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An Analytical Model for the Thermal Assessment of a Vertical Double U-Tube Ground-Coupled Heat Pump System in Steady-State Conditions

Ali H. Tarrad*

Université de Lorraine, CNRS, LEMTA, Nancy, F-54000, France

* Corresponding Author: Ali H. Tarrad. Email:

Fluid Dynamics & Materials Processing 2022, 18(4), 1111-1127.


An analytical model was built to predict the thermal resistance of a vertical double U-tube ground-coupled heat pump that operates under steady-state conditions. It included a geometry obstruction factor for heat transfer throughout the backfill medium due to the presence of the second loop. The verification of the model was achieved by the implementation of five different borehole configurations and a comparison with other correlations in the available literature. The model considered a U-tube spacing range between (2) and (4) times the U-tube outside diameter producing a geometry configuration factor range of (0.29–0.6). The results of the model were utilized for the assessment of the DX ground heat exchanger coupled heat pump system. For similar geometrical configurations, the borehole thermal resistance experienced a decrease as the geometry factor increased. The single U-tube borehole thermal resistance was higher than that of the double U-tube heat exchanger by (10–27)% for the examined geometry configurations. The borehole thermal resistance at tube spacing of twice the tube diameter was higher than the predicted value at the triple diameter and fell in the range of (18–34)%.


Cite This Article

Tarrad, A. H. (2022). Analytical Model for Thermal Assessment of a Vertical Double U-Tube Ground-Coupled Heat Pump System Operates at Steady-State Conditions. FDMP-Fluid Dynamics & Materials Processing, 18(4), 1111–1127.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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