Improvement in modeling of heat transfer in vertical ground heat exchangers

The heat transfer model of vertical ground heat exchangers for ground-source heat pump systems is discussed. An explicit solution of a finite line-source model has been derived to better describe temperature response of boreholes for long time steps, which can be easily incorporated into computer programs for thermal analysis of ground heat exchangers. A quasi-three-dimensional model is also presented for heat transfer inside the borehole, accounting for thermal interference between the U-tube legs. On this basis a concise expression is obtained for the thermal resistance inside the borehole. These models have a more solid theoretical basis, would help to improve design procedures recommended by available literature, and are yet suitable for engineering applications.