ABSTRACT
In this chapter, we solve the initial and boundary value problem of a typical shallow geothermal system using the spectral analysis method. We introduce a framework for devising a spectral model capable of simulating fully transient conductive-convective heat transfer processes in a shallow geothermal system consisting of a borehole heat exchanger embedded in a soil mass. The model combines the exactness of the analytical methods to an important extent of the generality of the numerical methods in describing initial and boundary conditions. It calculates temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass. We use the fast Fourier transform algorithm for modeling the time domain, and Fourier series and Fourier-Bessel series for modeling the spatial domain.
