Abstract
An analysis is presented to investigate the effect of radiation on mixed convection from a horizontal flat plate in a saturated porous medium. Both a hot surface facing upward and a cold surface facing downward are considered in the analysis. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary different equations. The important parameters of this problem are the radiation parameter R, the buoyancy parameter B, and the freestream to wall temperature ratio T ∞/T w for the case of a hot surface or the wall to freestream to wall temperature T w /T ∞ for the case of a cold surface.
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Abbreviations
- B :
-
Buoyancy parameter = (Ra x /Pe 3/2 x )
- c :
-
specific heat
- f :
-
dimensionless stream function defined by Equation (10)
- g :
-
acceleration due to gravity
- K :
-
permeability of the porous medium
- k t :
-
thermal conductivity of the saturated porous medium
- Nu:
-
local Nusselt number
- p :
-
pressure
- Pe x :
-
Péclet number (U ∞x /∝)
- q :
-
local heat flux
- q r :
-
radiative flux = −(4σ/3β *)(∂T 4/∂y)
- R :
-
radiation parameter = (4T 3 r σ/β * k t )
- Re x :
-
local Reynolds number = (U ∞x/v)
- Ra x :
-
local Rayleigh number
- T :
-
temperature
- u :
-
velocity in x direction
- v :
-
velocity in y direction
- U ∞ :
-
velocity in x direction outside the boundary layer
- x :
-
coordinate along the plate
- y :
-
coordinate normal to the plate
- α:
-
equivalent thermal diffusively
- β:
-
coefficient of thermal expansion
- β* :
-
extinction coefficient
- η:
-
dimensionless similarity variable defined in Equation (10)
- θ:
-
dimensionless temperature defined by Equation (10)
- σ:
-
Stefan-Boltzmann constant
- μ:
-
viscosity of convective fluid
- ν:
-
kinematic viscosity of the convective fluid
- ξ:
-
stream function
- ∞:
-
conditions at far away distance from the plate
- r :
-
reference conditions
- s :
-
saturated porous medium
References
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Bakier, A.Y., Reddy Gorla, R.S. Thermal radiation effect on mixed convection from horizontal surfaces in saturated porous media. Transp Porous Med 23, 357–363 (1996). https://doi.org/10.1007/BF00167104
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DOI: https://doi.org/10.1007/BF00167104