Laplace transforms were used in this paper to obtain analytical solutions for the axisymmetric problem under a constant well temperature using the convective heat transfer boundary condition, which included the conduction and convection in the aquifer as well as heat exchange at the boundary. This solution curve intuitively illustrates the temperature distribution within the aquifer. The effects of various parameters on this analytical solution were analyzed. According to this parametric analysis there exists a quasi-steady-state of temperature distribution in the axisymmetrical situation, which is different from the planar symmetry problem. In addition, the thermal breakthrough increases with the injected rate and decreases with the increasing convective heat transfer coefficient. Our analytical solution matched the results yielded by the numerical simulation quite well.

中文翻译：

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地质介质瞬态传热问题的轴对称解析解

本文采用拉普拉斯变换，利用对流换热边界条件（包括含水层中的传导和对流以及边界处的热交换）获得了恒定井温下轴对称问题的解析解。该解曲线直观地说明了含水层内的温度分布。分析了各种参数对该解析解的影响。根据该参数分析，在轴对称情况下存在一个准稳态的温度分布，这与平面对称问题不同。此外，热突破随着注入速率的增加而增加，随着对流传热系数的增加而减少。