Nusselt Number Correlation for Elliptical Helical Coils Based on Computational Fluid Dynamics and Experiments
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Abstract
A helical coil is an important component of wrapped helical-coil heat exchangers around an external tank, which helps reduce direct contact between the working fluid in the coil and the fluid inside the tank. Therefore, it is suitable for applications requiring contamination control. However, the design of this type of coil still has limitations, because the correlations used to predict the Nusselt number (𝑁𝑢), which is an indicator of heat transfer performance, have mostly been developed for circular-cross-section helical coils. Meanwhile, elliptical cross-section tubes have the potential to increase the contact area with the tank wall and modify the flow structure inside the tube. This study investigates the effects of cross-sectional ovality (δ) and coil curvature. Dh / Dcoil , and flow conditions on the Nusselt number (𝑁𝑢) and internal flow behavior of elliptical helical coils. Three elliptical cross-section coil configurations were used as experimental reference data, and nine computational fluid dynamics simulation cases were conducted under different values of δ and Dh / Dcoil . The results showed that increased with Reynolds number (𝑅𝑒) and Dean number (𝐷𝑛), while variations in and modified the secondary-flow distribution and the effectiveness of thermal boundary-layer disturbance. Higher ovality produced a more concentrated asymmetric velocity field, whereas lower ovality resulted in a broader velocity distribution across the tube cross-section. The newly developed correlation predicted with high accuracy, yielding R2. = 0.972, MAPE = 5.36%, RMSE = 1.84, and a cross-validation of MAPE 5.94%, supporting its use within the studied range.
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References
[1] Flayyih, R. A.; Alwan, K. J.; Aljaberi, H. A. Comparative heat transfer analysis of helical coil and straight tube heat exchangers. Case Stud. Therm. Eng. 2025, 76, 107386. https://doi.org/10.1016/j.csite.2025.107386
[2] Ying Chua, M. A. Y.; Kumar, P.; Shah, M.; Kurnia, J. C.; Wee, S. K. Heat transfer performance analysis of a helical coil tube with supercritical CO2 as a working fluid. J. Supercrit. Fluids 2026, 228, 106800. https://doi.org/10.1016/j.supflu.2025.106800
[3] Ghazanfari, V.; Shadman, M. M.; Mansourzade, F.; Amini, Y. Numerical investigation of thermal-hydraulic performance enhancement in helical coil heat exchangers with twisted tube geometries. Case Stud. Therm. Eng. 2024, 60, 104744. https://doi.org/10.1016/j.csite.2024.104744
[4] Liaw, K. L.; Kurnia, J. C.; Putra, Z. A.; Aziz, M.; Sasmito, A. P. Enhanced turbulent convective heat transfer in helical twisted multilobe tubes. Int. J. Heat Mass Transfer 2023, 202, 123687. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123687
[5] Gomaa, A.; Gamal, Y.; Abdelmagied, M. M. Enhancement of thermofluid characteristics via a triple-helical tube heat exchanger. Sci. Rep. 2025, 15(1), 6978. https://doi.org/10.1038/s41598-025-89730-6
[6] Jasim, D. J.; Mahdi, M. S.; Mahdy, O. S.; Basem, A.; Karouei, S. H. H.; Alinia-Kolaei, M. Hydrothermal analysis of hybrid nanofluid flow inside a shell and double coil heat exchanger: Numerical examination. Int. J. Thermofluids 2024, 23, 100770. https://doi.org/10.1016/j.ijft.2024.100770
[7] Al-Saaidi, H. A. I.; Prieto, C. Influence of helical coil geometry and carbon nanotube additives on the thermal performance of shell-and-helical coiled tube latent heat storage systems. J. Energy Storage 2026, 154, 121130. https://doi.org/10.1016/j.est.2026.121130
[8] Rahman, M. A. Review on heat transfer augmentation in helically coiled tube heat exchanger. Int. J. Thermofluids 2024, 24, 100937. https://doi.org/10.1016/j.ijft.2024.100937
[9] Tran, P.-L.; Seong, M.-H.; Kang, S.-C.; Kim, J.-K. Analysis of collapse response of offshore pipes under external pressure and bending considering sizing effect. Ocean Eng. 2026, 351, 124368. https://doi.org/10.1016/j.oceaneng.2026.124368
[10] Chater, H.; Asbik, M.; Mouaky, A.; Koukouch, A.; Belandria, V.; Sarh, B. Experimental and CFD investigation of a helical coil heat exchanger coupled with a parabolic trough solar collector for heating a batch reactor: An exergy approach. Renewable Energy 2023, 202, 1507–1519. https://doi.org/10.1016/j.renene.2022.11.108
