ABSTRACT
In this chapter, we present a framework for deriving a semi-analytical model for transient heat transfer in a borehole heat exchanger using the spectral element method. The spectral element method is a powerful tool for solving transient problems in multi-layer and multi-component systems. It solves the governing field equations in a homogeneous medium representing a layer or a component analytically. Combining the system layers or components together is done using the matrix assembly technique of the finite element method. This chapter gives an introduction to the spectral element method and the basic procedure for formulating a spectral element. We formulate a two-node spectral element for general heat pipes, and a one-node spectral element for a single U-tube borehole heat exchanger. Latter, we verify the spectral element model against analytical and finite element solutions.
