Hyperbolic Models of Non-stationary Heat Conduction

Аuthors

Kartashov E. M.¹^*, Nenakhov E. V.²^**

1. MIREA — Russian Technological University (Lomonosov Institute of Fine Chemical Technologies), 78, Vernadsky prospect, Moscow, 119454, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: kartashov@mitht.ru
**e-mail: newnew94@mail.ru

Abstract

The article considers practically important problems of non-stationary thermal conductivity for hyperbolic translation models. An analytical approach based on contour integration of operational solutions of hyperbolic models, leading to the new integral relationships convenient for numerical experiments was developed. The equivalence of new functional constructions and known analytical solutions for this class of problems is demonstrated. Based on the obtained relations, the wave character of the non-stationary thermal conductivity was described with account for the finite velocity of heat propagation; the jumps at the front of the heat wave were calculated. The proposed approach gives effective results while studying the thermal reaction to heating or cooling of regions bounded from within by a flat surface, either a cylindrical cavity or a spherical surface.

Keywords:

nonstationary heat conductivity, finite rate of heat propagation, new forms of analytical solutions

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