A segmented analytical solution heat transfer model of U-tube ground heat exchanger based on finite solid cylindrical heat source method

Effectively describing the heat transfer process of ground heat exchangers is crucial for fully utilizing geothermal energy. The current progress in heat transfer analysis models is to divide the soil into several non-isothermal soil layers based on the assumption of uniform borehole wall temperature and heat flux in traditional models, but the temperature and heat flux inside the layers are uniform. Rarely consider the non-uniformity of heat flux within the layer and the boundary problem of vertical heat flux at the ground level. This article adopts a composite medium method to modify the segmented model, considering the heat transfer problem between soil layers. The assumption of uniform temperature of the borehole wall was removed to improve the fluid analysis model. Afterwards, analyze the impact of the heat transfer process inside and outside the borehole on the heat flux of the borehole wall. Using the segmented trial-and-error technique to couple the fluid and soil heat transfer models, a new comprehensive model of the U-shaped grounded heat exchanger was established. Conducted initial underground soil temperature distribution and thermal response tests in different geomorphic units in Guanzhong, Shaanxi, and verified the model's reliability based on experimental data. Analyze three influencing factors, namely fluid mass flow rate, initial underground soil temperature considering variable temperature layer, and temperature difference between average initial underground soil temperature and inlet fluid temperature, to evaluate system performance. The results indicate that the recommended range of fluid mass flow rate in the Guanzhong region is 0.32–0.42 kg/s. It was found that the heat transfer capacity of the heat exchanger will be underestimated if it ignores the influence of the variable temperature layer. Furthermore, the determination of the heat extraction result is not due to the high inlet fluid temperature but rather to the high difference between the inlet fluid temperature and the initial underground soil temperature. This study can promote better system design and achieve higher system performance.