Weighted average of inlet and outlet temperatures in borehole heat exchangers

Vertical borehole heat exchangers are used to couple heat pumps to the ground, which serves as a source or sink of heat. These ground source heat pump systems heat and cool buildings efficiently with low maintenance costs. Many heat transfer models use the mean of the inlet and outlet circulating fluid temperatures as an average temperature along the entire borehole length. In this paper a weighting factor for the inlet and outlet temperatures has been developed that can be combined with 1D radial models in order to account for the variations in temperature with depth. The proposed method gives more accurate results than the mean temperature approximation without requiring computationally intensive 3D models. The method has been verified with measured data from thermal response tests on boreholes with single and double U-tubes, as well pipe-in-pipe (coaxial) boreholes. On the other hand, the usual mean temperature approximation sometimes leads to significant errors and unphysical temperatures.