A comprehensive review on 2D and 3D models of vertical ground heat exchangers

The ground source heat pumps (GSHPs) have been extensively applied to commercial and residential buildings owing to their high-energy efficiencies and low running costs. The key component of the GSHP is a ground heat exchanger (GHE). The state-of-the-art two-dimensional (2D) and three-dimensional (3D) heat transfer models for borehole heat exchanger (BHE) and energy pile (EP) systems are reviewed in this paper. The physical procedures of heat transfer and the derivation of energy conservation within different channels of BHE (e.g., U-, W-, helical-shaped or coaxial-shaped) are summarized, in addition to the primary merits and demerits of each model. The main influencing factors on 2D and 3D model solutions including axial heat transfer, friction heat, spacing shack, thermal resistance, thermal short-circuiting between the inlet-pipe and outlet-pipe, are analysed and compared. Furthermore, various applications of these 2D and 3D models are elaborated. Finally, the recommendations, standpoints and potential future research on BHE heat transfer model are highlighted. It is believed that the work presented will contribute to the record of information and experiences necessary to develop BHEs for GSHP systems.