Abstract: Based on the line source theory and superposition principle, a mathematical model for heat transfer underground with a multi-borehole heat exchanger of ground source heat pump (GSHP) was developed and solved by the Laplace transformation and numerical inverse technique. Variations of heat transfer capacity and outlet fluid temperatures were studied with uniform inlet fluid temperatures for all boreholes. It is found that at an early stage, performance of each of the multiple boreholes is the same as that of a single borehole. However, performance of the multi-borehole heat exchanger is reduced due to the interference among the boreholes. The average heat flux is lower and outlet fluid temperature is higher than that of a single borehole. In addition, the interference can be weakened when the spacing of the multiple boreholes is larger.

Key words: multi-borehole, line source, superposition principle, Laplace transformation