Data-Driven Unified Nusselt Correlation for All Pipe Flow Regimes

Abstract

Accurate prediction of convective heat transfer in internal pipe flow across laminar, transitional, and turbulent regimes remains challenging because most existing Nusselt number correlations are limited to narrow Reynolds number ranges and require regime-wise switching. In this work, a friction-factor-assisted model has been introduced for forced convection in circular pipes using a compiled database of 699 experimental data points spanning 3.63 ≤ Re ≤ 1 × 106 and 0.1 ≤ Pr ≤ 16,700. A generalized Anupam–Mani–Nusselt model incorporating the Darcy friction factor has been developed to couple hydrodynamic resistance with thermal transport. Separate regime-specific correlations have also been formulated for laminar, transitional, and turbulent flows, together with a Unified Pre-Transition–Turbulent (UPTT) correlation for continuous prediction over 1000 ≤ Re ≤ 1 × 106 without explicit regime switching. Validation against the compiled database and comparison with established correlations, including those of Dittus–Boelter, Sieder–Tate, Gnielinski, Hausen, Churchill, and Taler, demonstrated improved predictive agreement, particularly in the transitional regime where conventional models commonly exhibit large deviations. The proposed regime-specific correlations yielded MARD values of approximately 3.5–7.1%. The results demonstrate that explicit incorporation of the Darcy friction factor provides an effective engineering framework for improving predictive continuity and statistical consistency in internal forced-convection heat-transfer correlations for circular pipes. A generalized single equation for the entire Reynolds number range investigated has also been proposed and is hereafter referred to as the Anupam–Nusselt correlation.