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Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

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Abstract

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.

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Abbreviations

b,c:

empirical constants

C :

inertia co-efficient

C p :

fluid heat capacity

C f :

local skin-friction co-efficient

d :

particle diameter

F :

reduced stream function

g :

acceleration due to gravity

Gr :

Grashof number g β(T w −T ∞)L 3/ν 2

k e :

porous medium effective thermal conductivity

k f :

fluid thermal conductivity

k s :

thermal conductivity of the porous medium

K :

porous medium permeability

L :

characteristic plate length

Nu x :

local Nusselt number

Q 0 :

dimensional heat generation or absorption coefficient

P r :

Prandtl number μ C p /k f

r k :

ratio of k e and k f

Re :

flow Reynolds number ρ U ∞ L/μ

Re w :

Reynolds number based on the particle diameter, ρ U ∞ d/μ

Re x :

local Reynolds number

N r :

thermal radiation parameter

q r :

radiative heat flux

k * :

mean absorption co-efficient

T :

fluid temperature

T w :

wall temperature

T ∞ :

free-stream temperature

Da :

Darcy’s number

u :

x component of fluid velocity

v :

y component of fluid velocity

U ∞ :

free-stream velocity

x :

vertical or tangential distance

y :

normal distance

β :

coefficient of thermal expansion

δ :

heat-generation or absorption coefficient

η :

transformed normal coordinate

ψ :

stream function

σ * :

Stefan-Boltzmann constant

ε :

porous medium porosity

ε 0 :

free-stream porosity

μ :

fluid dynamic viscosity

ν :

fluid kinematic viscosity, μ/ρ

ξ :

transformed tangential coordinate

ρ :

fluid density

θ :

dimensionless temperature, (T−T ∞)/(T w −T ∞)

λ :

assisting λ=1 or opposing λ=−1 flow constant

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Authors and Affiliations

  1. Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan, 731 235, West Bengal, India

    Dulal Pal

  2. Department of Mathematics, Bengal Institute of Technology and Management, Santiniketan, 731236, West Bengal, India

    Hiranmoy Mondal

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  1. Dulal Pal
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  2. Hiranmoy Mondal
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Correspondence to Dulal Pal.

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Pal, D., Mondal, H. Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity. Meccanica 44, 133–144 (2009). https://doi.org/10.1007/s11012-008-9156-0

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  • DOI: https://doi.org/10.1007/s11012-008-9156-0

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