ON THE CALCULATION OF EDDY VISCOSITY AND OF HEAT TRANSFER IN A TURBULENT BOUNDARY LAYER ON A FLAT SURFACE

This paper describes a method of calculating the distribution of eddy viscosity and of rate of heat transfer in forced convection from a flat plate through a develop-ing, incompressible, turbulent boundary layer. It is necessary to know (a) the main stream velocity and plate temperature (both assumed to be independent of down-stream position), and (b) empirical formulae for the distribution of surface shearing stress, temperature in the laminar and transition sub-layers (involving the Prandtl number a), and mean velocity in the fully turbulent, transition, and laminar layers. A similarity law for the distribution of mean velocity in the fully turbulent layer is calculated from these empirical formulae, and is used in an integration of the boundary layer equations of mean flow. This enables the distribution of Reynolds shearing stress and of eddy viscosity to be calculated. The distribution of eddy heat diffusivity is then available, using Reynolds analogy, and the method of calculation developed recently by Davies and Bourne (1) is applied to evaluate rates of heat transfer in the case of air (a = 0-72). These calculated values are found to be in reasonable agreement with measured values given by Elias (4). Finally, it is suggested that this new method of calculation may be applicable in other important problems, involving convective heat transfer, where measured velocity profiles are available and eddy viscosity can be computed from the equations of mean flow. 1