Temperature State of the Layer of Translucent Material with Depending on Temperature Thermal Conductivity and Absorption of Penetrating Radiation

The paper shows differential form of a mathematical model, describing steady-state process of thermal energy transfer in flat or circular/cylindrical layers under penetrating radiation. Thermal conductivity of semitransparent material for these layers depends on temperature, while the material has a property to absorb penetrating radiation with intensity, which nonlinearly increases with the temperature local value. Using the variational formulation of the nonlinear problem of stationary thermal conductivity, we transform the model's differrentional form to the variational form. The latter inlcudes the functional, whose stationary point's analysis makes it possible to set conditions, defining implementability of the stationary temperature state of the layer under study

References

[1] Eliseev V.N., Tovstonog V.A. Teploobmen i teplovye ispytaniya materialov i konstruktsiy aerokosmicheskoy tekhniki pri radiatsionnom nagreve [Heat transfer and heat testing of materials and aerospace structures with radiant heating]. Moscow, Bauman MSTU Publ., 2014. 396 p.

[2] Zarubin V.S. On working ability of a shell with spatial absorption of penetrating radiation. Trudy MVTU im. N.E. Baumana, 1974, no. 205, pp. 105–109.

[3] Frank-Kamenetskiy D.A. Diffuziya i teploperedacha v khimicheskoy kinetike [Diffusion and heat transfer in chemical kinetics]. Moscow, Nauka Publ., 1987. 502 p.

[4] Orlenko L.P., red. Fizika vzryva. V 2 t. T. 1 [Explosion physics. In 2 vols. Vol. 1]. Moscow, Fizmatlit Publ., 2002. 832 p.

[5] Siegel R., Howell J.R. Thermal radiation heat transfer. McGraw Hill, 1972. 814 p.

[6] Muchnik G.F., Rubashov I.B. Metody teorii teploobmena. Ch. 2. Teplovoe izluchenie [Methods of heat exchange theory. P. 2. Heat radiation]. Moscow, Vysshaya shkola Publ., 1974. 272 p.

[7] Prokhorov A.M., red. Fizicheskiy entsiklopedicheskiy slovar [Encyclopaedical dictionary on physics]. Moscow, Sovetskaya entsiklopediya Publ., 1983. 928 p.

[8] Zarubin V.S., Kuvyrkin G.N. Mathematical modeling of thermomechanical processes under intense thermal effect. High Temperature, 2003, vol. 41, no. 2, pp. 257–265. DOI: 10.1023/A:1023390021091 Available at: https://link.springer.com/article/10.1023%2FA%3A1023390021091

[9] Zarubin V.S., Stankevich I.V. Raschet teplonapryazhennykh konstruktsiy [Calculation of heat-stressed constructions]. Moscow, Mashinostroenie Publ., 2005. 352 p.

[10] Zarubin V.S. Modelirovanie [The modelling]. Moscow, Akademiya Publ. Center, 2013. 336 p.

[11] Eliseev V.N., Tovstonog V.A., Pavlova Ya.M. Thermal regime analysis of the shell of the powerful gas-discharge emitting source for structure thermal testing. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mechan. Eng.], 2015, no. 4, pp. 49–62 (in Russ.). DOI: 10.18698/0236-3941-2015-4-49-62

[12] Kask N.E., Radchenko V.V., Fedorov G.M., Chopornyak D.B. Temperature dependence of the absorption coefficient of optical glasses exposed to laser radiation. Soviet Journal of Quantum Electronics, 1979, vol. 9, no. 2, pp. 193–198. DOI: 10.1070/QE1979v009n02ABEH008731 Available at: http://iopscience.iop.org/article/10.1070/QE1979v009n02ABEH008731

[13] Zarubin V.S., Selivanov V.V. Variatsionnye i chislennye metody mekhaniki sploshnoy sredy [Variational and numerical methods of solid mechanics]. Moscow, Bauman MSTU Publ., 1993. 360 p.

[14] Zarubin V.S. Inzhenernye metody resheniya zadach teploprovodnosti [Engineering methods for solving heat conduction problems]. Moscow, Energoatomizdat Publ., 1983. 328 p.

[15] Vlasova E.A., Zarubin V.S., Kuvyrkin G.N. Priblizhennye metody matematicheskoy fiziki [Approximate methods of mathematical physics]. Moscow, Bauman MSTU Publ., 2001. 700 p.

[16] Vanko V.I., Ermoshina O.V., Kuvyrkin G.N. Variatsionnoe ischislenie i optimalnoe upravlenie [Variational calculus and optimum control]. Moscow, Bauman MSTU Publ., 2006. 488 p.

[17] Zarubin V.S., Ivanova E.E., Kuvyrkin G.N. Integralnoe ischislenie funktsiy odnogo peremennogo [Integral calculus of one-variable function]. Moscow, Bauman MSTU Publ., 2006. 528 c.

[18] Attetkov A.V., Zarubin V.S., Kanatnikov A.N. Vvedenie v metody optimizatsii [Introduction to optimisation methods]. Moscow, INFRA-M Publ., 2008. 272 p.

[19] Attetkov A.V., Zarubin V.S., Kanatnikov A.N. Metody optimizatsii [Optimisation methods]. Moscow, INFRA-M Publ., 2012. 270 p.

[20] Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel [Analitycal methods in heat conduction theory of solid bodies]. Moscow, Vysshaya shkola Publ., 2001. 550 p.