An approximate solution of the compressible laminar boundary layer on a flat plate

Abstract

Following a major assumption that enthalpy and velocity are dependent only on local conditions, an enthalpy-velocity relation ... is obtained for the laminar boundary layer on a flat plate where subscripts p refer to the plate, 1 to the free stream and e to the equilibrium temperature condition at the plate. When compared with general results, this relation (exact for Prandtl number a = 1) gives a close approximation to Crocco's numerical results for a = 0.725 and 1.25, up to u/us = 0.8. Using the above relation in conjunction with the approximate viscosity-temperature relation suggested by Chapman and Rubesin, and with Young's suggested first approximation for shearing stress it is shown that close approximations to displacement thickness and velocity distribution are given by ... These have the advantage of being algebraic in form whereas previous results have involved complex numerical integrations for individual cases.