Self-similar heat transfer processes in a transparent for radiation solid body with absorbing inclusion in the form of a spherical layer

Аuthors

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

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

In connection with theoretical and applied significance of studies of auto-model («self-similar») processes of heat transfer in solid bodies, problems of determination of non-stationary temperature field of isotropic solid body with absorption of penetrating radiation inclusion as a spherical shape layer have been formulated. The analysed mathematical model of the heat trans-fer process in the studied system is based on the hypothesis that absorbing inclusion is thermally thin, i.e. the implementation of the idea of «concentrated capacitance,» and is a mixed task for the equation in second-order partial derivatives of the parabolic type with a specific regional condition actually taking into account the presence of absorbing inclusion in the system. Suffi-cient conditions are identified, fulfilment of which provides possibility of implementation of self-similar process of heat transfer in analysed system. It is theoretically justified that the feasi-bility of the heat transfer process under study is directly related to the fulfilment of the condi-tions represented by the set of two equations. These conditions fully and unambiguously deter-mine the structure of the laser radiation flux, the realized mode of heat exchange in the analysed system and the law of temperature change of the medium filling the spherical cavity. In order to obtain meaningful information on properties of self-similar process of heat transfer, physical properties of studied process are qualitatively investigated and its specific features are estab-lished. It has been found that the implementation of the auto-model process of heat transfer pro-vides the possibility of thermostating the boundary of the spherical cavity, which has an inclu-sion absorbing penetrating radiation.

Keywords:

isotropic solid body, laser radiation, absorbing inclusion in the form of a spheri-cal layer, temperature field, self-similar solution.

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