A coupled heat transfer model of medium-depth downhole coaxial heat exchanger based on the piecewise analytical solution

Abstract To describe the heat transfer processes of medium-depth downhole coaxial heat exchangers (MDCHEs) effectively, an analytical solution that couples the transient heat conduction in surrounding soil (or rock) with the quasi-steady heat transfer process in borehole was developed in this study. The piecewise calculation method was adopted both on the time scale and in the depth dimension in this model. With MATLAB as the programming platform, the proposed model was validated with reported experiments and numerical simulations, and the heat extraction efficiency was defined for comprehensive evaluation of heat transfer performance of MDCHEs. Afterwards, the impacts of Reynolds number, geothermal temperature gradient and inlet fluid temperature on the heat transfer performance of MDCHEs were analyzed. It is found that the analytical model with the time-piecewise function of the heat flux through the borehole wall instead of the temperature at the borehole wall as the coupling interface yielded more accurate heat transfer rates and fluid temperatures. Besides, the concave curves of fluid temperature were in better accordance with the practicalities. It was also found that the heat transfer of MDCHEs can be improved by increasing Reynolds number, but its increments gradually decreased. The recommended value of Reynolds number ranges from 1 × 104 to 4 × 104 and the heat extraction efficiency is recommended to be greater than 70% in engineering applications. The decrease of inlet fluid temperature and the increase of geothermal temperature gradient enhance the heat transfer rate at a steady pace. The analytical solution facilitates convenient design and optimal operation of MDCHEs.