New quasi-3D model for heat transfer in U-shaped GHEs (ground heat exchangers): Effective overall thermal resistance

U-shaped GHEs (ground heat exchangers) are critical components in ground-coupled heat pumps and seasonal ground heat storage. This article reports a new quasi-3D heat transfer model for the circulating fluid in U-shaped GHEs to tackle the variation of the fluid temperature along the U-shaped channels. The model is derived from a full-scale temperature response function (G-function). The fluid temperatures in the descending and ascending legs are derived as functions of time and borehole depth. The quasi-3D model, together with the full-scale G-function, yields several effective overall thermal resistances of analytical forms. We also revise and improve the design formula proposed in the ASHRAE handbook by applying the effective thermal resistances. The improved design rule requires fewer input parameters but can address more influencing factors than the original ASHRAE's design formula.