Spectral framework for geothermal borehole heat exchangers

Purpose - This paper aims to present a framework for deriving analytical and semi-numerical models for coupled conductive-convective heat transfer processes in a borehole heat exchanger subjected to general initial and boundary conditions. Design/methodology/approach - The discrete Fourier transform and the spectral element method have been utilized for deriving two spectral models for a single U-tube borehole heat exchanger in contact with a soil mass. Findings - Verification and numerical examples have shown that the developed models are accurate and computationally very efficient. It is illustrated that one spectral element is capable of producing results which are more accurate than those produced by 200 finite elements. Practical implications - The gained computational efficiency and accuracy will boost considerably the possibilities for more insight into geothermal analysis, which will improve the procedure for designing competitive energy extraction systems. Originality/value - The models are capable of calculating exactly the temperature distribution in all involved borehole heat exchanger components and their thermal interactions.