Spherical aircraft elements are related to a number of their fragments influ-enced by the maximum heat fluxes. As a result calculating thermal and force loading of a hemisphere is of particular interest. This problem is one of the most acute within the extremely high Reynolds numbers that correspond to laminar-turbulent gas flow in a boundary layer over a hemisphere. At the same time, the fundamental monograph  on the aircraft convective heat exchange, which summarizes the results of many years of research on this problem, doesn’t pay proper attention to this issue. At the same time, the work  shows that using the approaches for a hemisphere outlined in the monograph  is associated with a number of significant errors within the range of extremely high Reynolds numbers. Calculating heat transfer and friction on the porous wall which correct solution has been missing by now is one of the least studied problems of laminar-turbulent heat exchange. The purpose of this article is to develop a highly accurate engineering method for calculating heat transfer and friction in a laminar-turbulent boundary layer on a hemisphere.
Горский В.В., Локтионова А.Г. Моделирование теплообмена и трения в тонком воздушном ламинарно-турбулентном пограничном слое над поверхностью полусферы. Математическое моделирование и численные методы, 2019, № 2, с. 51–67.