HEAT TRANSFER FROM A FLAT PLATE THROUGH A TURBULENT BOUNDARY LAYER

A similarity solution of the heat transfer equation, suggested by Townsend's recent experiments, is obtained for a turbulent boundary layer overlying a flat semi-infinite heated plate, provided that the temperature difference between the plate and the free stream is small, and an expression is derived describing the mean rate of heat transfer from a section of the plate. The application of this solution requires a knowledge of the observed mean velocity and turbulent shear stress profiles, and is based on the assumption that heat diffusivity is proportional to momentum diffusivity. The measurements made recently by Townsend of mean velocity and turbulent shear stress profiles in flow over a smooth plane wall enable the distribution of temperature in a turbulent boundary layer to be calculated. The theoretical results are compared with temperature measurements made by Elias over a heated flat plate, and the comparison indicates a value in the neighbourhood of 1–0 for the ratio of heat diffusivity to momentum diffusivity.