A new semi-analytical solution addressing varying heat transfer rates for U-shaped vertical borehole heat exchangers in multilayered ground

Abstract

Existing analytical solutions for vertical borehole heat exchangers (BHEs) in a multilayered ground normally require a prescribed heat transfer rate at the borehole wall, such as a constant heat transfer rate. However, in reality, the heat transfer rate between a BHE and its surrounding ground varies along the length of the borehole. To account for this variation, this study proposed a new semi-analytical solution named the “MVQ solution”—Multilayered ground with Varying heat transfer rates (Q). The MVQ solution was first verified with an equivalent three-dimensional (3-D) finite-element (FE) model. The results showed that the MVQ solution had a mean absolute percent error (MAPE) of less than 2.50% for the average borehole wall temperature. In comparison, the conventional constant heat transfer rate solution was found to potentially overpredict the temperature by up to 50.82%. Lastly, a parameter study revealed that the inhomogeneity of ground thermal properties strengthened the heat transfer rate variation along the borehole length. Thus, the MVQ solution is indispensable for thermal performance predictions of BHEs in the multilayered ground, and it can improve the design of BHE systems in shallow geothermal applications.