STUDIES OF THE TWO-DIMENSIONAL HEAT CONDUCTION EQUATION WITH EXPONENTIAL AND POWER-LAW DEPENDENCES OF SOIL COEFFICIENTS ON TEMPERATURE

Abstract

This paper investigates a two-dimensional nonlinear heat conduction equation describing temperature fields in soil. The authors consider two types of temperature dependencies for the thermal conductivity and heat capacity coefficients: exponential and power-law. The main solution method involves linearizing the equation by introducing new dependent variables, which reduces the complex problem to classical partial differential equations. The article presents analytical solutions in the form of separation of variables, as well as via degenerate hypergeometric Gaussian functions (Pohgammer functions). The results obtained allow for calculations of heat propagation in soil, taking into account their actual thermophysical characteristics.