Heat transfer in a liquid film over an unsteady stretching sheet

The effects of viscous dissipation, non-uniform heat source/sink, magnetic field, and thermal radiation on heat transfer characteristics of a thin liquid film flow over an unsteady stretching sheet are analyzed. A similarity transformation is used to reduce the governing time dependent momentum and energy equations into non-linear ordinary differential equations. The resulting differential equations with the appropriate boundary conditions are solved by an efficient shooting algorithm with fourth order Runge–Kutta technique. The effects of the physical parameters on the flow and heat transfer characteristics are presented through graphs and analyzed. The numerical results for the wall temperature gradient (Nusselt number) are calculated and presented through tables. Also, the effects of the physical parameters on the heat transfer characteristics are brought out: suggestions are made for efficient cooling. Furthermore, the limiting cases are obtained and are found to be in good agreement with the previously published results.