Local Conduction Heat Transfer in U-pipe Borehole Heat Exchangers

The most common way to exchange heat with the bedrock in Ground Source Heat Pump (GSHP) applications is circulating a fluid through a U-formed closed loop in vertical boreholes drilled several tenths of meters into the ground. The quality of the heat exchange depends on the flow conditions along the channels, the pipe properties, and the relative position of the flow channels to each other and to the rock wall. One of the ways to measure the performance of such heat exchangers is determining and evaluating a thermal resistance that accounts for all these factors, the borehole thermal resistance. This study presents and compares the results of eight cross sectional U-pipe Borehole Heat Exchanger configurations, modeled with the software COMSOL Multi-physics. Values from recent experimental temperature measurements and calculated heat transfer coefficients are used as boundary conditions. The two dimensional problem is solved with steady state heat transfer equations, and the net heat exchanged with the ground is obtained. The borehole thermal resistance is subsequently calculated and a quantitative comparison among all cases is presented. Isothermal lines and heat flow directions illustrate the results, pointing out how opportune the use of certain U-pipe BHE configurations is.