Dynamic thermal analysis of a single U-tube vertical ground heat exchanger using Al₂O₃/water nanofluid: full Crank–Nicolson scheme with temperature-dependent fluid properties

Recently, the impact of nanofluids on the performance of thermal energy storage systems, such as ground heat exchangers, has attracted increasing research attention. However, their precise effect on energy storage performance has not been thoroughly reported. This study presents a dynamic thermal study of a single U-tube vertical GHE employing an Al₂O₃/water nanofluid as the working medium. A full Crank–Nicolson finite-difference scheme is coupled with a thermal resistance–capacitance network to model the transient energy exchange among the U-tube fluid, grout, and surrounding soil. The model incorporates a polynomial regression–based machine learning approach to account for temperature-dependent thermophysical properties of the base fluid. Model validation against experimental and numerical data from the literature confirms high predictive accuracy. Comparative simulations between nanofluid and pure water reveal that, despite enhanced thermal conductivity, nanofluids exhibit lower overall energy storage due to reduced specific heat capacity. At a 2.0 % nanoparticle concentration, the grout and soil energy storage capacities decrease by approximately 0.5 %, and the U-tube fluid storage decreases by 2.0 % after 1000 hours of operation. These results indicate that pure water remains a superior heat transfer fluid for long-term energy storage in vertical GHEs under the conditions studied. This work provides a computationally efficient alternative to conventional finite-element simulations, enabling accurate long-term performance assessment while capturing temperature-dependent fluid property variations. The findings offer design guidance for selecting optimal working fluids in ground source heat pump (GSHP) applications.