[11] Lai, Y.; Wang, S.; Guo, Y. Numerical study of tube bundle rotational direction effect on flow and heat transfer in helical coil once-through steam generator. Int. Commun. Heat Mass Transfer 2024, 159, 108277. https://doi.org/10.1016/j.icheatmasstransfer.2024.108277
[12] Xijun, Z.; Kaiwen, Q.; Xiaobin, T. Simulation of flow field characteristics around longitudinally staggered variable-curvature helical coil bundles. Nucl. Eng. Des. 2026, 446, 114632. https://doi.org/10.1016/j.nucengdes.2025.114632
[13] Kiss, A.; Kiss, B. Validation of CFD models of horizontal and vertical upward water flow in straight tubes under supercritical conditions. Nucl. Eng. Des. 2026, 448, 114674. https://doi.org/10.1016/j.nucengdes.2025.114674
[14] Cai, L.; Liu, J.; Mi, S.; Xu, C. Interpretable machine learning-based prediction and analysis on flow and heat transfer characteristics of phase change material slurry in helically coiled tube with twisted tape insert for energy storage. J. Energy Storage 2025, 133, 118016. https://doi.org/10.1016/j.est.2025.118016
[15] Xin, R.; Ebadian, M. The effects of Prandtl numbers on local and average convective heat transfer characteristics in helical pipes. J. Heat Transfer 1997, 119(3), 467–473. https://doi.org/10.1115/1.2824120
[16] Schmidt, E. F. Wärmeübergang und Druckverlust in Rohrschlangen. Chem. Ing. Tech. 1967, 39(13), 781–789. https://doi.org/10.1002/cite.330391302
[17] Pawar, S. S.; Sunnapwar, V. K. Experimental studies on heat transfer to Newtonian and non-Newtonian fluids in helical coils with laminar and turbulent flow. Exp. Therm. Fluid Sci. 2013, 44, 792–804. https://doi.org/10.1016/j.expthermflusci.2012.09.024
[18] Dravid, A. N.; Smith, K.; Merrill, E.; Brian, P. Effect of secondary fluid motion on laminar flow heat transfer in helically coiled tubes. AIChE J. 1971, 17(5), 1114–1122. https://doi.org/10.1002/aic.690170517
[19] Pimenta, T. A.; Campos, J. B. L. M. Heat transfer coefficients from Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil. Int. J. Heat Mass Transfer 2013, 58(1–2), 676–690. https://doi.org/10.1016/j.ijheatmasstransfer.2012.10.078
[20] Chua, M. A. Y. Y.; Kumar, P.; Shah, M. T.; Kurnia, J. C.; Wee, S. K. Computational study of helical coil heat exchanger: Energy, entropy, exergy, entransy (4E) analysis and application of field synergy principle. Int. J. Refrig. 2025, 172, 41–63. https://doi.org/10.1016/j.ijrefrig.2025.01.026
[21] Ali, S. A.; Jamil Alrikaby, N.; Kadhim, H. K. Computational analysis of dimples surface tube on heat transfer forced convection using turbulence model of low Reynolds number with different cases. ASEAN J. Sci. Technol. Rep. 2025, 28(3). https://doi.org/10.55164/ajstr.v28i3.256103
[22] Hedau, A.; Singal, S. K. Development of Nusselt number and friction factor correlations for double-pass solar air heater duct. Appl. Therm. Eng. 2023, 234, 121227. https://doi.org/10.1016/j.applthermaleng.2023.121227
[23] Guo, H.; Zhang, X.; Feng, L.; Wu, Y.; Wu, Y. Experimental Nusselt number correlations for heat transfer of a single spherical particle in turbulent flow. Int. J. Heat Mass Transfer 2026, 256, 127939. https://doi.org/10.1016/j.ijheatmasstransfer.2025.127939
[24] Shrivastava, A.; Kumar, V. Statistical correlations for Nusselt number and friction factor in rectangular pyramid-shaped roughened solar air collectors. Int. Commun. Heat Mass Transfer 2026, 170, 109995. https://doi.org/10.1016/j.icheatmasstransfer.2025.109995
[25] Sharipova, A.; Shafiee, M.; Lotfi, M.; Bekturganova, N. Y. Enhanced thermohydraulic performance in helical coil heat exchangers using synthesized Cu-doped TiO2 nanofluids: An experimental approach. Int. J. Therm. Sci. 2026, 220, 110338. https://doi.org/10.1016/j.ijthermalsci.2025.110338
[26] Abdelmagied, M. Thermo-hydraulic and exergy characteristics of a triple tube helical coil with inner triangular twisted tube. Int. J. Air-Cond. Refrig. 2024, 32(1). https://doi.org/10.1007/s44189-024-00065-9
[27] Zakeralhoseini, S.; Sajadi, B.; Akhavan Behabadi, M. A.; Azarhazin, S.; Fazelnia, H. Experimental investigation of the heat transfer coefficient and pressure drop of R1234yf during flow condensation in helically coiled tubes. Int. J. Therm. Sci. 2020, 157, 106516. https://doi.org/10.1016/j.ijthermalsci.2020.106516
[28] Yadav, A.; Doshi, H.; Jayaprakash, B.; Hasan, N. A.; Mohammad, H.; Kundlas, M.; Bharathi, B.; Sahu, P. K.; Vats, S.; Ranjbar, F. Prediction of the heat transfer coefficient during condensation within spirally coiled tubes of various orientations: Artificial intelligence modeling and correlation development. Int. J. Heat Fluid Flow 2026, 119, 110314. https://doi.org/10.1016/j.ijheatfluidflow.2026.110314