Abstract
A mathematical model is presented for analyzing the boundary layer forced convective flow and heat transfer of an incompressible fluid past a plate embedded in a Darcy-Forchheimer porous medium. Thermal radiation term is considered in the energy equation. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. It is noticed that the boundary layer decreases with an increase in the value of inertial parameter and in this case the temperature profile is found to decrease smoothly within the boundary layer. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter. The rate of heat transfer increases with the increasing values of Prandtl number. The effect of thermal radiation on temperature field is also analyzed.
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Abbreviations
- c p :
-
specific heat at constant pressure.
- F :
-
non-dimensional stream function.
- F′:
-
streamwise velocity.
- k :
-
Darcy permeability of the porous medium.
- k′:
-
Forchheimer resistance factor.
- k 1 :
-
parameter of the porous medium.
- k 2 :
-
inertial parameter.
- k ∗ :
-
absorption coefficient.
- N :
-
radiation parameter.
- Pr:
-
Prandtl number.
- q r :
-
radiative heat flux.
- S :
-
suction parameter.
- T :
-
temperature of the fluid.
- T w :
-
temperature of the wall of the surface.
- T ∞ :
-
free-stream temperature.
- u ∞ :
-
free stream velocity.
- υ w :
-
velocity of suction [υ w >0].
- η :
-
similarity variable.
- κ :
-
coefficient of thermal conductivity.
- μ :
-
dynamic viscosity.
- ν:
-
kinematic viscosity.
- ψ :
-
stream function.
- σ :
-
Stefan-Boltzman constant.
- ρ :
-
density of the fluid.
- θ :
-
non-dimensional temperature.
- θ r :
-
temperature ratio parameter.
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Mukhopadhyay, S., De, P.R., Bhattacharyya, K. et al. Forced convective flow and heat transfer over a porous plate in a Darcy-Forchheimer porous medium in presence of radiation. Meccanica 47, 153–161 (2012). https://doi.org/10.1007/s11012-011-9423-3
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DOI: https://doi.org/10.1007/s11012-011-9423-3