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 4m-long shell of 40mm diameter and configurations of 2 or 3 inner tubes with diameters D_i=5.77, 7.07, and 10.0mm. 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 1,000–2,500Wm⁻²K⁻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 R² of 0.998. Propagated uncertainty analysis shows a typical 95% confidence half-width of 13Wm⁻²K⁻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.