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Extremal problems of heat transfer to three-dimensional bodies at hypersonic speeds. (English. Russian original) Zbl 0787.76070

J. Appl. Math. Mech. 56, No. 4, 545-558 (1992); translation from Prikl. Mat. Mekh. 56, No. 4, 643-657 (1992).
The design of shuttle-like hypersonic spacecraft gives rise to the problem of investigating the spatial configurations that are optimum from the point of view of thermal heating and other characteristics, which enable the weight of the required thermal protection to be reduced. The problem of optimizing the weight of thermal protection depends on many parameters and has not yet been solved in a rigorous mathematical formulation. A brief review is given of research which has been done to determine the convective and radiation heating of three-dimensional bodies and the fundamental formulae for the wave drag, the friction drag, and the convective and radiation fluxes to three-dimensional bodies moving in dense layers of planetary atmospheres are presented. The formulae depend explicitly on the conditions of entry into the atmosphere of the planet and on the geometry of the body, which enables variational problems to be formulated on determining the three-dimensional shape of the body from the conditions for minimum overall heating (convective and radiation) of the surface along the trajectory of motion.

MSC:

76M30 Variational methods applied to problems in fluid mechanics
76K05 Hypersonic flows
80A20 Heat and mass transfer, heat flow (MSC2010)
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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