An analytical skin friction and heat transfer model for compressible, turbulent, internal flows

An analytical skin friction model for compressible, turbulent, internal, fully developed flow involving adiabatic and non-adiabatic, smooth and rough flows has been developed by extending the incompressible law-of-the-wall relation to compressible cases. The formula recovers Prandtl's incompressible law of friction for pipes (within 2%) for incompressible flow. The model also shows good correlation with available data for compressible, adiabatic flows and flows involving cold wall heat transfer (within 15%). Comparison with hot wall data is only moderate (15–30%). Finally, using Reynold's analogy, the Stanton number and Nusselt numbers may be estimated.