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Matematicheskoe modelirovanie, 1990, Volume 2, Number 6, Pages 40–54
(Mi mm2396)
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Mathematical models of phenomena and processes
A mathematical model of heat transmission in essentially nonlinear conjugate media
L. A. Uvarova, V. K. Fedyanin Joint Institute for Nuclear Research
Abstract:
Heat transmission in conjugate systems (cubes, cylinders, spheres) with travelling boundary line is investigated on the basis of the heat-conductivity nonlinear equation with a heat source obtained from the solution of an electrodynamic problem in a nonlinear medium whose dielectric penetrability depends on the field according to the law
$$
\varepsilon_i=\varepsilon_{0i}-|\alpha_i|E_i^2,\qquad i=1,2.
$$
The analysis carried out points out some nontrivial effects accompanying the heat transmission: the appearance of adiabatic surfaces, emergence of solition solutions and the conditions with sharpening in self-focusing media. All the considered effects are essentially defined by the values of $\alpha_i$ nonlinear parameters, nature of dependences of dielectric penetrabilities on the temperature,
and the character of movement of the boundary surface.
Received: 16.09.1989
Citation:
L. A. Uvarova, V. K. Fedyanin, “A mathematical model of heat transmission in essentially nonlinear conjugate media”, Matem. Mod., 2:6 (1990), 40–54
Linking options:
https://www.mathnet.ru/eng/mm2396 https://www.mathnet.ru/eng/mm/v2/i6/p40
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Abstract page: | 542 | Full-text PDF : | 187 | References: | 1 | First page: | 1 |
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