A high-accuracy CFD-based correlation for single-phase turbulent flow in axial multi-tube heat exchangers

This study presents a CFD-based investigation of a counter-flow multi-tube heat exchanger (MTHX) featuring a 4 m -long shell of 40 mm diameter and configurations of 2 or 3 inner tubes with diameters D i = 5.77 , 7.07, and 10.0 mm . A total of 60 RANS–SST simulations were performed over turbulent flow regimes, with hot-side Reynolds numbers ranging from 7 , 000 to 24 , 000 and cold-side Reynolds numbers from 4 , 000 to 17 , 000 . The computed overall heat transfer coefficients U span 1 , 000 – 2 , 500 W m − 2 K − 1 . A mesh-independence study confirmed discretization uncertainty below 0.089%. The resulting dataset was used to construct a compact six-parameter correlation that expresses U as a function of the Reynolds numbers, tube-to-tube spacing ratio, and tube count. Cross-validation yielded a mean absolute percentage error (MAPE) of 1.1% and an R 2 of 0.998. Propagated uncertainty analysis shows a typical 95% confidence half-width of 13 W m − 2 K − 1 . Benchmarking against classical and recent literature models—including Dittus–Boelter, Gnielinski, Sieder–Tate, and a recent overall- U correlation—demonstrates that the proposed model halves the median prediction error to 1%. Sensitivity analysis identifies the hot-side hydraulic diameter and Reynolds number as the most influential parameters. The proposed correlation thus offers a high-fidelity yet computationally efficient tool for the design of axial multi-tube exchangers under turbulent liquid conditions, removing the need for repeated CFD simulations across varying geometries and flow regimes.