A conformal-mapping method for predicting the thermal properties of U-shaped borehole heat-exchangers

• Investigates the thermal properties of U-shaped borehole heat-exchangers (UBHE).
• Conformal-mapping method is employed to calculate the thermal resistance of UBHE.
• Analytical solutions are compared with the experimental data to verify the accuracy of this method.
• Provide a simple and accurate prediction of outlet temperature of UBHE.
• Temperature distribution of UBHE can be calculated.

This article investigates the thermal properties of U-shaped borehole heat-exchangers (UBHE), and the effects of related variables on the outlet temperature of UBHE. The conformal-mapping method, a simple and accurate thermal resistance calculation method, is employed to carry out UBHE design. The thermal analysis includes both the outside and the inside of the borehole. Outside the borehole, the finite line-source model calculates the wall temperature of the borehole in a steady state condition. Inside the borehole, the quasi-three-dimensional theory evaluates the temperature distribution of the working fluid. The results show that the conformal-mapping method yields an accurate solution for the outlet temperature of UBHE. The calculated solutions were compared with four cases of experimental data with good accuracy (within 6%). Under conditions of heat dissipation (cooling), the conformal-mapping method predicts results that are more accurate than the Hellström method (within about 1.33%). Sensitivity analysis shows that the heat backflow of UBHE can be reduced by increasing the distance of branch pipes and the liquid flow rate of the U-tube and reducing the depth of well.