ANALYTICAL SOLUTIONS OF NON-LINEAR HEAT CONDUCTION PROBLEMS

Abstract

The paper contains information about analytical solutions of a non-linear heat conduction equation. Taking into account the fact that till the present moment physically substantiated methods for solving this equation are not found, analytical formulae have been derived for the first time. An example of calculations in the case of variable coefficients of thermal conductivity and radiative heating transfer on the boundaries is considered in the paper. The paper presents calculation of heat conduction process with a change in the physical state of substance. Mathematical functions suitable for obtaining analytical formulae are determined by means of a detailed analysis of physical model.