A correlation for U-value for laminar and turbulent flows in concentric tube heat exchangers

This paper introduces a novel empirical correlation designed to predict the overall heat transfer coefficient (U) in concentric tube heat exchangers. The study utilizes a comprehensive dataset of 2700 data points from CFD simulations, examining the impact of critical variables including hot and cold fluid Reynolds numbers (Reh, Rec), Prandtl numbers (Prh, Prc), and heat exchanger dimensions (tube hydraulic diameter Dh, annular space hydraulic diameter Dc, and overall length L). The analysis incorporates a range of fluid combinations in the tube and annular sections – air–air, air–water, water-air, and water–water – across Reynolds number ranges from 1000 to 20000, covering both laminar and turbulent flow regimes. The correlation was developed using the Adam optimizer to minimize the Weighted Mean Squared Error (WMSE), achieving an impressive convergence to an average prediction error of 6.7% compared to actual U values. The model categorizes flow into four distinct categories, each corresponding to a combination of flow patterns in the tube and annular spaces regimes – Laminar–Laminar, Laminar–Turbulent, Turbulent–Laminar, and Turbulent–Turbulent – integrating both hydrodynamic and thermal entry effects to enhance prediction accuracy. Rigorous error analysis revealed a median error of 5.18%, substantially outperforming existing models. Notably, 10% of the predictions deviate by less than 1%, with 90th percentile errors staying below 15%. Parameters were finely tuned through extensive numerical simulations, ensuring accurate application of the correlation across diverse operational conditions. The study concludes by highlighting the model’s potential to significantly enhance the design and efficiency of heat exchangers and proposes future enhancements to further improve its predictive accuracy.