Thermal radiation effects on magnetohydrodynamic free convection heat and mass transfer from a sphere in a variable porosity regime

A mathematical model is presented for multiphysical transport of an optically-dense, electrically-conducting fluid along a permeable isothermal sphere embedded in a variable-porosity medium. A constant, static, magnetic field is applied transverse to the cylinder surface. The non-Darcy effects are simulated via second order Forchheimer drag force term in the momentum boundary layer equation. The surface of the sphere is maintained at a constant temperature and concentration and is permeable, i.e. transpiration into and from the boundary layer regime is possible. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. Increasing porosity (ε) is found to elevate velocities, i.e. accelerate the flow but decrease temperatures, i.e. cool the boundary layer regime. Increasing Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing both porosity and radiation parameters.