On some applications of the hyperbolic heat equation and the methods for solving it

  • Khankhasaev Vladislav N., hanhvladnick@mail.ru East-Siberian State University of Technology and Management, 40B, Building 1 Klyuchevskaya Street, Ulan-Ude, 670013 Russia
  • Darmakheev Erdeni V., erdenid.90@mail.ru East-Siberian State University of Technology and Management, 40B, Building 1 Klyuchevskaya Street, Ulan-Ude, 670013 Russia
Keywords: hyperbolic-parabolic equations, hyperbolic heat equation, alternating direction scheme, Navier-Stokes equations, heat balance

Abstract

Creation of new technological processes based on the use of high-intensity energy fluxes makes it necessary to take into account the final rate of heat propagation when determining the temperature state. This account can be realized with the help of the hyperbolic heat equation obtained by A. V. Lykov in the framework of nonequilibrium phenomenological thermodynamics as a consequence of the generalization of the Fourier law for flows and the heat balance equation. In the previous works by V. N. Khankhasaev, the process of switching off the electric arc in a spiral gas flow was simulated using this equation. In this paper, a mathematical model of this process is developed with the addition of a period of steady burning of the arc until the moment of disconnection and replacement of the strictly hyperbolic heat conduction equation by a hyperbolic-parabolic equation. For the resulting mixed heat conduction equation, a number of boundary value problems in the Fortran and Matcad software environments are correctly posed and numerically solved, obtaining temperature fields that are in good agreement with the available experimental data.

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How to Cite
Khankhasaev, V. and Darmakheev, E. ( ) “On some applications of the hyperbolic heat equation and the methods for solving it”, Mathematical notes of NEFU, 25(1), pp. 98-111. doi: https://doi.org/10.25587/SVFU.2018.1.12772.
Section
Mathematical Modeling