Nearly parallel Blasius flow with slip

The steady boundary layer flow past a moving horizontal flat plate with a slip effect at the plate in a free stream with constant speed, slightly different from the plate speed is studied. An analytic perturbation solution of order two is obtained for the velocity. With respect to the parallel flow both the boundary layer and the inverted boundary layer characters of the flow are plotted and discussed. It is observed that under high slip, the flow becomes a nearly parallel flow with an increased speed.