Simple equations to evaluate the mean fluid temperature of double-U-tube borehole heat exchangers

The design of ground-coupled heat pump systems requires the knowledge of the mean temperature Tfm of the working fluid in borehole heat exchangers. This quantity is usually approximated by the arithmetic mean of inlet and outlet temperature. The approximation yields an overestimation of the thermal resistance of the heat exchanger in thermal response tests, as well as errors in the estimation of the outlet fluid temperature in the dynamic simulation of ground-coupled heat pumps. Recently (Applied Energy 206, 2017, 1406-1415), Zanchini and Jahanbin determined, by finite element simulations, correlations that allow an immediate evaluation of Tfm in any working condition, with reference to double U-tube boreholes with length 100 m and shank spacing 85 mm. In this paper, the analysis presented there is extended to double U-tube boreholes with any length, between 50 and 200 m, and any shank spacing, between 65 and 105 mm. The results hold for every thermal conductivity of the sealing grout between 0.9 and 1.6 W/(m K), every volume flow rate between 12 and 24 L per minute, every diameter of the BHE and every working condition (heating, cooling, thermal response test), both in quasi-stationary and in transient regime.