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Natural convection from a permeable sphere embedded in a variable porosity porous medium due to thermal dispersion. (English) Zbl 1237.76186

Summary: We consider the laminar natural convection boundary-layer flow of an electrically-conducting fluid from a permeable sphere embedded in a porous medium with variable porosity. The non-Darcy effects including convective, boundary, inertial and thermal dispersion effects are involved in this analysis. The sphere surface is maintained at a constant heat flux and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are non-dimensionalized and transformed into a nonsimilar form, and then are solved numerically by using the second-level local non-similarity method that is used to convert the non-similar equations into a system of ordinary differential equations. Comparisons with previously published work are performed, and excellent agreement is obtained. A parametric study of physical parameters is conducted, and a representative set of numerical results for velocity and temperature profiles as well as local skin-friction coefficient and the Nusselt number are graphically to show features of Darcy number, inertia coefficient, t to magnetic parameter, dimensionless coordinate, dispersion parameter, the Prantdl number and suction/blowing parameter.

MSC:

76R10 Free convection
76S05 Flows in porous media; filtration; seepage
76W05 Magnetohydrodynamics and electrohydrodynamics
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
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