Analytical models for heat transfer around a single ground heat exchanger in the presence of both horizontal and vertical groundwater flow considering a convective boundary condition

Abstract

Ground heat exchanges (GHEs) are widely applied in the ground source heat pump (GSHP) system for exploration of shallow geothermal energy. Heat transfer around a single GHE in the presence of both horizontal and vertical groundwater flow under a convective boundary condition is investigated. To describe the heat transfer process, three typical GHE models including the solid cylindrical heat source (SCS) model, the ring coil heat source (RCS) model and the finite line source (FLS) model are improved by incorporating the effect of horizontal and vertical groundwater flow and considering convection between the air and the ground surface. After introducing a new variable, analytical solutions for the three improved models are established using the Green's function method. Comparison between the analytical solution and a numerical solution of COMSOL is made, and the agreement between the two solutions confirms the derivation and programming process of the analytical solution. Effects of horizontal and vertical groundwater flow on the temperature increment caused by a SCS are investigated using the analytical solution. For situations with high velocities of horizontal groundwater flow, the curve relating the temperature increment and the depth has a depth-independent segment, and the temperature increment for locations near the mid-depth of heat source remains unchanged with the velocity of vertical groundwater flow changing; the variation of average temperature increment of pipe wall with the variation of vertical groundwater velocity is negligible. For situations with low velocities of horizontal groundwater flow (Pex = 10), strong vertical groundwater flow (Pez = 100) makes the aforementioned depth-independent segment disappear, and the temperature increment at a downstream location increases from 0.58 °C to 7.79 °C with the depth increasing from 0 to lc. With Pez increasing from 10 to 100, the average temperature increment of pipe wall decreases from 10.14 °C to 6.92 °C, which reduces the thermal resistance of ground and improves the economic performance of the GSHP system.