Heat transfer mechanism and parameter analysis of the U-tube borehole ground heat exchanger of middle-shallow geothermal energy

Middle-shallow geothermal energy systems have gained increasing attentions because their initial cost is lower than middle-deep layer systems, and their heat exchange ability is better than the shallow layer's effect. A U-tube borehole ground heat exchanger (BGHE) is a typical form, but the existing studies have ignored the geothermal gradient and therefore the calculation errors are inevitable. This paper innovatively investigated the heat transfer mechanism and the parameters' influence for the U-tube BGHE. First, the governing equations of energy conservation and the corresponding conditions are demonstrated for the U-tube BGHE, the vertical and the radial directions adopt equal and unequal step sizes, respectively, employing the principle of equal proportion. Second, the novel node equations are established for both the circulating fluid and the underground rock-soil while considering the geothermal gradient. The U-tube is regarded as a combination of descending and ascending tubes. Afterward, the significant factors that influence the heat transfer performance of single U-tube BGHE are investigated. Next, the heat transfer equations of multiple U-tube BGHEs are assessed, and then the factors influencing heat transfer performance are explored. The research results of this paper reveal the heat transfer characteristics of the U-tube BGHE and can promote the popularization and application of the middleshallow geothermal energy.