Analytical approach to solving the problem of heat transfer in multilayer structures

This work presents an analytical approach to solving the problem of heat transfer in multilayer structures with fixed boundary conditions. The aim of the study is to analyze heat transfer processes in systems with different thermal characteristics and to develop methods for determining the exact temperature distribution in each layer. Using the heat conduction equation, the corresponding equations are analytically solved for each layer, taking into account the continuity of temperature and heat flux at the boundaries between the layers. Particular attention is paid to stationary and nonstationary processes. The results of the study can be used to optimize multilayer structures in construction, energy, and other industries where it is important to ensure effective thermal insulation or heat distribution. The analytical approach provides accurate modeling of temperature fields in complex systems and allows predicting the effect of boundary conditions on heat transfer in multilayer materials.