Axisymmetrical analytical solution to the transient heat transfer problem in geological media

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.