An analytic, closed-form friction formula for turbulent, internal, compressible, fully developed flow was derived by extending the incompressible law-of-the-wall relation to compressible cases. The model is capable of analyzing heat transfer as a function of constant surface temperatures and surface roughness as well as analyzing adiabatic conditions. The formula reduces to Prandtl's law of friction for adiabatic, smooth, axisymmetric flow. In addition, the formula reduces to the Colebrook equation for incompressible, adiabatic, axisymmetric flow with various roughnesses. Comparisons with available experiments show that the model averages roughly 12.5 percent error for adiabatic flow and 18.5 percent error for flow involving heat transfer. Dechant, Lawrence J. and Tattar, Marc J. Unspecified Center NASA-CR-191185, E-8096, NAS 1.26:191185 NAS3-25266; RTOP 505-69-50...

The report concerns the calculation of coupled skin friction and heat transfer in compressible, turbulent, three-dimensional boundary layers. It presents an integral method of solution which assumes law-of-the-wall velocity and temperature correlations and results in three, coupled partial differential equations whose dependent variables are the dimensionless components of local skin friction and the dimensionless local heat transfer. The method allows for the specification of arbitrary distributions of free stream pressure, Mach number and wall temperature. The present theory is capable of handling problems of extreme complexity with moderate difficulty. (Modified author abstract).

The effects of the injection of a light, medium, and heavy gas on the skin friction and heat transfer characteristics of the laminar boundary layer flow over a flat plate were investigated. This was done by a numerical solution of the governing differential equations for injection rate parameters of -0, -0. 1, -0.2; Mach numers from 0 to 3; and wall-to-stream temperature ratios of 0.25, 0.50, and 1.00. The results show that the selection of discrete injection systems must represent a favorable compromise between conflicting factors (such as small molecular weight and large molecular diameters) which influence the amount of reduction in skin friction and heat transfer desired.

This Memorandum presents a simplified analysis of binary boundary-layer flow on a flat plate. A simple computational method previously used by Meksyn has been extended and applied to the present problem. Analytical formulas of skin friction, surface mass transfer, and heat trans fer are derived. The effects on skin friction of various parameters, such as P (Prandtl number), L (Lewis number), and molecular-weight ratio, and heat transfer in binary boundary layers are exhibited explicitly in these analytical formulas. The results agree well with more exact numerical calculations. In addition, some int coupling of viscosity, heat con duction, and diffusion is exhibited-for ex ample, coupling between recovery temperature and skin friction, and coupling between conduc tive heat transfer and diffusion effects. (Author).