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The existence of groundwater flow adds a convective heat component to shallow geothermal heat pump systems, significantly improving heat transfer efficiency. Numerous analytical and numerical methods have been proposed to assess the impact of groundwater flow on ground heat exchangers. However, numerical simulations often require significant resources and time, while conventional analytical solutions overlook the time and depth-varying heat transfer rates, leading to inaccurate temperature predictions. This study proposes a computationally efficient semi-analytical solution by extending the line source solution and coupling it with a thermal resistance model. This approach addresses variations in heat transfer rate over time and depth, overcoming the limitations of conventional analytical solutions. Compared to a three-dimensional numerical model constructed in COMSOL Multiphysics, the average absolute percentage error (MAPE) of borehole wall temperatures for a U-shaped borehole heat exchanger (BHE) is approximately 1 %, across a wide range of water flow velocities and thermal conductivity ratios between two contacting geological layers. A significant advantage of the proposed solution is its computational efficiency. The proposed solution can complete long-term simulations with over 9,000 time steps in about 10 min, as opposed to numerical models that typically require several hours. The excellent computational efficiency and substantial accuracy make the proposed solution a simple and effective tool for the design and optimization of BHEs in engineering applications.
Guo et al. (Wed,) studied this question.