282 (1996). https://doi.org/10.1007/BF00140984

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  • DOI: https://doi.org/10.1007/BF00140984

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