Abstract
Numerical analysis of the free convection coupled heat and mass transfer is presented for non-Newtonian power-law fluids with the yield stress flowing over a two-dimensional or axisymmetric body of an arbitrary shape in a fluid-saturated porous medium. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by the similarity transformation. The resulting system of equations is solved by a finite difference method. The parameters studied are the rheological constants, the buoyancy ratio, and the Lewis number. Representative velocity, temperature, and concentration profiles are presented and discussed. It is found that the results depend strongly on the values of the yield stress parameter and the power-law index of the non-Newtonian fluid.
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Abbreviations
- a :
-
constant, 0 ⩽ a < 1
- a 1 :
-
non-dimensional constant
- C :
-
concentration
- D :
-
effective mass diffusivity
- f :
-
similarity stream function
- g :
-
gravity
- h :
-
local heat transfer coefficient
- h m :
-
local mass transfer coefficient
- K :
-
permeability
- k e :
-
effective thermal conductivity
- Le :
-
Lewis number
- l :
-
reference length
- m :
-
constant
- m w :
-
local surface mass transfer rate
- n :
-
power index, n ⩾ 0
- Nu l :
-
local Nusselt number
- q w :
-
local surface heat transfer rate
- Ra m :
-
modified Rayleigh number
- r :
-
radial distance
- S :
-
variable of shape
- Sh l :
-
local Sherwood number
- T :
-
temperature
- u, ν :
-
Darcian velocity components in the x-and y-directions
- x, y :
-
Cartesian coordinates
- α 0 :
-
threshold gradient, a 1 τ 0 \( \sqrt K \)
- α e :
-
effective thermal diffusivity
- β T :
-
coefficient of thermal expansion
- β C :
-
coefficient of concentration expansion
- γ :
-
angle
- ζ :
-
dimensionless variable of body of shape
- η :
-
similarity variable
- θ :
-
dimensionless temperature
- ξ :
-
dimensionless variable
- ρ :
-
density of fluid
- τ 0 :
-
yield stress
- ϕ :
-
dimensionless concentration
- ψ :
-
stream function
- Ω :
-
dimensionless rheological parameter
- 0:
-
reference property
- e:
-
effective property
- w:
-
wall property
- l:
-
local property
- ∞:
-
ambient property of porous medium
- *:
-
dimensionless property
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Abdel-Gaied, S.M., Eid, M.R. Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media. Appl. Math. Mech.-Engl. Ed. 32, 179–188 (2011). https://doi.org/10.1007/s10483-011-1404-6
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DOI: https://doi.org/10.1007/s10483-011-1404-6