The fluid extracts or rejects heat from subsurface by downward leg of pipe(DLP)and upward leg of pipe(ULP)in vertical borehole heat exchangers(BHEs).As the borehole diameter is only 0.11 m to 0.2 m

the temperature difference between DLP and ULP inevitably leads to thermal short-circuiting.In order to build accurate heat transfer model for the BHEs

the vertical underground heat exchangers with different boreholes

pipe diameters and arrangements were investigated numerically

and a best-fit correlation for the thermal short-circuiting resistance was presented in dimensionless form.A 3-D equivalent rectangular numerical model for BHEs was established and the influences of velocity and borehole depth on the short-circuiting loss rate were analyzed.Smaller velocity leads to larger thermal short-circuiting loss rate and lower average heat flux per unit length

but too large velocity has no obvious effect on reducing short-circuiting loss rate.The temperature difference between inlet and outlet increases with the borehole depth

while the heat transfer between DLP and ULP also increases greatly.The relationship between the thermal short-circuiting and the fluid temperature change is explored. The geometric mean fluid temperature ignoring the short-circuiting is always higher than the integral mean fluid temperature.With an in situ thermal conductivity test rig established in Nanjing

the results indicate that lower velocity results in lower effective subsurface conductivity and smaller heat transfer capacity in the BHEs.The measured subsurface thermal conductivity with 50 m borehole is 2.50 W·(m·K)-1

31.8% higher than that with 100 m borehole

which is 1.896 W·(m·K)-1.The heat exchange amount

short-circuiting and investment should be taken into account while determining the borehole depth.