Effects of the temperature distribution on the thermal resistance of double u-tube borehole heat exchangers

The effects of the surface temperature distribution on the thermal resistance of a double U-tube Borehole Heat Exchanger (BHE) are studied by finite element simulations. It is shown that the thermal resistance of a BHE cross section is not influenced by the bulk-temperature difference between pairs of tubes, but is influenced by the thermal conductivity of the ground when the shank spacing is high. Then it is shown that, if the real mean values of the fluid bulk temperature and of the BHE external surface are considered, the 3D thermal resistance of the BHE coincides with the thermal resistance of a BHE cross section, provided that the latter is invariant along the BHE. Finally the difference between the BHE thermal resistance and the effective BHE thermal resistance, defined by replacing the real mean temperature of the fluid with the average of inlet and outlet temperature, is evaluated in some relevant cases.