Effects of slip on sheet-driven boundary layer flow revisited

Abstract

The study of laminar boundary layer flow over a stretching sheet has received considerable attention in the past due to its immense applications in the industries. There are adequate papers on Newtonian and non-Newtonian flows past a stretching sheet subject to conventional no-slip boundary conditions. Literature study reveals that more attention is required to see the effects of partial slip on the boundary layer flow over past a stretching sheet. The no-slip boundary condition (the assumption that a liquid adheres to a solid boundary) is one of the central tenets of the Navier-Stokes theory. Mathematically the no-slip condition is given by v_n = 0 and v_t = 0, where v_n and v_t are the normal and the tangential component of the velocity on the wall. In certain situations, however, the assumption of no-slip does no longer apply and should be replaced by a partial slip boundary condition. Navier [12] proposed a slip boundary condition wherein the amount of relative slip depends linearly on the local shear stress. In this work the steady laminar boundary layer flow over a stretching sheet is studied subject to partial slip boundary condition. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting non-linear partial differential equation into ordinary differential equation. The resulting highly nonlinear ODE with slip boundary condition is solved by using classical shooting method along with fourth order Runge-Kutta method. It is interesting to find the slip has a prominent effects on the velocity proles and on the skin friction coefficient. It is observer that with the increase in slip parameter boundary layer thickness decreases.