Heat transfer over an unsteady stretching surface with variable heat flux in the presence of a heat source or sink

Unsteady boundary layer flow of an incompressible fluid over a stretching surface in the presence of a heat source or sink is studied. The unsteadiness in the flow and temperature fields is caused by the time dependence of the stretching velocity and the surface heat flux. The nonlinear boundary layer equations are transformed to nonlinear ordinary differential equations containing the Prandtl number, heat source/sink parameter and unsteadiness parameter. These equations are solved numerically by applying a shooting technique using the Runge–Kutta method. Comparison of the numerical results is made with previously published results under special cases, and the results are found to be in good agreement. Effects of the Prandtl number, heat source/sink parameter and unsteadiness parameter on the flow and heat transfer are studied.