Wave Heat Transfer in an Anisotropic Plate under Action of the Thermal Energy Point Source

Abstract

The paper presents mathematical model and method for analytical solution of the heat transfer problem in a thin anisotropic plate, which thermal conductivity tensor components depend on the temperature (nonlinear media) and exposed to action of the thermal energy point source. By selecting a chain of self-similar variables, the Cauchy problem for nonlinear heat transfer equation in the anisotropic plate was reduced to the nonlinear Cauchy problem for the ordinary differential equation. Its analytical solution showed the heat transfer wave nature, when the region with perturbed temperature distribution was bounded by the non-stationary moving ellipses. Discontinuities in thermal characteristics were observed at points of those ellipses, including temperature, temperature gradients, heat fluxes and temperature derivatives with respect to spatial variables of the second and third orders and above. It was established that temperature and non-linear heat fluxes were not disrupted in the nonlinear medium in the thermal wave plane fronts, where each point was moving in different directions and with different velocities, but temperature gradients and derivatives of the second, third orders and further were disruptive in space variables. The results obtained confirm conclusions that the wave heat transfer source is the medium nonlinearity, i.e., the heat transfer characteristics dependence on the temperature

The work was carried out with the state financial support of the Russian Foundation for Basic Research (RFBR project no. 22-21-00776)

Please cite this article in English as:

Formalev V.F., Garibyan B.A., Kolesnik S.A. Wave heat transfer in an anisotropic plate under action of the thermal energy point source. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2023, no. 5 (110), pp. 48--62 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2023-5-48-62

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