Magnetohydrodynamic convection flow from a sphere to a non-Darcian porous medium with heat generation or absorption effects: network simulation

The magnetohydrodynamic free convection from a sphere embedded in an electrically-conducting fluid-saturated porous regime with heat generation is examined theoretically and numerically in this paper. A viscous flow model is presented using boundary-layer theory comprising the momentum and heat conservation equations. These coupled non-linear partial differential equations are transformed using appropriate variables to render the problem dimensionless. In the limit of infinite permeability (i.e. infinite Darcy number), the model is shown to reduce to that considered in an earlier study by Molla et al. (2005). Numerical solutions for the non-similar equations are obtained using the Network Simulation Method (NSM). Computations are compared with the earlier studies by Huang and Chen (1987), Molla et al. (2005) and Nazar et al. (2007) and found to be in excellent agreement. Specifically we investigate here in detail the influence of Darcy number (Da), Forchheimer number (Fs), hydromagnetic number (Nm), heat generation parameter (Q) and Grashof number (Gr) on the temperature and velocity fields and derivative functions. An increase in Darcy number accelerates the flow (i.e. increases velocity) but reduces temperature in the fluid. Increasing magnetic field (Nm) causes a reduction in velocity but enhances temperature. With heat generation (H>0), i.e. a heat source, velocity and temperature are increased with the converse behaviour computed for heat absorption, i.e. heat sink (H<0). An increase in inertial porous drag parameter, Fs, causes a decrease in velocity and also surface shear stress. Increasing free convection parameter, Gr, decreases velocity and also surface temperature gradient. The present model finds applications in energy systems and magnetic materials processing.