An Analytical Diffusion Model and Its Application to Soil Heat Conduction

Abstract

This paper presents an alternative approach to solving an initial and boundary value problem (IBVP) related to the one-dimensional non-homogeneous diffusion equation with constant coefficients, applied to heat conduction in soil. Unlike the traditional Fourier separation of variables, the proposed approach is based on the fundamental solution (Green’s function), the antisymmetric extension of the initial condition, and the principles of Duhamel and superposition. The methodology involves analyzing the Cauchy problem for the heat equation in unbounded and semi-infinite domains using variable transformation and integration techniques. Preliminary results indicate that this technique can be effectively applied in future studies on ground-air heat exchangers, aimed at thermal comfort in indoor environments. This study is an important initial step towards developing more efficient and accurate solutions that describe soil behavior.