The coaxial borehole heat exchangers (CBHEs) are efficient geothermal energy utilization method, which has recently attracted increasing attention. However, this method still has no suitable or efficient analysis method, which limits the wide application of CBHEs. Moreover, the non-uniformity of the ground has less been considered in related analyses, which will lead to estimation errors in CBHEs heat exchange efficiency. Hence, an analytical solution for coaxial borehole exchangers considering non-uniformity of the ground with high calculation efficiency is introduced in this paper. By comparing the CBHEs analytical model with typical experimental results, the reliability of this model is verified. Next, using reliability theory, we further investigate the heat exchange efficiency of CBHEs considering the non-uniformity of the ground, the temperature gradient, the fluid inlet direction, and the working temperature difference between the inlet and initial ground. The results show that the changes (±10%) of basic thermal conductivity will decrease the heat exchange efficiency by 4.5% and increase by 4.1%, respectively. With an increase in the ground's non-uniformity (from 0.2 to 0.6 W/m·K), the heat exchange efficiency of the CBHEs will decrease (from 0.4% to 1.4%). Compared to the results without considering the temperature gradient, the heat exchange efficiency of the CBHEs increased by 0.3%, 0.9%, and 1.3% (corresponding to 1, 2, and 3 °C temperature gradients at a 200 m depth). The CBHEs with the annular region as the inlet presented better heat exchange efficiency (by about 0.3%) than CBHEs with the round region as the inlet. the increase in the working temperature difference between the inlet and initial ground was found to greatly improve the heat exchange efficiency of the CBHEs. Moreover, according to the experimental and design cases, the necessity of considering soil non-uniformity has been proved. This study will provide a useful analytical simulation tool and an important guide to optimize CBHEs design considering the ground non-uniformity in the horizontal and vertical direction.

同轴埋管换热器（CBHEs）是一种高效的地热能利用方法，近年来受到越来越多的关注。然而，该方法仍然没有合适或有效的分析方法，限制了CBHE的广泛应用。此外，相关分析中较少考虑地面的不均匀性，这将导致CBHE热交换效率的估计错误。因此，本文介绍了一种计算效率高、考虑地面不均匀性的同轴埋管换热器解析解。通过将CBHEs分析模型与典型实验结果进行比较，验证了该模型的可靠性。接下来，使用可靠性理论，我们进一步研究了考虑地面不均匀性的 CBHE 的热交换效率，温度梯度、流体入口方向以及入口与初始地面之间的工作温差。结果表明，基本导热系数的变化（±10%）会使换热效率分别降低4.5%和4.1%。随着地面不均匀度的增加（从 0.2 到 0.6 W/m·K），CBHE 的热交换效率将降低（从 0.4% 到 1.4%）。与不考虑温度梯度的结果相比，CBHEs 的热交换效率分别提高了 0.3%、0.9% 和 1.3%（对应于 200 m 深度的 1、2 和 3 °C 温度梯度）。以环形区域为入口的 CBHE 比以圆形区域为入口的 CBHE 具有更好的热交换效率（约 0.3%）。发现入口和初始地面之间工作温差的增加大大提高了 CBHE 的热交换效率。此外，根据试验和设计案例，证明了考虑土体非均匀性的必要性。该研究将为考虑水平和垂直方向的地面非均匀性优化 CBHE 设计提供有用的分析模拟工具和重要指南。