An approximate mathematical model of the heat transfer processes in the laminar and turbulent boundary layers, which occur near the surface of an aircraft moving at the hypersonic speed in the Earth's atmosphere, is derived. This mathematical model makes it possible to calculate the convective heat transfer on the surface of typical structural elements of modern perspective aircrafts. 2D versions of the calculations of convective heat fluxes for bodies of simple geometric shapes are performed. (C) 2018 Elsevier Ltd. All rights reserved.