The Effects of Heat Transfer on Laminar-Boundary-Layer Separation in Supersonic Flow

Abstract

Summary By generalising earlier work, an approximate method is derived for calculating compressible laminar boundary layers with an unfavourable pressure gradient, with the wall temperature and Prandtl number arbitrary and some allowance made for the viscosity-temperature law. The method merely requires two quadratures and uses tables of universal functions. On the basis of this method it is suggested that when the wall is at uniform temperature the viscosity-temperature law should make little difference to the results, and that, when the wall temperature varies spatially by a factor of two, the use of a linear relationship may introduce errors of order 4 per cent in the momentum thickness. It is further suggested that the effects of Prandtl number differing from unity will increase as either the Mach number is increased or the wall is cooled. These general conclusions are borne out by detailed numerical calculations in a few selected cases.