Natural Convection from a Permeable Sphere Embedded in a Variable Porosity Porous Medium Due to Thermal Dispersion - El-Kabeir, S. M. M. M. M.; El-Hakiem, M. A. A.; Rashad, A. M. M. (Nonlinear Analysis: Modelling and Control, 2007)
The laminar natural convection boundary-layer flow of an electricallyconducting fluid from a permeable sphere embedded in a porous medium with variable porosity is considered. The non-Darcy effects including convective, boundary, inertial and thermal dispersion effects are included 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 nondimensionalized and transformed into a nonsimilar form and then solved numerically by using the secondlevel 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 the physical parameters is conducted and a representative set of numerical results for the velocity and temperature profiles as well as the local skin-friction coefficient and the Nusselt number are illustrated graphically to show interesting features of Darcy number, inertia coefficient, the magnetic parameter, dimensionless coordinate, dispersion parameter, the Prantdl number and suction/blowing parameter.
Keywords: porous medium; natural convection; non-Darcy; Forchheimer number; thermal dispersion; sphere