Heat generation/absorption effects on magnetohydrodynamic natural convection flow over a sphere in a non-Darcian porous medium

In this article, the magnetohydrodynamic natural convection boundary-layer flow on a sphere in a porous medium is studied numerically. The porous medium is saturated with an electrically conducting fluid and the fluid is subject to heat generation/absorption. A viscous flow model is presented using boundary-layer theory comprising the momentum and energy conservation equations. The governing boundary-layer equations are transformed into non-dimensional form using appropriate reference quantities. The resulting coupled non-linear system of partial differential equations is solved numerically using the differential quadrature method (DQM). The advantage of DQM, which was introduced as a promising method two decades ago, is that the solution is converged with a few grid points and hence the computational costs are reduced. Comparison is made between the results obtained by the DQM method and those obtained using the finite-difference method for the same operating conditions. A validation test is carried out for the case of infinite permeability (i.e. infinite Darcy number). The results of the present study were compared with the results of a similar investigation available in the literature. Close agreement between the two sets of results was noticed. A parametric study was performed in which the effect of various parameters on temperature and velocity fields, local Nusselt numbers, and wall friction coefficient were investigated.