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One of the possible variants of the approximate solution of nonlinear thermal conductivity problems

Abstract

One of the possible variants of the approximate solution of nonlinear thermal conductivity problems

Ivanov V.V., Karaseva L.V.

Incoming article date: 03.04.2019

An approximate method for calculating the temperature field in solids heated by convection and radiation at the same time, when the thermophysical properties of the substance depend on temperature, is described. The method is based on the complex use of linearization functions and methods of numerical analysis. In the paper an example of calculation of radiation-convective heating of an unlimited plate, during which the heat capacity and thermal conductivity of the material change with temperature, is presented. The results obtained are in good agreement with the data of the finite difference method. The proposed method makes it possible to solve nonlinear problems of thermal conductivity with other boundary conditions, since the technique of solving such problems is not fundamentally different from one another. The article was published in the framework of the program of the International Forum "Victorious may 1945".

Keywords: temperature field,radiation-convective heating, thermal conductivity and heat capacity coefficients, linearizing transformation