Dual-model approach for U-tube ground heat exchangers: semi-analytical and efficient finite element models

This study presents a novel dual-model approach designed for accurate modeling of transient heat transfer in U-tube ground heat exchangers (GHEs), which is essential for optimizing the performance of ground source heat pump (GSHP) systems. First, we develop a simple semi-analytical model that couples the classical infinite line-source (ILS) kernel with a time-marching fluid energy balance, avoiding explicit load aggregation. It accepts continuous inlet-temperature and mass-flow inputs and returns depth-resolved borehole wall and outlet temperatures under non-uniform, time- and depth-dependent ground temperature conditions. Second, we provide a streamlined three-dimensional FEM model implemented with the core COMSOL Multiphysics package (no premium add-ons). This model effectively resolves axial conduction, near-surface effects, and spatiotemporal subsurface fields while maintaining practical runtimes. Both models have been validated against experimental data available in the literature, including constant and interrupted heat inputs. Overall, the study illustrates how the proposed semi-analytical model and the 3D FEM model can be used to investigate transient heat transfer in U-tube ground heat exchangers.