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

In underground U-tube heat exchangers (boreholes) it is important to predict its heating performance to design and select the proper parameters such as length, diameter, material etc. to have an optimized borehole from the point of view of heat capacity and economical aspects. For this reason, having trusty equations is vital to foresee borehole heating performance and applying it in design issues. In this study a single vertical U-tube borehole with constant wall temperature is considered and analytical equations for temperature distribution in the surrounding ground around the borehole is evaluated based on one and two dimensional heat conduction respectively. The analytical equation is compared to experimental data for a borehole with 50 m depth in which warm water of 40 C is pumped into it 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 a 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, entropy generation number is decreased by increasing its length and by decreasing the borehole radius and pipe outer radius.