Mathematical modeling of heating temperature mode for a heat exchange system of the type "pipe in pipe"

A mathematical model of heating of inhomogeneous medium "TEH-sand-air" was constructed and investigated as an initial-boundary value problem for the heat equation in polar coordinate system with boundary conditions that take into account the peculiarities of thermal processes at the boundaries of the inhomogeneous medium. A solution is given to the initial-boundary problem and an algorithm is proposed for calculating the thermal characteristics of the heating process and regular temperature conditions. The study is relevant for development of a computer virtual model of the heating process of an inhomogeneous medium in order to clearly demonstrate the heating process over a short period of time, as well as to calculate the corresponding thermal characteristics based on real experimental data.