Self-Similar Heat Transfer Processes in a Radiation-Transparent Solid Body Containing an Absorptive Inclusion with the System Featuring Phase Transitions

Authors: Attetkov A.V., Volkov I.K., Gaydaenko K.A. Published: 22.04.2019
Published in issue: #2(125)/2019  

DOI: 10.18698/0236-3941-2019-2-60-70

Category: Mechanical Engineering and Machine Science | Chapter: Technology and Equipment of Mechanical and Physical Processing  
Keywords: isotropic solid, laser radiation, spherical absorptive inclusion, phase transitions, temperature field, self-similar solution

The paper considers the problem of determining temperature field parameters in a radiation-trans-parent isotropic solid body containing an absorptive inclusion, when the system features phase transitions. We identify sufficient conditions, meeting which ensures the possibility of self-similar heat transfer process taking place in the system under con-sideration. We qualitatively investigated physical properties of the self-similar process under study and determined its specifics. We provide a theoretical validation of implementing a thermostating mode of the moving phase transition boundary in the heat transfer process investigated


[1] Assovskiy I.G. Fizika goreniya i vnutrennyaya ballistika [Combustion physics and interior ballistics]. Moscow, Nauka Publ., 2005.

[2] Chernay A.V. On the mechanism of ignition of condensed secondary explosives by a laser pulse. Combust. Explos. Shock Waves, 1996, vol. 32, no. 1, pp. 8–15. DOI: 10.1007/BF01992185

[3] Burkina R.S., Morozova E.Yu., Tsipilev V.P. Initiation of a reactive material by a radiation beam absorbed by optical heterogeneities of the material. Combust. Explos. Shock Waves, 2011, vol. 47, no. 5, pp. 581–590. DOI: 10.1134/S0010508211050121

[4] Kriger V.G., Kalenskiy A.V., Zvekov A.A., et al. Gas-jet method for deposition of metal nanoparticles into the fluorine-polymer matrix. Thermophys. Aeromech., 2013, vol. 20, no. 3, pp. 375–379. DOI: 10.1134/S0869864313030165

[5] Aduev B.P., Ananina M.V., Zvekov A.A., et al. Micro-hot-spot model for the laser initiation of explosive decomposition of energetic materials with melting taken into account. Combust. Explos. Shock Waves, 2014, vol. 50, no. 6, pp. 704–710. DOI: 10.1134/S0010508214060112

[6] Kalenskiy A.V., Zvekov A.A., Nikitin A.P. Micro-hot-spot model taking into account the temperature dependence of the laser pulse absorption efficiency factor. Russ. J. Phys. Chem. B, 2017, vol. 11, no. 2, pp. 282–287. DOI: 10.1134/S199079311702018X

[7] Pudovkin M.A., Volkov I.K. Kraevye zadachi matematicheskoy teorii teploprovodnosti v prilozhenii k raschetam temperaturnykh poley v neftyanykh plastakh pri zavodnenii [Boundary problems of thermal conduction theory applying to temperature field calculation in oil beds under water flood]. Kazan, Izd-vo Kazanskogo un-ta Publ., 1978.

[8] Attetkov A.V., Volkov I.K., Gaydaenko K.A. [Heat transfer processes in radiation-transparent solids with absorbing spherical inclusion]. Tr. 7 Ross. nats. konf. po teploobmenu. T. 3 [Proc. 7 Russ. conf. on heat exchange. Vol. 3]. Moscow, 2018, pp. 7–11 (in Russ.).

[9] Zeldovich 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.

[10] Samarskiy A.A., Galaktinov V.A., Kurdyumov S.P., et al. Rezhimy s obostreniem v zadachakh dlya kvazilineynykh parabolicheskikh uravneniy [Blow-up regimes in problems for quasilinear parabolic equations]. Moscow, Nauka Publ., 1987.

[11] Volosevich P.P., Levanov E.I. Avtomodelnye resheniya zadach gazovoy dinamiki i teploperenosa [Self-similar solutions of gas dynamics and heat transport problems]. Moscow, MIPT Publ., 1997.

[12] Attetkov A.V., Volkov I.K. On the possibility of the realization of thermostating mode of a spherical hot-spot boundary. Izv. RAN. Energetika [Proceedings of the Russian Academy of Sciences. Power Engineering], 2016, no. 3, pp. 141–147 (in Russ.).

[13] Attetkov A.V., Volkov I.K. Self-similar solution of heat transport problems in a solid with a spherical hot-spot having a thermally thin coating. Teplovye protsessy v tekhnike [Thermal Processes in Engineering], 2016, vol. 8, no. 7, pp. 297–300 (in Russ.).

[14] Attetkov A.V., Volkov I.K., Gaydaenko K.A. Self-similar solution of the problem of heat transfer in a solid with spherical hot-spot, which moving boundary has a firm coating. Teplovye protsessy v tekhnike [Thermal Processes in Engineering], 2017, vol. 9, no. 4, pp. 178–183 (in Russ.).

[15] Budak B.M., Fomin S.V. Kratnye integraly i ryady [Multiple integrals and rows]. Moscow, Nauka Publ., 1965.

[16] Attetkov A.V., Volkov I.K. Temperature field of domain with spherical source of heating. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2001, no. 1, pp. 42–50 (in Russ.).