Complex Finite Fourier Transform Techniques Applied to Thermal Energy Storage Problems

Abstract

Fourier series techniques have been applied in the past to many heat conduction problems governed by elliptic and parabolic partial differential equations. Fourier transform techniques may be used when a problem is not suitable for application of the separation of variables technique. Underground thermal energy storage problems typically lead to problems governed by parabolic type partial differential equations having solutions of periodic behaviour for large values of the time coordinate. Asymptotic solutions of thermal energy storage problems valid for large times can be properly obtained in closed form by application of the complex finite Fourier transform technique. Exact periodic solutions for such transient heat conduction problems are reported in this study. Solutions presented can be utilized in seasonal thermal energy storage system simulation studies in cylinderical and spherical coordinates.