A new analytical model to study heat transfer in Borehole heat exchangers in a short time periods

This paper presents a new analytical model to study the thermal behavior of borehole heat exchangers (BHE) in short time periods. Transient heat transfer considered inside the borehole and at the ground around the borehole, transient heat conduction is considered inside the borehole and ground around the borehole. For this purpose, the analytical solution has been developed in two stages. First, a new analytical equation is provided for the short-time thermal response of the BHE (dimensionless G-function). In the second phase, the outlet temperature calculation using the G-function is described. Inside the borehole, the analogy between thermal and electrical conduction is used for derivation heat balance equations. For this purpose, a new equivalent thermal network for modeling of the heat transfer inside the borehole is developed. In ground around the borehole, the conduction equation in the radial direction is considered. The governing equations are solved by Laplace transform. Finally, the mean fluid temperature and short thermal response of the BHE is computed. Then in the second phase, the outlet temperature in the on and off times of the system is calculated using the G-function. The solution of the proposed analytical model is compared with experimental measurements. Results show that the outlet temperature of the analytical model matches very well with the reference experimental measurements.