New Relations for Analytical Solution of the Local Non-Equilibrium Heat Transfer

Abstract

The paper develops generalized model representations of the locally non-equilibrium heat transfer in terms of the theory of non-stationary heat conduction for the hyperbolic type equations. The model simultaneously includes three coordinate systems: 1) Cartesian coordinates--a massive body bounded by a flat surface (one-dimensional case); 2) spherical coordinates--a massive body with an internal spherical cavity (central symmetry); 3) cylindrical coordinates--a massive body with an internal cylindrical cavity (radial heat flow). Three types of intensive heating (cooling) are considered: 1) temperature; 2) thermal; 3) media heating. Examples of locally non-equilibrium heat transfer of a wave nature are provided taking into account the finite speed of heat propagation. The wave character is expressed by the Heaviside step function in analytical solution to the basic problems for the partially bounded regions. Isochrones for the temperature functions were constructed. It is shown that the temperature profile is having discontinuity on the surface of the traveling wave front. This leads to a delay in the heat outflow beyond the discontinuity boundary, which is a characteristic feature in analytical solutions to the wave equations. Functional constructions of analytical solutions to basic problems of the locally non-equilibrium heat transfer are presented in a region with the moving boundary, it is a practically new case in analytical thermophysics. The presented material has wide practical application

Please cite this article in English as:

Kartashov E.M. New relations for analytical solution of the local non-equilibrium heat transfer. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2023, no. 6 (111), pp. 4--24 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2023-6-4-24

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