An analysis of second-order effects on laminar boundary-layer flow

Abstract

Treated in the present paper are the second-order effects, i.e. the effect of displacement thickness, longitudinal curvature, external shear and slip, on the two-dimensional laminar boundary-layer flow of incompressible fluid. The analysis is developed in terms of the stream-function co-ordinates proposed for the analysis of the rotational flow by the senior author previously. An inverse problem is set in the co-ordinates plane, and, within the framework of the second-order approximation, the problem is reduced to solving a parabolic partial differential equation for the total head. An implicit finite-difference scheme is then devised to solve the equation, and the practical computations are carried out for the flow along a flat plate or the one around a parabolic body, by making use of an electronic computer.