Relation Between Mean Fluid Temperature and Outlet Temperature for Single U-Tube Boreholes

Ground-coupled heat pump (GCHP) systems usually utilize buried vertical heat exchangers, named borehole heat exchangers (BHEs). The accurate design or simulation of a GCHP system requires the calculation of the time-dependent outlet temperature from the BHEs, Tout. However, the most widely employed BHE simulation models yield the time evolution either of the mean temperature of the BHE-ground surface, Tsm, or of that of the fluid, Tfm. In transient regime, it is not easy to relate Tout to either Tsm or Tfm. In this paper we determine, through 3D finite element simulations, simple expressions of a dimensionless coefficient φ allowing the calculation of Tout by means of a simulation model that yields Tfm. These expressions hold for single U-tube BHEs, both in quasi-steady and in unsteady working conditions. We validate our 3D simulation code by comparison with an analytical BHE model. Then, we present applications of our expressions of φ to calculate the time-dependent values of Tout through a BHE model that yields those of Tfm. Finally, we show that the values of φ in quasi-steady working conditions can be used for a simple calculation of the effective borehole thermal resistance.