An analytical model for heat transfer outside a single borehole heat exchanger considering convection at ground surface and advection of vertical water flow

Abstract

Borehole heat exchangers (BHEs) are widely used with ground source heat pump (GSHP) system for utilization of shallow geothermal energy. In this paper, heat transfer between a single BHE and the surrounding soil is investigated, in which convection at ground surface and advection of vertical water flow are considered in heat conduction process. The length of the borehole is much greater than its diameter, hence it is treated as a line source, and then an improved finite line source model is developed to describe the heat transfer process. The governing equations of the model are presented, and an analytical solution is established by introducing a new variable and using the Green’s function method. The analytical solution is compared with a numerical solution to confirm the derivation and programming process, and then computational examples of the analytical solution are presented. The effect of vertical water flow on the temperature response of the ground outside the borehole is demonstrated; the line source model under a convective boundary condition is compared with that under a prescribed surface temperature to show the error caused by neglecting the surface convection effect; the mean borehole wall temperature and the total heat flux at ground surface are computed, and their responses to variations of external factors are analyzed.