Unsteady MHD flow and heat transfer over a shrinking sheet with ohmic heating

The problem of unsteady magnetohydrodynamic (MHD) stagnation point flow over a stretching/shrinking sheet in a viscous fluid with viscous dissipation and ohmic heating is studied in this paper. The physical problem is modeled using a system of nonlinear partial differential equations and are then transformed into ordinary (similarity) differential equations using a proper transformation. These equations along with the corresponding boundary conditions are solved numerically using bvp4c in Matlab software. The solution is found to be dependent on the governing parameters including the magnetic field parameter, the Eckert number, unsteadiness parameter and the Prandtl number. The results illustrated include the velocity and temperature profiles, as well as local skin-friction coefficient and the local Nusselt number. It is found that dual (first and second) solutions exist only for the shrinking sheet case. It is also observed that the magnetic and unsteadiness parameters give prominent effects on the fluid flow and heat transfer. These two parameters cause a rise in the skin friction coefficient and the rate of heat transfer.