Mathematical Models and Analysis of Temperature Regime in a Plate with a Foreign Thermocreative Element

Linear and nonlinear mathematical models of the heat conduction process for an isotropic plate with a foreign semi-through inclusion in which internal heat sources are uniformly concentrat-ed have been developed. For this purpose, the thermophysical parameters of the inhomogene-ous plate are described using asymmetric unit functions. As a result, linear and nonlinear heat conduction equations with discontinuous and singular coefficients have been obtained. A line-arizing function has been introduced to the nonlinear differential equation and boundary condi-tions and a quasi-linear boundary value problem has been obtained. For its complete lineariza-tion, the temperature has been approximated as a function of spatial coordinates on the inclu-sion surfaces and the plate boundary surface. This made it possible to obtain a linear boundary value problem with respect to the linearizing function. To solve the boundary value problems of thermal conductivity, the integral Fourier transform was used and analytical and analytical-numerical solutions were obtained in the form of improper convergent integrals. On this basis, an algorithm and software tools were developed that made it possible to obtain the temperature distribution in spatial coordinates and analyze the heat transfer processes in the given struc-ture