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Transport in Porous Media

, Volume 25, Issue 3, pp 275–282 | Cite as

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

  • Rama Subba Reddy Gorla
  • A. Y. Bakier
  • L. Byrd
Article

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.

Key words

combined convection porous media heat transfer thermal stratification thermal dispersion 

Nomenclature

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

qw

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)

Greek Symbols

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

Subscripts

condition at infinity

s

saturated porous medium

w

wall conditions

0

reference conditions

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References

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Rama Subba Reddy Gorla
    • 1
  • A. Y. Bakier
    • 2
  • L. Byrd
    • 3
  1. 1.Department Mechanical EngineeringCleveland State UniversityClevelandUSA
  2. 2.Department of MathematicsAssiut UniversityAssiutEgypt
  3. 3.FIBE Loads and Criteria SectionWright Patterson Air Force BaseUSA

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