﻿ Heat Transfer and Friction in a Thin Air Laminar Boundary Layer over Semi-Sphere Surface | HERALD OF THE BAUMAN MOSCOW STATE STATE TECHNICAL UNIVERSITY
|

# Heat Transfer and Friction in a Thin Air Laminar Boundary Layer over Semi-Sphere Surface

 Authors: Gorskiy V.V., Loktionova A.G. Published: 30.04.2020 Published in issue: #2(131)/2020 Category: Aviation and Rocket-Space Engineering | Chapter: Aerodynamics and Heat Transfer Processes in Aircrafts Keywords: convective heat transfer, friction, momentum thickness, boundary layer

A qualitative solution to the problem of calculating convective heat transfer can be obtained only by numerically integrating the differential equations of the boundary layer, which is associated with overcoming a number of computational problems. Consequently, it is important to develop relatively simple, but fairly high-precision calculation methods. As a first approximation to solving this problem, we can consider the use of the effective length method. From the practical point of view, this method is characterized by satisfactory accuracy of calculating convective heat transfer, which has led to its widespread use in aeronautical design engineering. However, this method is also characterized by a relatively high complexity, although it is much lower than that in numerical integration of the differential equations of the boundary layer. The most effective approach to solving heat transfer and friction problems in engineering practice is to use simple algebraic formulae obtained on the basis of approximating the results of rigorous numerical calculations, or experimental studies. Unfortunately, there is no information in literary sources about the accuracy of these formulae under various conditions of product functioning. This problem is solved on the basis of a systematic numerical calculation of the equations of the boundary layer in the most rigorous theoretical calculation, as well as a detailed analysis of the accuracy of the obtained algebraic formulae and their literary analogues

## References

[1] Hirschfelder J.O., Curtiss Ch.F., Bird R.B. Molecular theory of gases and liquids. New York, Wiley; London, Chapman and Hall, 1954.

[2] Predvoditelev A.S., ed. Tablitsy termodinamicheskikh funktsiy vozdukha [Tables of dynamical functions of the air]. Moscow, Vychislitelʼnyy tsentr AN SSSR Publ., 1962.

[3] Gorskiy V.V. Teoreticheskie osnovy rascheta ablyatsionnoy teplovoy zashchity [Theoretical fundamentals of ablative heat shield calculation]. Moscow, Nauchnyy mir Publ., 2015.

[4] Gorskiy V.V., Fedorov S.N. An approach to calculation of the viscosity of dissociated gas mixtures formed from oxygen, nitrogen, and carbon. J. Eng. Phys. Thermophy., 2007, vol. 80, no. 5, pp. 948--953. DOI: https://doi.org/10.1007/s10891-007-0126-5

[5] Aoki M. Introduction to optimization techniques. Fundamentals and applications of nonlinear programming. Los Angeles, Macmillan Co., 1971.

[6] Linnik Yu.V. Metod naimenʼshikh kvadratov i osnovy matematiko-statisticheskoy teorii obrabotki nablyudeniy [Least squares method and fundamentals of mathematic-statistic theory of observation results processing]. Moscow, Fizmatlit Publ., 1958.

[7] Zemlyanskiy B.A., ed. Rukovodstvo dlya konstruktorov. Konvektivnyy teploobmen izdeliy RKT [Designer guidebook. Convection heat transfer of rocket-space technique]. Korolev, TsNIImash Publ., 2010.

[8] Murzinov I.N. Laminar boundary layer on blunt bodies with account for vorticity of the external flow. Fluid Dyn., 1966, vol. 1, no. 6, pp. 80--83. DOI: https://doi.org/10.1007/BF01022286

[9] Avduevskiy V.S., Koshkin V.K. Osnovy teploperedachi v aviatsionnoy i raketno-kosmicheskoy tekhnike [Heat transfer fundamentals in aerotechnics and spacecraft]. Moscow, Mashinostroenie Publ., 1975.

[10] Zemlyanskiy B.A., ed. Konvektivnyy teploobmen letatelʼnykh apparatov [Convective heat transfer of the aircraft]. Moscow, Fizmatlit Publ., 2014.

[11] Paskonov V.M., Polezhaev Yu.V. Nestatsionarnoe plavlenie vyazkogo materiala v okrestnosti tochki tormozheniya. V: Chislennye metody v gazovoy dinamike [Nonstationary melting of viscous material in stagnation point neighborhood. In: Numerical methods in gas dynamics]. Moscow, Izd-vo Moskovskogo universiteta Publ., 1963, pp. 123--134.

[12] Narimanov G.S., Tikhonravov M.K. Osnovy teorii poleta kosmicheskikh apparatov [Fundamentals of spacecraft flight theory]. Moscow, Mashinostroenie Publ., 1972.

[13] Polezhaev Yu.V., Yurevich F.B. Teplovaya zashchita [Thermal protection]. Moscow, Energiya Publ., 1976.

[14] Anfimov N.A. Heat and mass transfer near the stagnation point with injection and suction of various gases through the body surface. Fluid Dyn., 1966, vol. 1, no. 1, pp. 14--20. DOI: https://doi.org/10.1007/BF01016262

[15] Devey C.F. Use of local similarity concepts in hypersonic viscous interaction problem. AIAA J., 1963, vol. 1, no. 1, pp. 171--179. DOI: https://doi.org/10.2514/3.1464

[16] Emmons H.W., Leigh D.C. Tabulation of the Blasius function with blowing and suction. Aerounaut. Rec-Council. Current Papers, 1954, no. 157.