Analytical heat transfer analysis of multiple ground heat exchangers in layered soils considering thermal contact resistance

Owing to the effect of sedimentary history, the natural ground surrounding vertical ground heat exchangers (GHEs) often exhibits significant vertical stratification. Nevertheless, imperfect contact between adjacent soil layers can lead to thermal resistance at the soil interface, a phenomenon referred to as thermal contact resistance (TCR). In this paper, the heat transfer characteristics of multiple GHEs in layered soils are investigated using the the finite Hankel transform and separation of variables to derive the corresponding analytical solution. The proposed analytical model is validated the existing analytical model and existing experimental data, demonstrating its ability to accurately capture temperature discontinuities at soil layer interfaces. Furthermore, by introducing the temperature difference and the rate of temperature change, the influence of key parameters, including TCR, soil thermal conductivity, and the length-to-diameter ratio of GHE, on the temperature distribution within the surrounding soil during the simultaneous operation of multiple GHEs is further investigated. The parametric analysis revealed the following sensitivities: a 0.01 m²·K·W⁻¹ increase in TCR elevates these differences by 0.18–1.39 °C (representing a 1.3 %–8.6 % change rate), a 0.1 W·m⁻¹·K⁻¹ rise in thermal conductivity difference further increases them by 0.29–0.84 °C (a 1.9 %–5.8 % growth rate), and a 0.01 m increment in GHE radius raises them by 0.15–0.50 °C (a 2.2 %–3.9 % growth rate).