Accurate solutions of the laminar-boundary-layer equations, for flows having a stagnation point and separation

Abstract

An accurate method of solution is developed for steady incompressible laminar boundary layers whose main-stream velocity U(x) is expressible as an odd polynomial in distance x measured along the wall. The velocity distribution within the boundary layer is expanded in a similar series, the coefficients of the first six terms being given as sums of multiples of known universal functions. The relatively small contribution of the subsequent terms is estimated by using an idea of Howarth, whereby the cdefficients of the seventh and subsequent terms are assumed to have the same dependence upon the distance normal to the wall as does the sixth term. With this approximation the equation for the non-dimensional skin-friction is reduced to a very simple first-order non-linear ordinary differential equation.