Analytical solution of steady-state heat equation in polar coordinates for multilayer soils

This paper investigates the inverse problem for the two-dimensional Laplace equation formulated in polar coordinates. The direct problem is solved using the method of separation of variables, providing an analytical foundation for further analysis. The proposed approach enables the determination of spatially distributed parameters based on boundary measurements, which is essential for modeling heat transfer processes in complex environments. The relevance of this study lies in its practical applicability: the results can be used to improve the efficiency and reliability of urban district heating networks and can also be applied in the agro-industrial sector for thermal analysis of soil systems. This work contributes to the development of accurate mathematical models that support sustainable energy management and optimized thermal regulation in diverse engineering applications.