A new analytical heat transfer model for deep borehole heat exchangers with coaxial tubes

• An analytical model for heat transfer inside deep borehole heat exchangers (DBHE). • Convolution theorem to address vertically increasing borehole wall temperature. • Relationships between DBHE thermal performance and various parameters. • An effective tool fast and easy enough for the design and optimization of DBHE. Deep borehole heat exchangers (DBHE) provide an effective solution for ground coupled heat pump (GCHP) systems in cold climate region where heating is dominant. Concerning the analytical heat transfer models, the simplification that borehole wall temperature is constant along the depth of ground heat exchangers (GHE) which the existing quasi-three-dimensional models have assumed in the application of shallow borehole GHE, can no longer be accepted in the application of DBHE due to the geothermal gradient in deep ground. Making this simplification cannot give the real temperature distribution of circulating fluid along the depth of DBHE. Therefore, this paper developed a new analytical model for DBHE with coaxial pipes by successfully addressing the increasing borehole wall temperature using the convolution theorem, so that the widely employed quasi-three-dimensional models for shallow borehole GHE is extended for DBHE with coaxial pipes for the first time. The new analytical model is validated by comparing with an existing numerical model. Using the newly developed analytical model, the trends revealing the relationships between thermal performance of DBHE and various parameters are firstly plotted. Because of the high accuracy and quick calculation, this new analytical model can be used as a benchmark for numerical models. More importantly, the proposed analytical model can be an effective tool for the design and optimization of DBHE, since current numerical models are always calculation-demanding, time-consuming and difficult for engineers and designers to use. Also, the method this paper proposed to address the varying borehole wall temperature can certainly be employed to improve the existing quasi-three-dimensional models for shallow borehole GHE so that they can be applicable in some other cases, for example, GHE installed in layered soils, or affected by underground seepage flow in partial depth.