A simplified analytical model for predicting the heating performance of single U-tube underground heat exchangers

To ensure an optimized borehole in terms of heat capacity and coste effctiveness, it is necessary to predict the heating performance of underground U-tube heat exchangers (boreholes) so that proper parameters such as length, diameter, material, etc. can be designed and selected. To this end, employing reliable equations is essential to predicting the heating performance of a borehole and also, to resolving the design issues. In this study, a single vertical U-tube borehole with a constant wall temperature is considered and analytical equations for temperature distribution in the surrounding ground around the borehole are evaluated based on one- and two-dimensional heat conduction, respectively. The analytical equation is compared with experimental data for a borehole with 50 m depth in which warm water at 40C is pumped into it within a time period of 120 hours and the heat transfer rate per unit length is recorded. The comparison between analytical expression and experimental data shows good agreement between them. Also, the borehole entropy generation number is studied and the optimized parameters are evaluated to minimize it. It is concluded that for the considered borehole, the entropy generation number decreases upon an increase in its length and a decrease in the borehole radius and pipe outer radius.