The Two-Parameter Integral Method for Unsteady Laminar Incompressible Boundary Layer over a Semi-Infinite Flat Plate

Abstract

This paper deals with an unsteady laminar incompressible boundary layer over a semi-infinite plate set in motion impulsively, in order to elucidate an unsteady boundary layer which develops over a flat plate inserted into a shock tube. Expressing the velocity profiles in the boundary layer by polynomials with two unknown parameters (a boundary layer thickness and a form parameter) and dividing the boundary layer into two regions, there are obtained two momentum integrals, which are reduced to simultaneous differential equations. And the solutions making a smooth transition from upstream (Blasius'solution) to downstream (Rayleigh's solution) are obtained.