Self-Similar Solution of Heat Transport Problems in Solid with Heat-Absorbing Coating Spherical Hot Spot
Authors: Attetkov A.V., Volkov I.K. | Published: 10.08.2016 |
Published in issue: #4(67)/2016 | |
DOI: 10.18698/1812-3368-2016-4-97-106 | |
Category: Physics | Chapter: Thermal Physics and Theoretical Heat Engineering | |
Keywords: isotropic solid, spherical hot spot, thermal thin heat-absorbing coating, temperature field, selfsimilar solution |
The problem of determining the temperature field of the isotropic solid with a spherical hot spot having a thermally thin heat-absorbing coating was considered. The non-stationary mode of heat transfer with time-varying heat transfer coefficient and the temperature of the hot spot was investigated. Sufficient conditions were determined, the fulfillment of which allows the realization of self-similar process of the heat transfer in the test system. Qualitative studies of the physical properties of the self-similar process and set of its specific features were conducted. The feasibility of boundary regimes in the spherical hot spot was theoretically proved.
References
[1] Carslaw H.S., Jaeger J.C. Conduction of heat in solids. London, Oxford University Press, 1959.
[2] Lykov A.V. Teoriya teploprovodnosti [The theory of heat conduction]. Moscow, Vyssh. shk. Publ., 1967. 600 p.
[3] Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel [Analytical methods in heat conduction of solid bodies]. Moscow, Vyssh. shk. Publ., 2001. 550 p.
[4] Pudovkin M.A., Volkov I.K. Kraevye zadachi matematicheskoy teorii teploprovodnosti v prilozhenii k raschetam temperaturnykh poley v neftyanykh plastakh pri zavodnenii [Boundary value problems of heat conduction mathematical theory applied to the calculations of temperature fields in the oil reservoirs at waterflooding]. Kazan’, Kazanskiy univ. Publ., 1978. 188 p.
[5] Kartashov E.M., Kudinov V.A. Analiticheskaya teoriya teploprovodnosti i prikladnoy termouprugosti [Analytical theory of heat conduction and thermoelasticity]. Moscow, URSS Publ., 2012. 653 p.
[6] Attetkov A.V., Volkov I.K., Pilyavskiy S.S. The hierarchy of mathematical models of heat transfer process in a solid with coated spherical hot spot. Tr. XVII Shkoly-seminara molodykh uchenykh i spetsialistov pod rukovodstvom akad. RAN A.I. Leont’eva [Proc. of the XVII School-Seminar of Young Scientists and Specialists under the leadership of RAS academician A.I. Leontyev]. Moscow, 2009, vol. 1, pp. 166-169 (in Russ.).
[7] Attetkov A.V., Volkov I.K., Pilyavskiy S.S. Temperature field of the isotrpic firm body with the spherical center of the warming up possessing covering. Izv. RAN. Energetika [Proceedings of the Russian Academy of Sciences. Power Engineering], 2010, no. 3, pp. 92-98 (in Russ.).
[8] Attetkov A.V. On the possibility of control action on the temperature field of a solid body with a spherical heating-up spot having a heat-absorbing coating. Teplovye protsessy v tekhnike [Thermal Processes in Engineering], 2012, vol. 4, no. 10, pp. 475-480 (in Russ.).
[9] Attetkov A.V., Volkov I.K. The singular integral transformations as a method of solution for one class of non-stationary heat conduction problems. Izv. RAN. Energetika [Proceedings of the Russian Academy of Sciences. Power Engineering], 2016, no. 1, pp. 148-156 (in Russ.).
[10] Attetkov A.V., Volkov I.K. "A refined model of concentrated capacity" of heat transfer in a solid with coated spherical hot spot. Teplovye protsessy v tekhnike [Thermal Processes in Engineering], 2016, vol. 8, no. 2, pp. 92-98 (in Russ.).
[11] Sedov L.I. Similarity and dimensional methods in mechanics. Tenth Ed. CRC Press, Inc., 1993. 496 p.
[12] Zel’dovich Ya.B., Rayzer Yu.P. Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavleniy [Physics of shock waves and high-temperature hydrodynamic phenomena]. Moscow, Nauka Publ., 1966. 686 p.
[13] Volosevich P.P., Levanov E.I. Avtomodel’nye resheniya zadach gazovoy dinamiki i teploperenosa [Self-similar solutions of problems of gas dynamics and heat thermal conductions]. Moscow, MFTI Publ., 1997. 240 p.
[14] Samarskiy A.A., Galaktionov V.A., Kurdyumov S.P., Mikhaylov A.P. Blow-up in quasi-linear parabolic equations. Berlin, Walter de Gruyter, 1995. 535 p.
[15] Ladyzhenskaya O.A., Solonnikov V.A., Ural’tseva N.N. Lineynye i kvazilineynye uravneniya parabolicheskogo tipa [Linear and quasi-linear equations of parabolic type]. Moscow, Nauka Publ., 1967. 736 p.
[16] Margolin A.D., Krupkin V.G. Bubble development in a liquid in the presence of a gas source. Combustion, Explosion, and Shock Waves, 1985, vol. 21, iss. 2, pp. 198-202.