Summary
The Forchheimer free convection heat and mass transfer near a vertical surface embedded in a fluid saturated porous medium has been analyzed. A similarity solution is presented for constant wall temperature and concentration distributions with specified power function form (Ax −1/2) of mass flux parameter. The effect of Grashof number (Gr), the buoyancy ratio (N), the Lewis number (Le) and the surface mass flux (f w ) on the nondimensional heat and mass transfer coefficients are presented.
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Abbreviations
- A :
-
real constant
- c :
-
inertial coefficient
- D :
-
concentration molecular diffusion
- f :
-
dimensionless stream function
- g :
-
gravitational acceleration in thex direction
- Gr:
-
the non-dimensional inertial parameter\(\frac{{c\sqrt K Kg\beta _T \theta _w }}{{v^2 }}\)
- K :
-
permeability
- k :
-
thermal conductivity
- Le:
-
Lewis number\(\frac{\alpha }{D}\)
- N :
-
Buoyancy ratio parameter\(\left( {\frac{{\beta _C \phi w}}{{\beta _T \theta w}}} \right)\)
- p :
-
pressure
- q :
-
local heat flux
- m :
-
local mass flux
- Ra x :
-
modified Rayleigh number\(\left( {\frac{{Kg\beta _T \theta _w x}}{{\alpha v}}} \right)\)
- T :
-
temperature
- C :
-
concentration
- u, v :
-
velocity components inx andy directions respectively
- x, y :
-
Cartesian coordinates
- α:
-
effective thermal diffusivity
- β T :
-
thermal expansion coeffcient
- β c :
-
concentration expansion coefficient
- θ:
-
dimensionless temperature variable
- ϕ:
-
dimensionless concentration variable
- η:
-
similarity parameter
- μ:
-
viscosity
- v :
-
kinematic viscosity
- θ:
-
dimensionless temperature
- ϱ:
-
fluid density
- ω:
-
evaluated at wall condition
- ∞:
-
evaluated at the outer edge of the boundary layer
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Murthy, P.V.S.N., Singh, P. Heat and mass transfer by natural convection in a non-Darcy porous medium. Acta Mechanica 138, 243–254 (1999). https://doi.org/10.1007/BF01291847
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DOI: https://doi.org/10.1007/BF01291847