A Comparison Study of the Short-Time Responses of Borehole Ground Heat Exchangers by Using Numerical and Analytical Methods

In this paper, short-time performance of borehole GHEs is examined by using numerical and analytical methods. The numerical model can account for effect of heat capacities of circulating water, U-shaped tubes, as well as grouting materials, by using a novel time-varying boundary condition on the inner walls of U-tube legs. Both the numerical and the analytical composite-medium models are validated by an independent sandbox experiment. Comparisons between the two models are also made for different parameters, including heating rate, spacing of U-tube legs, thermal properties, and borehole radius. Overall, the composite-medium line-source model gives the virtually same results as the numerical model except for very early times: the analytical solution overestimates temperature responses for the first several min (about 5 min). This discrepancy is caused by the composite-medium line-source assumption, ignoring heat capacities of circulating fluid and U-shaped pipe.