On the laminar similarity boundary layer equations

Abstract

The deduction of the boundary layer equations from Navier Stokes equations was one of the most important advances in fluid dynamics Using an order of magnitude analysis the well known governing Navier Stokes equations of viscous fluid flow can be greatly simplified within the boundary layer By making the boundary layer approximation, the flow is divided into an inviscid portion that is easier to be solved by a number of methods, and the boundary layer which is governed by a set of partial differential equations which are still non linear and not easily newlinesolvable except for a few precise flows newlineThe boundary layer equations are the set of non linear partial differential equations which are complicated for the close form solutions Therefore with the similarity techniques they are transformed to the set of ordinary differential equations which are still non linear The similarity technique essentially consists in converting the partial differential equations to ordinary differential equations newlineThe reduction of the system to a set of ordinary differential equations is achieved by way of transforming the dependent and independent variables to suitable non dimensional dependent and independent variables called the similarity variables with the aid of a transformation known as similarity transformation The conditions imposed on the coefficients of all terms in the equations obtained after the application of the transformation, in order to obtain ordinary differential equations are similarity conditions or the similarity requirements newline