Temperature field of a two-phase porous material with penetrating radiation absorbing inclusions in the form of ball layer

Аuthors

Attetkov A. V.^*, 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

To overcome the originated difficulties the work suggests the other option of the analytical solution to the problem under consideration. Applying the theory of general integral transformations, the finite integral transformation was developed over the spatial variable for the two-layer area, its core, eigenvalues spectrum and weight function were identified. The obtained results were employed to find analytically closed solution of the problem, represented by the mathematical model under study of heat transfer in the radiation transparent two-phase porous material with absorbing inclusions in the form of the ball layer.

The presented results demonstrate that while performing parametric analysis of the studied temperature field, significant technical difficulties stipulated by the complex nature of the dependence of the core and the eigenvalues spectrum of the developed integral transformation on the parameters of the original model may arise. It is advisable, in this regard, to develop hierarchy of simplified analogues, using the initial model as a basic one, with further determination of the range of possible application of each.

Keywords:

two-phase material, laser radiation, absorbing inclusions in the form of ball layer, temperature field, integral transformation

References

1. 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.

2. Aduev B.P., Anan’eva M.V., Zvekov A.A., Kalenskii A.V., Kriger V.G., Nikitin A.P. Micro-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.

3. 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.

4. 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.

5. 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 engineerin4g, 2020, vol. 12, no. 1, pp. 18–24. In Russ. DOI 10.34759/tpt-2020-12-1-18-2

6. 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.