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Non-Darcy mixed convection in power-law fluids along a non-isothermal horizontal surface in a porous medium. (English) Zbl 1211.76116

Summary: The non-similar non-Darcy mixed convection from a horizontal surface in a porous medium saturated with a power-law type non-Newtonian fluid has been studied. Non-similarity solutions have been obtained for the case of a variable surface temperature of the form \(T_{w}(x)=T_{\infty }\pm Ax^{\lambda }\), \(\lambda \neq 1/2\). It has been found that for \(\lambda =1/2\), self-similar solution exists. A single mixed convection parameter has been used which covers the entire regime of mixed convection from pure forced convection to pure free convection limits. Both these limiting flows admit self-similar solutions. The partial differential equations governing the non-similar flow and the ordinary differential equations governing the self-similar flow have been solved numerically. The buoyancy force and the wall temperature have significant influence on the heat transfer and the velocity at the wall. For a fixed buoyancy force, the heat transfer and the velocity at the wall decrease with increasing non-Newtonian parameter, non-Darcy parameter and Peclet number.

MSC:

76S05 Flows in porous media; filtration; seepage
76R05 Forced convection
76R10 Free convection
76A05 Non-Newtonian fluids
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