Heat transfer processes in a solid with an inclusion, absorbing penetrating radiation, as 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

The article considers a problem concerning temperature field determining of an isotropic solid with an inclusion in the form of a spherical layer, absorbing penetrating radiation. The ana- lyzed mathematical model of the heat transfer process in the studied system is based on the hy- pothesis that the absorbing inclusion is thermally thin, i.e. on the «concentrated capacitance» idea realization. It represents a mixed problem for the second-order equation in partial deriva- tives of a parabolic type with the specific edge condition, accounting, in fact, for the presence of the absorbing inclusion in the system. Approximate analytical method, employing integral rep- resentation of the solution of the non-stationary heat transfer problem being considered, is pro- posed. This method is based on the solution representation as an expansion in a small determin- ing parameter of the mathematical model being realized with subsequent mixed integral Fourier transform application over the spatial variable to the sought functions finding. The obtained re- sults were applied to theoretical estimation of the effect of spherical layer width, absorbing pene- trating radiation, on the temperature field, being formed, of the object under study.

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