Heat transfer processes in two-phase material with spherical inclusions, absorbing penetrating radiation

Аuthors

Attetkov A. V.^*, Volkov I. K., Gaydaenko K. A.^**, Kotovich A. V.

Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

*e-mail: fn2@bmstu.ru
**e-mail: kseniyagaydaenko@gmail.com

Abstract

The article proposes mathematical model of the heat transfer process in the two-phase material with penetrating radiation absorbing inclusions in the sphere stratum form. The mathematical model being realized assumes thermal insulation of the spherical stratum external boundary and represents mixed problem for the system of two equations in the second order partial derivations of parabolic type in the presence of thermal source in the system. The article indicates the difficulties of principal character, occurring while analytical solution of the problem under consideration using integral Laplace transform along the temporal variable. To cope with these occurred difficulties by application of the general theory of integral transforms, finite integral transform over the spatial variable for the two-layer area was developed. The obtained results are employed for finding an analytically closed solution of the problem represented by the mathematical model of the heat transfer process being studied in the two-phase material transparent for radiation with absorbing inclusions in the form of the spherical stratum.

References

1. Assovsky I.G. Fizika goreniya i vnutrennyaya ballistika [Combustion physics and internal ballistics]. Moscow: Nauka, 2005. 357 p. In Russ.

2. Chernai A.V. O mekhanizme zazhiganiya kondensirovannykh vtorichnykh VV lazernym impul'som [On the mechanism of ignition of condensed secondary explosives by a laser pulse]. Fizika goreniya i vzryva – Physics of Combustion and Explosion, 1996, vol. 32, no. 1, pp. 11–19. In Russ.

3. Burkina R.S., Morozova E.Y., Tsipilev V.P. Initiation of a reactive material by a radiation beam absorbed by optical heterogeneities of the material. Combustion, Explosion, and Shock Waves, 2011, vol. 47, no. 5, pp. 581–590.

4. Kriger V.G., Kalenskii A.V., Zykov I.Y., Nikitin A.P., Zvekov A.A. Heat-transfer processes upon laser heating of inert-matrix-hosted inclusions. Thermophysics and Aeromechanics, 2013, vol. 20, no. 3, pp. 367–374.

5. Aduev B.P., Anan'eva M.V., Zvekov A.A., Kalenskii A.V., Kriger V.G., Nikitin A.P. Miro-hotspot model for the laser initiation of explosive decomposition of energetic materials with melting taken into account. Combustion, Explosion, and Shock Waves, 2014, vol. 50, no. 6, pp. 704–710.

6. Kalensky A.V., Zvekov A.A., Nikitin A.P. Mikrochagovaya model' s uchetom zavisimosti koeffitsienta effektivnosti pogloshheniya lazernogo impul'sa ot temperatury [Micro-focal model taking into account the dependence of the efficiency coefficient of a laser pulse absorption on temperature]. Khimicheskaya fizika – Chemical Physics, 2017, vol. 36, no. 4, pp. 43–49. In Russ.

7. Kalenskii A.V., Gazenaur N.V., Zvekov A.A., Nikitin A.P. Critical conditions of reaction initiation in the PETN during laser heating of light-absorbing nanoparticles. Combustion, Explosion, and Shock Waves, 2017, vol. 53, no. 2, pp. 219–228.

8. Attetkov A.V., Volkov I.K., Gaydaenko K.A. Temperaturnoe pole prozrachnogo dlya izlucheniya tverdogo tela s pogloshhayushhim sfericheskim vklyucheniem [Temperature field of transparent for radiation solid with absorbing spherical inclusion]. Teplovye protsessy v tekhnike – Thermal processes in engineering, 2018, vol. 10, no. 5–6, pp. 256–264. In Russ.

9. Lykov A.V. Teoriya Teploprovodnosti [Theory of heat conductivity]. Moscow: Vysshaya shkola, 1967. 600 p. In Russ.

10. Kartashov E.M. Analiticheskie Metody v Teorii Teploprovodnosti Tvyordyh Tel [Analytical methods in the theory of the thermal conductivity of solids]. M.: Vysshaya shkola, 2001. 552 p. In Russ.

11. Pudovkin M.А., Volkov I.K. Kraevye Zadachi Matematicheskoj Teorii Teploprovodnosti v Prilozhenii k Raschetam Temрeraturnykh Polej v Neftyanykh Plastakh pri Zavodnenii [Boundary-value problems of the mathematical theory of heat conduction in application to calculations of temperature fields in oil reservoirs in water flooding]. Kazan: Publishing house of Kazan University, 1978. 188 p. In Russ.

12. Attetkov A.V., Volkov I.K., Gaydaenko K.A. Protsessy teploperenosa v tverdom tele s pogloshhayushhim pronikayushhee izluchenie vklyucheniem v vide sharovogo sloya [Heat transfer processes in a solid with an inclusion, absorbing penetrating radiation, as a spherical layer]. Teplovye protsessy v tekhnike – Thermal processes in engineering, 2020, vol. 12, no. 1, pp. 18–24. In Russ. DOI 10.34759/tpt-2020-12-1-18-24

13. Attetkov A.V., Volkov I.K., Gaydaenko K.A. Аvtomodel'nye protsessy teploperenosa v prozrachnom dlya izlucheniya tverdom tele s pogloshhayushhim vklyucheniem v vide sharovogo sloya [Self-similar heat transfer processes in a transparent for radiation solid body with absorbing inclusion in the form of a spherical layer]. Teplovye protsessy v tekhnike – Thermal processes in engineering, 2020, vol. 12, no. 5, pp. 219–224. In Russ. DOI: 10.34759/tpt-2020-12-5-219-224

14. Nigmatulin R.I. Dinamika mnogofaznykh sred. V 2-kh ch. [Dynamics of multiphase media. In 2 parts]. Moscow: Nauka, 1987. 464 p. (part I), 359 p. (hart II). In Russ.

15. Koshlyakov N.S., Gliner E.B., Smirnov M.M. Uravneniya v Chastnykh Proizvodnykh Matematicheskoj Fiziki [Partial differential equations of mathematical physics]. Moscow: Vysshaya shkola, 1970. 712 p. In Russ

16. Volkov I.K., Kanatnikov A.N. Integral'nye Preobrazovaniya i Operatsionnoe Ischislenie [Integral transformations and operational calculus]. Moscow: Publishing house Bauman, 2015. 228 p. In Russ.

17. El'sgol'c L.E. Differencial'nye Uravneniya i Variacionnoe Ischislenie [Differential equations and calculus of variations]. Moscow: Nauka, 1969. 424 p. In Russ.