Gas-dynamic and heat transfer mathematical model of supersonic flow over flying vehicles is developed. The model is taken into account with medium compressibility and dissipative effects leading to an increase of heating rate. Proposed model is based on physical interaction of shock wave and boundary layer. Three dimensional numerical models of flying vehicles in gas-dynamic states are developed in order to investigate different configurations concerning such systems as case - sharp swept fin, case - perpendicular cylinder, case - gas jet, case - sharp unswept fin.
Using the experimental and theoretical approach both heat transfer and gas-dynamics of two complex vortex and swirling flows have been studied in details. New regularities regarding the local and average heat transfer have been established in the cylindrical channel with initial tangentially-inclined flow swirl at the stationary conditions, as well as in the radial rotating channel. The new similarity correlations have been obtained for the different boundary conditions arranged at the channel exit.