12. Mixed Convection Heat Transfer in MHD Non-Darcian Flow Due to an Exponential Stretching Sheet Embedded in a Porous Medium in Presence of Non-uniform Heat Source/Sink

A mathematical analysis has been carried out to describe mixed convection heat transfer in MHD non-Darcian flow due to an exponential stretching sheet embedded in a porous medium in presence of non-uniform heat source/sink. Approximate analytical similarity solutions of the highly non-linear momentum and energy equations are obtained. The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations and are solved very efficiently by using fifth order Runge–Kutta–Fehlberg method with shooting technique for various values of the governing parameters. The numerical solutions are obtained by considering an exponential dependent stretching velocity and prescribed boundary temperature on the flow directional coordinate. The computed results are compared with the previously published work on various special cases of the problem and are in good agreement with the earlier studies. The effect of various physical parameters, such as the Prandtl number, the Grashoff number, the Hartmann number, porous parameter, inertia coefficient and internal heat generation on flow and heat transfer characteristics are presented graphically to show some interesting aspects of the physical parameter.