An analysis has been carried out to determine the local and overall heat-transfer rates, the adiabatic wall temperature, and the forces exerted when a high-speed, free-molecule flow is incident on a concave cylindrical surface. The flow may impinge on the surface at an arbitrary angle of attack. Additionally, the thermal accommodation coefficient may be arbitrary, and the degree of concavity of the surface may be varied at will from a semicircular cross section to a relatively flat circular arc. The concavity causes molecules to interreflect back and forth between surface elements. Even with the interreflections, the heat-transfer rate continues to depend linearly on the difference between the wall temperature and the adiabatic wall temperature. The interreflections are found to have a greater effect on both the heat transfer and the force results as the accommodation co-efficient decreases and as the degree of concavity and the angle of attack increase.
Discussion: “Heat Transfer and Forces for Free-Molecule Flow on a Concave Cylindrical Surface” (Sparrow, E. M., Jonsson, V. K., Lundgren, T. S., and Chen, T. S., 1964, ASME J. Heat Transfer, 86, pp. 1–9)
