Analytical and semi-analytical solutions for short-time transient response of ground heat exchangers

Short-time transient temperature response of ground heat exchangers in ground source heat pump systems is of considerable interest as this has important bearing on the aggregate design length of the U-tube heat exchangers. Recent analytical solutions take into account the thermal capacity of the aggregate fluid mass in the system representing the U-tubes as an equivalent single core. This however is limited to only homogenous media. In this paper, Laplace domain solutions have been obtained for the equivalent single core of the U-tube in grouted boreholes. Both the average fluid temperature and borehole boundary temperature have been obtained using Gaver–Stehfest numerical inversion algorithm from these solutions. The temperature values obtained match the results of finite elements models of the actual U-tube geometry of the grouted borehole. With this solution it is possible to obtain both borehole boundary temperatures and the usual water temperature values. Results of this work show that the ‘early time’ borehole boundary temperature data can be analyzed for measurement of the thermal conductivity of the medium in thermal response tests. This approach would reduce the duration of the thermal response test in single strata subsurface ground zone. This solution also can be incorporated in the building energy simulation programs.