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ANALYTICAL SOLUTIONS OF HYPERBOLIC MODELS OF NON-STATIONARY HEAT CONDUCTION

https://doi.org/10.32362/2410-6593-2018-13-2-81-90

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Abstract

Practically important problems of non-stationary heat conduction for hyperbolic transport models are considered. An analytical approach based on contour integration of operational solutions of hyperbolic models is developed. This leads to new integral relationships convenient for numerical experiments. The equivalence of new functional constructions and known analytical solutions of this class of problems is shown. On the basis of the obtained relations, the wave character of the nonstationary thermal conductivity is described taking into account the finite velocity of heat propagation. The jumps at the front of the heat wave are calculated. The proposed approach gives effective results when studying the thermal reaction to heating or cooling regions bounded from within by a flat surface, either a cylindrical cavity or a spherical surface.

About the Author

E. M. Kartashov
Moscow Technological University (M.V. Lomonosov Institute of Fine Chemical Technologies)
Russian Federation

D.Sc. (Physics and Mathematics), Professor of the Chair of Higher and Applied Mathematics

86, Vernadskogo Prospect, Moscow, 119571, Russia



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For citation:


Kartashov E.M. ANALYTICAL SOLUTIONS OF HYPERBOLIC MODELS OF NON-STATIONARY HEAT CONDUCTION. Fine Chemical Technologies. 2018;13(2):81-90. (In Russ.) https://doi.org/10.32362/2410-6593-2018-13-2-81-90

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ISSN 2410-6593 (Print)
ISSN 2686-7575 (Online)