Equilibrium temperature of ballistic capsule blunt surface when returning to the earth at a parabolic velocity

Аuthors

Dornyak O. R.^*, Popov V. M.^*

Voronezh State University of Forestry and Technologies Named after G.F. Morozov, Voronezh, 394087, Russia

*e-mail: ordornyak@mail.ru

Abstract

The article considers options of thermal boundary conditions on the solids’ mating surfaces. Practical computations of temperature fields employ most frequently the ideal contact conditions. Specificity of real contact leads to temperature and thermal flow surges at the conditional boundary. The majority of studies of unideal thermal contact of both experimental and theoretical character consider only the temperature surge. The article studies the thermal flow surge impact on the temperature profiles formation in the junction of two diversified materials. The non-stationary one-dimensional conjugate problem for the steel 45-heat-insulating material, based on basalt fibers, contact pair was studied numerically. All thermophysical parameters are considered constant. The thermal flow surge is being determined by thermal resistance coefficients, which values differ by approximately an order of magnitude for the elements of the pair. Computations revealed that accounting for the temperature and thermal flow discontinuity at the conditional mating surface of the bodies subjected to the intensive thermal processing might drastically affect the temperature distribution specifics in contact pairs. Analytical problem solution in stationary setting, obtained in the presented article, was used for the numerical study results verification. This solution may be applied as well for the settled temperature surge prediction at the internal boundary in the contact pair. It was substantiated that this valued was directly proportional to the temperature difference of the heater and fridge, and inversely proportional to the sum of the Bio numbers for the joint elements.

Keywords:

contact heat exchange, boundary conditions of unideal contact, thermal resistance of a contact, mathematical modeling

References

1. Alifanov O.M., Cherepanov V.V. Identifikatsiya modelei i prognoz fizicheskikh svoistv vysokoporistykh teplozashchitnykh materialov. Inzhenerno-fizicheskii zhurnal, 2010, vol. 83, no. 4, pp. 770–782. https://doi.org/10.1007/s10891-010-0396-1
2. Lykov A.V. Teplomassoobmen: Spravochnik (Heat and mass transfer: Handbook). Moscow, Energiya, 1978. 480 p.
3. Boley B.A., Weiner I.H. Theory of thermal stresses. New York, Wiley, 1960. 586 p.
4. Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel (Analytical methods in the theory of thermal conductivity of solids). Moscow, Vysshaya shkola, 2001. 550 p.
5. Patankar S. Chislennoe reshenie zadach teploprovodnosti i konvektivnogo teploobmena pri techenii v kanalakh (Computation of Conduction and Duct Flow Heat Transfer. Innovative Research). Translated by Kalabin E.V., in Yan’kov G.G. (ed), Moscow, Izdatel’stvo MEI, 2003. 312 p.
6. Nigmatulin R.I. Osnovy mekhaniki geterogennykh sred (Fundamentals of mechanics of heterogeneous media), Moscow, Nauka, 1978. 336 p.
7. Karimbaev T.D., Rapilbekova N.S. K resheniyu zadachi upravleniya napravleniem teplovykh potokov v sploshnykh sredakh (To the solution of the problem of controlling the direction of heat flows in continuous media), Izvestiya Samarskogo nauchnogo tsentra Rossiiskoi akademii nauk. 2014, vol. 16, no. 6, pp. 263‒269.
8. Popov V.M. Teploobmen v zone kontakta raz’emnykh i neraz’emnykh soedinenii (Heat exchange in the contact zone of detachable and non-removable connections), Moscow, Energiya, 1971. 216 p.
9. Mesnyankin S.Yu., Vikulov A.G., Vikulov D.G. Sovremennyi vzglyad na problemy teplovogo kontaktirovaniya tverdykh tel. Uspekhi fizicheskikh nauk, 2009, vol. 179, no. 9, pp. 945‒970. DOI: 10.3367/Ufnr.0179.200909p.0945
10. Dornyak O.R., Popov V.M., Anashkina N.A. Matematicheskoe modelirovanie termicheskogo soprotivleniya v kontaktnykh parakh iz gomogennykh i geterogennykh materialov. Teplovye protsessy v tekhnike, 2019, vol. 11, no. 1, pp. 24‒33.
11. Dornyak O.R., Popov V.M., Anashkina N.A. Mathematical Modeling of Contact Thermal Resistance for Elasto-strained Solid Bodies by the Methods of Multiphase Systems Mechanics. Journal of Engineering Physics and Thermophysics, 2019, vol. 92, no. 5, pp. 1117‒1129. DOI: 10.1007/s10891-019-02027-0
12. Dornyak O.R., Popov V.M. Matematicheskoe modelirovanie vypryamleniya teplovogo potoka v kontaktnykh parakh. Teplovye protsessy v tekhnike, 2020, vol. 12, no. 8, pp. 364‒373. DOI: 10.34759/tpt-2020-12-8-364-373
13. Chumak, K.A, Martynyak, R.M. The Combined Thermal and Mechanical Effect of an Interstitial Gas on Thermal Rectification Between Periodically Grooved Surfaces. Frontiers in Mechanical Engineering, 2019, vol. 5. DOI: 10.3389/fmech.2019.00042
14. Murashov M.V., Panin S.D. Mikromekhanika materialov: protsessy na sherokhovatykh poverkhnostyakh. Teplovye protsessy v tekhnike, 2010, vol. 2, no. 4, pp. 164‒168.
15. Komkov M.A., Badanina Yu.V., Timofeev M.P. Razrabotka i issledovanie termostoikikh pokrytii truboprovodov iz korotkikh bazal’tovykh volokon. Inzhenernyi zhurnal: nauka i innovatsii, 2014, no. 2, pp. 7‒7. URL: http://eng-journal.ru/catalog/machin/hidden/1203.htm