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In the analysis given herein, which was made at the NACA Lewis laboratory, the expression for eddy diffusivity given in reference 1 is modified in order to account for the effect of kinematic viscosity in reducing the turbulence in the region close to the wall. The effects of variable viscosity and of length-to-diameter ratio are also investigated.

A previous analysis of turbulent heat transfer and flow with variable fluid properties in smooth passages is extended to flow over a flat plate at high Mach numbers. Velocity and temperature distributions are calculated for a boundary layer in which the effects of both frictional heating and external heat transfer are appreciable. The viscosity and thermal conductivity are assumed to vary as a power of the temperature, while the Prandtl number and specific heat are taken as constant. Skin-friction and heat-transfer coefficients are calculated and compared with the incompressible values. The relation between boundary-layer thickness and distance along the plate is obtained for various Mach numbers. The analytical results are compared with representative experimental data.

An analysis is made to determine how the energy in a weak homogeneous turbulence with buoyancy and shear changes with time. It is shown that, although the turbulence ultimately decays when buoyancy is absent, the presence of buoyancy counteracts the decay, and the turbulent energy grows at large times.