Approximate solution of the unsteady boundary layer equation

Abstract

An investigation on the approximate solutions of the unsteady boundary layer equations have been made here by using an approximate integral method proposed by Bianchini at al. Based on this method, similarity solutions due to different boundary layer models are obtained. For this PUrpose, the potential flow of the basic twodimensional equations governing the unsteady incompressible laminar boundary layer flow is, in general, taken to be a function of time . 't r and the longitudinal distance 'x' of the flow. The basic 90verning equations arB then made similar by introducing a similarity variable with a scale function taken to be a function of time r t' and 'x'. The introduction of this scale function thus reduce the basic tWo-dimensional non-linear partial differential equations to a simple ordinary differential equation. Based on this differential equation, closed form solutions for different unsteady cases and the corresponding steady cases are obtained. These solutions are presented in the form of velocity profiles. Some of these results show fairly well agreement with known solutions. In both the unsteady and steady cases mentioned (i ) above, skin-friction Co-efficlents correspondig to ,the velocity distributions are also obtained and Compared with known results. In particular, flate plate boundary layer solutions both for Unsteady and steady cases show very good agreement with the results showed by Rosenhead and Blasius respectively.