Revised heat transfer modeling of double-U vertical ground-coupled heat exchangers

This article deals with analytical heat transfer modeling of double-U borehole heat exchangers. We propose five original, plain and comprehensive expressions to evaluate both heat flux at BHE surface and return temperature with respect to any geometrical characteristic, flow arrangement within U-ducts (series or parallel), and operative condition (i.e. inlet temperature and flow rate). Traditional ∈-NTU heat exchanger theory is applied, together with revised two-dimensional and quasi-three-dimensional approaches for double-U boreholes modeling. In particular, we present both heat transfer effectiveness and borehole thermal resistance in a useful dimensionless form depending on the NTU value. This approach leads to an immediate evaluation of borehole performance, also providing quantitative information on the effect of different parallel and series flow arrangements. Then, we compare double-U and single-U configurations to analyze heat transfer effectiveness with respect to head losses. The proposed formulas represent a useful and effective tool for BHE performance predictions: they can be successfully applied to borehole design, thermal response tests, sensitivity analysis, and overall GSHPs performance simulation and optimization.