Forced Convection Near Laminar Separation

Abstract

SummaryThe singular behaviour of an incompressible boundary layer at separation has been well established by the works of Howarth (1938), Goldstein (1948), Stewartson (1958), Curie (1958) and Terrill (1960). Stewartson (1962) remarked that the existence of the singularity at separation can be regarded as fully established and understood. The skin friction vanishes like where x is the distance to separation, and the stream function close to the wall is described by a series of powers of , with coefficients that are functions of , where y measures distance normal to the wall. At some stages in the expansion of the stream function, terms in log x have to be included. The case of the compressible flow is less satisfactory. Stewartson (1962) was unable to establish singularity at separation and concluded that the general compressible boundary layer cannot have a singularity at separation unless there is no heat transfer from the wall. This has been contradicted by the works of Merkin (1968) and Buckmaster (1970). Curie (1958) also reported that the difficulty encountered in computing the temperature field right down to the point of separation might be due to the singularity there. In this paper, the Goldstein-Stewart son approach is applied to laminar boundary layer flow at low speeds in which density is sensibly constant and the Prandtl number σ is taken as unity. Singularity is established at separation for the temperature field. The heat transfer does not vanish at separation point and is of the form