Slip Effects on the Unsteady Stagnation Point Flow with Variable Free Stream

We perform a study for the boundary layer flow of viscous fluid about a stagnation point on an unsteady stretching sheet in the presence of variable free stream. Both the velocity and thermal slip conditions are taken into consideration. The stretching velocity and the surface temperature are time-dependent. In the solutions we adopt the homotopy analysis method (HAM). The analysis related to convergence of the solutions is explicitly discussed. The dependence of velocity and temperature profiles on various quantities is discussed by displaying graphs. Comparison of the present solution yields an excellent agreement with an exact solution in a limiting sense.