Paper Title
Slip Effects on The Stagnation Flow Over a Stretching/Shrinking Sheet

Abstract
In the present study, we consider a stagnation point flow over a stretching or shrinking sheet with slip effect at the boundary. The external flow and the stretching/shrinking velocities are assumed to vary linearly from the stagnation point. Different from the previous studies, we consider both stretching and shrinking cases, as well as the slip effect at the boundary. In certain situations, the assumption of the flow field obeys the conventional no-slip condition at the boundary does no longer apply and should be replaced by partial slip boundary condition. For example, in rarefied gases, there is a slip regime where the Navier�Stokes equation is valid but slip occurs. Some coated surfaces resist adhesion. The solid surface may be rough or porous such that equivalent slip is present. In these cases the no slip condition is replaced by Navier�s partial slip condition, where the slip velocity is proportional to the local shear stress. Compared to a stretching sheet, less work has been done on the flow over a shrinking sheet. The flow over a shrinking sheet is unlikely to exist unless adequate suction on the boundary is imposed since the vorticity of the shrinking sheet is not confined within a boundary layer. However, with an added stagnation flow to contain the vorticity, similarity solutions may exist. Thus, in the present study, we consider a stagnation flow, to confine the vorticity within the boundary layer. It is well known that the solutions for the flow over a shrinking sheet are not unique. As reported previously by many authors, there exist multiple solutions for a certain range of parameters. It is the aim of the present study to investigate, by a stability analysis, which solutions are stable and thus physically realizable. The governing partial differential equations are first transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c.