Analytical and numerical solutions for temperature distribution in topsoil layers

Abstract

The article analyzes the analytical and numerical solutions of heat conduction under the theory of inhomogeneous bodies. The distribution of sub-zero temperature in an inhomogeneous half-space and accounting for the continuous inhomogeneity of the heat conduction rate and internal heat dissipation sources are given for the first time. The evaluation of the obtained results and the known solutions as per the European and national standards are reviewed. The comparison of numerical and analytical solutions for the test problems proves the accuracy of the obtained results. Given the availability of appropriate coefficients, these solutions are also correct for solving problems of chemical reactions with the release of heat, moisture transmission, diffusion, corrosion cracking, and other problems described by the equation of heat conduction.