Considering buried depth in the moving finite line source model for vertical borehole heat exchangers—a new solution

Abstract The currently available moving finite line source (MFLS) model for design and simulation of vertical borehole heat exchangers (BHEs) neglects the effect of buried depth, i.e., the vertical distance between the ground surface and the BHEs. We propose a new analytical solution of the MFLS model with the buried depth added in a single integral form—it is named as the MFLS solution considering buried depth (MFLSD). The MFLSD solution extends the validity of the MFLS model by considering the effect of buried depth. A customized MATLAB code was deployed to compute the MFLSD solution. The correctness of the analytical solution was numerically verified with an equivalent three-dimensional (3D) finite-element (FE) model developed in COMSOL Multiphysics. Then a sensitivity analysis was carried out to evaluate the effect of the buried depth on the heat transfer at BHEs. Results indicate that the negligence of buried depth leads to an over-prediction about the exploitable heat. This over-prediction increases with simulation time, and it increases when borehole length decreases. In this regard, buried depth becomes an essential parameter for predicting the exploitable heat under long simulation time and short BHE lengths. For the first time, the MFLSD solution has considered the combined effects of buried depth and groundwater flow. The MFLSD solution is, therefore, a crucial improvement for BHE design: when the Peclet number (Pe) is smaller than 22, the MFLSD should be used over the MFLS model.