Natural Convection from a Permeable Sphere Embedded in a Variable Porosity Porous Medium Due to Thermal Dispersion

• Main Authors: S. M. M. El-Kabeir, M. A. El-Hakiem, A. M. Rashad
• Format: Article
• Language: English
• Published: Vilnius University Press 2007-07-01
• Series: Nonlinear Analysis
• Subjects: porous medium; natural convection; non-Darcy; Forchheimer number; thermal dispersion; sphere
• Online Access: http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/14693

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.