Blasius flow of a viscous fluid revisited

Abstract

The simplest example of the application of the boundary layer equations is afforded by the flow along a flat plate. Historically, this was the first example illustrating the application of Prandtl's boundary layer theory. The problem was discussed by Heinrich Blasius in his doctoral thesis at Gottingen. That is why the flow is widely known as the Blasius flow. Literature study reveals hardly any attention has been given to the effects of partial slip on the boundary layer flow over a flat plate. The no-slip boundary condition 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 proposed a slip boundary condition. wherein the amount of relative slip depends linearly on the local shear stress. The motivation behind our study is to see the effects of slip on the boundary layer flow of a viscous fluid past an infinite plate. The present investigation is not only important because of its technological significance but also in view of the interesting mathematical features presented by the equations governing the steady, laminar flow with slip boundary conditions. The partial slip is controlled by a dimensionless slip factor, which varies between zero and infinity. The resulting third order nonlinear similarity equation has been numerically integrated using shooting method, along with fourth order Runge-Kutta method. It is observed that the horizontal component of velocity increases with an increase in slip. Thus, the boundary layer thickness decreases with an increase in slip. It is interesting to observe that the skin friction coefficient decreases exponentially with an increase in slip