A. V. Zhiber, N. M. Tsirelman, “Determining temperature fields in a spatially inhomogeneous nonlinear medium”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 162,Pages <nobr>34

Determining temperature fields in a spatially inhomogeneous nonlinear medium

A. V. Zhiber^a, N. M. Tsirelman^b

^a Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa
^b Ufa State Aviation Technical University

Abstract: A method of determining temperature fields in a spatially inhomogeneous medium with temperature-dependent thermophysical properties of the material is shown. For this purpose, point and nonlocal transformations of the nonstationary heat conduction equation are used. Examples of applying the theory for various boundary conditions in the spherical symmetric case are given.

Keywords: inhomogeneity, nonlinearity, spherical symmetry, point and nonlocal transformations, hollow ball, boundary conditions.

UDC: 536.2:517.9

MSC: 35Q51, 37K60