Effects of Magnetic Field and Heat Generation/Absorption on Natural Convection from an Isothermal Surface in a Stratified Environment†

The problem of steady, laminar, buoyancy-induced flow by natural convection along a vertical permeable surface immersed in a thermally-stratified environment in the presence of magnetic field and heat generation or absorption effects is studied numerically. Conditions for similarity solutions are determined for arbitrary stable and unstable thermal environment stratification. Numerical solution of the resulting similarity equations is performed using an implicit, iterative, tridiagonal finite-difference method. Comparisons with previously published work are performed and the results are found to be in excellent agreement. The effects of the Hartmann number, heat generation or absorption coefficient, ambient temperature power index, and the wall mass transfer parameter on the velocity and temperature profiles as well as the skin-friction coefficient and Nusselt number are presented in graphical form. It is found that both the magnetic field and heat absorption effects eliminate the occurrence of the fluid backflow and temperature deficit in the outer part of the boundary layer predicted for the non-magnetic case.