The steady laminar incompressible boundary-layer problem as an integral equation in crocco variables: investigation of the similarity flows

Abstract

The steady flow incompressible laminar boundary-layer problem in two-dimensions is posed as an integral equation in Crocco variables in the most general case. Numerical investigations are then made of the 'similarity' flows. A transformation is utilised which weakens the singularity at the outer edge of the boundary layer and thereby gives improved numerical results over those obtained from the un-transformed equation. An extensive numerical comparison is made with Polhausen's exact analytical solution. Results are also presented in tabular and graphical form illustrating the approach of the boundary-layer characteristics cy, 61, 62, 63 to their asymptotic values for strong suction for a very wide range of similarity flows. These are in complete agreement with the results obtained by other investigators, and form an extension to the cases previously considered.