, Volume 44, Issue 2, pp 133–144 | Cite as

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



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.


Convection Non-Darcy Thermal radiation Boundary layer flow Mechanics of fluids 



empirical constants


inertia co-efficient


fluid heat capacity


local skin-friction co-efficient


particle diameter


reduced stream function


acceleration due to gravity


Grashof number g β(T w T )L 3/ν 2


porous medium effective thermal conductivity


fluid thermal conductivity


thermal conductivity of the porous medium


porous medium permeability


characteristic plate length


local Nusselt number


dimensional heat generation or absorption coefficient


Prandtl number μ C p /k f


ratio of k e and k f


flow Reynolds number ρ U L/μ


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


local Reynolds number


thermal radiation parameter


radiative heat flux


mean absorption co-efficient


fluid temperature


wall temperature


free-stream temperature


Darcy’s number


x component of fluid velocity


y component of fluid velocity


free-stream velocity


vertical or tangential distance


normal distance

Greek symbols


coefficient of thermal expansion


heat-generation or absorption coefficient


transformed normal coordinate


stream function


Stefan-Boltzmann constant


porous medium porosity


free-stream porosity


fluid dynamic viscosity


fluid kinematic viscosity, μ/ρ


transformed tangential coordinate


fluid density


dimensionless temperature, (TT )/(T w T )


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


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Siksha BhavanaVisva-Bharati UniversitySantiniketanIndia
  2. 2.Department of MathematicsBengal Institute of Technology and ManagementSantiniketanIndia

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