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Horizontal boundary-layer natural convection in a porous medium saturated with a gas

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Abstract

Boundary-layer analysis is performed for free convection flow over a hot horizontal surface embedded in a porous medium saturated with a gas of variable properties. The variable gas properties are accounted for via the assumption that thermal conductivity and dynamic viscosity are proportional to temperature. A similarity solution is shown to exist for the case of constant surface temperature. Numerical results for the stream function, horizontal velocity, and temperature profiles within the boundary layer as well as for the mass of entrained gas, surface slip velocity, and heat transfer rate at different values of the wall-temperature parameter are presented. Asymptotic solutions for large heating are also available to support the numerical work.

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Abbreviations

C h :

heat transfer coefficient

C p :

specific heat

f(η) :

similarity stream function

F(ξ) :

similarity stream function (large Δ formulation)

g :

acceleration due to gravity

g(η) :

similarity temperature function

G(ξ) :

similarity temperature function (large Δ formulation)

k :

thermal conductivity

K :

permeability of the porous medium

L :

characteristic length of the plate

n j :

unit vector in the direction of gravitational force

p :

pressure

q :

heat transfer rate

Ra:

Modified Rayleigh number

u, v :

velocity components in x y directions

U, V :

boundary-layer velocity components in X Y directions

x y :

Cartesian coordinates

X, Y :

boundary-layer coordinates

Z :

Howarth—Dorodnitsyn coordinate

α :

thermal diffusivity

Δ:

heating or cooling parameter

ɛ :

small parameter

ɛ, ξ:

similarity variables

θ :

temperature

μ :

dynamic viscosity

ϱ :

density

ψ :

stream function

′ :

differentiation with respect to η or ξ.

o :

condition in the undisturbed state

W :

condition at the plate

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Authors and Affiliations

  1. Faculty of Mathematics, University of Cluj, Cluj, Romania

    Ioan Pop

  2. Department of Mechanical Engineering, Cleveland State University, 44115, Cleveland, OH, USA

    Rama Subba Reddy Gorla

Authors
  1. Ioan Pop
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  2. Rama Subba Reddy Gorla
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Pop, I., Reddy Gorla, R.S. Horizontal boundary-layer natural convection in a porous medium saturated with a gas. Transp Porous Med 6, 159–171 (1991). https://doi.org/10.1007/BF00179278

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  • DOI: https://doi.org/10.1007/BF00179278

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