An analytical solution to periodical heat transfer problems of multilayer rocks for thermal energy storage in underground mines

Abstract

Thermal energy storage is crucial in improving the utilization efficiency of intermittent renewable energy. Conventional analytical solutions to solve transient heat conduction problems have been limited to underground mine rocks during thermal energy storage application, due to multilayer rock formations and periodical temperature boundary conditions. An analytical solution to solve transient heat conduction in multilayer rocks with periodical temperature boundary condition was developed in this work, to reveal the heat transfer happening in underground mines during thermal energy storage and extraction. The periodical temperature boundary condition was reformulated as a sequence of a periodical temperature in cosine function and a constant temperature problem. The periodical temperature part was solved by Laplace transform method, while the constant temperature part was solved by thermal resistance principle. The temperature of multilayer rocks during thermal energy storage and extraction can be solved as a superposition of the periodical temperature condition and constant condition. Comparison of the proposed analytical solution with numerical calculations validated the applicability and accuracy of the proposed analytical solution to periodical heat transfer of multilayer rocks, which will provide valuable guidance in selecting appropriate energy storage layer.