Startseite Technik Anisotropic turbulent flow of water through converging wavy-aluminum-circular pipe with five half-cycles: insight into the significance of four-branch minor-inlet angle
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Anisotropic turbulent flow of water through converging wavy-aluminum-circular pipe with five half-cycles: insight into the significance of four-branch minor-inlet angle

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Veröffentlicht/Copyright: 1. Juli 2025
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Abstract

Accurately predicting turbulent water flow in duct systems remains a challenging problem, particularly when anisotropic turbulence effects are significant. Bridging the gap between industrial applications and academic research requires a deeper understanding of such complex flows. This study investigates a less commonly analyzed configuration involving a horizontal aluminum duct transitioning into a converging wavy duct. The wavy section consists of 2.5 full sinusoidal periods, ending in a reduced outlet diameter. In addition, the effect of incorporating four minor/secondary inlets, arranged as branches at different angles, was examined and presented herein. Aluminum was selected for its low density and corrosion resistance, which are beneficial in experimental and industrial setups. Initially, the duct was analyzed in an unbranched configuration. The study then progressed to include the four secondary/minor branch inlets at various angles. The simulation results were validated by comparison with a solution for a simple flow in a 70 mm duct. Additional verification was provided by employing other CFD codes, along with grid convergence index and mesh sensitivity analyses, improving the confidence in the simulation results. Branch angles influences turbulence intensity depending on flow conditions and angle magnitude. Sharper branch angles are particularly effective, inducing greater turbulence at the converged outlet. Higher inlet temperatures and velocities lead to increased Reynolds stress due to enhanced energy transfer and elevated turbulent kinetic energy. Specifically, an increase in inlet velocity at a 45° branch angle further augments turbulent momentum transfer, resulting in more controlled mixing along the duct.

2020 Mathematics Subject Classification: 80Axx; 76–10; 35Qxx; 80Mxx; 76Fxx

Corresponding author: Isaac Lare Animasaun, Department of Mathematical Sciences, Fluid Dynamics and Survey Research Group, Federal University of Technology, Akure, PMB 704, Nigeria; Physical Sciences, Engineering, and Technology Working Group, Nigerian Young Academy, Lagos, Nigeria; and National Water and Energy Center, United Arab Emirates University, Al Ain, Abu Dhabi, PMB 15551, United Arab Emirates, E-mail:

Isaac Lare Animasaun these contributed equally to the work.


Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, KSA for funding this work through Small Groups Project under grant number RGP.1/281/44.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors declare no conflicts of interest regarding this article.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

References

[1] F. Z. Wang, I. L. Animasaun, T. Muhammad, and S. S. Okoya, “Recent advancements in fluid dynamics: drag reduction, lift generation, computational fluid dynamics, turbulence modelling, and multiphase flow,” Arabian J. Sci. Eng., vol. 49, no. 8, pp. 10237–10249, 2024, https://doi.org/10.1007/s13369-024-08945-3.Suche in Google Scholar

[2] D. P. Cokijat, Turbulence Models for Non-circular Ducts and Channels, Doctoral dissertation, City University London, London, 1993.Suche in Google Scholar

[3] A. Kalpakli Vester, R. Orlu, and P. H. Alfredsson, “Turbulent flows in curved pipes: recent advances in experiments and simulations,” Appl. Mech. Rev., vol. 68, no. 5, p. 050802, 2016, https://doi.org/10.1115/1.4034135.Suche in Google Scholar

[4] Y. Mou, Reliability Of Advanced Reynolds Averaged Turbulence Models in CFD of Early Development Stages of Cross-Flow Jets, Master’s thesis, United Kingdom, The University of Manchester, 2017.Suche in Google Scholar

[5] X. Shen, R. Li, H. Cai, J. Feng, and H. Wan, “Characteristics of secondary flow and separation zone with different junction angle and flow ratio at river confluences,” J. Hydrol., vol. 614, p. 128537, 2022, https://doi.org/10.1016/j.jhydrol.2022.128537.Suche in Google Scholar

[6] B. Lakshminarayana, “Turbulence modeling for complex shear flows,” AIAA J., vol. 24, no. 12, pp. 1900–1917, 1986, https://doi.org/10.2514/3.9547.Suche in Google Scholar

[7] A. Randriamampianina, R. Schiestel, and M. Wilson, “The turbulent flow in an enclosed corotating disk pair: axisymmetric numerical simulation and Reynolds stress modelling,” Int. J. Heat Fluid Flow, vol. 25, no. 6, pp. 897–914, 2004, https://doi.org/10.1016/j.ijheatfluidflow.2004.03.003.Suche in Google Scholar

[8] A. J. Revell, T. J. Craft, and D. R. Laurence, “Turbulence modelling of unsteady turbulent flows using the stress strain lag model,” Flow Turbul. Combust., vol. 86, no. 1, pp. 129–151, 2011. https://doi.org/10.1007/s10494-010-9297-9.Suche in Google Scholar

[9] M. Karbon and A. K. Sleiti, “Turbulence modeling using Z-F model and RSM for flow analysis in Z-SHAPE ducts,” J. Eng., vol. 2020, no. 1, pp. 4854837–10, 2020, https://doi.org/10.1155/2020/4854837.Suche in Google Scholar

[10] B. N. Murthy and J. B. Joshi, “Assessment of standard k-e, RSM and LES turbulence models in a baffled stirred vessel agitated by various impeller designs,” Chem. Eng. Sci., vol. 63, no. 22, pp. 5468–5495, 2008, https://doi.org/10.1016/j.ces.2008.06.019.Suche in Google Scholar

[11] A. Meslem, A. Dia, C. Beghein, M. El Hassan, I. Nastase, and P. J. Vialle, “A comparison of three turbulence models for the prediction of parallel lobed jets in perforated panel optimization,” Build. Environ., vol. 46, no. 11, pp. 2203–2219, 2011, https://doi.org/10.1016/j.buildenv.2011.04.037.Suche in Google Scholar

[12] R. G. Ainsworth, Ed., Safe Piped Water, London, IWA Publishing, 2004.Suche in Google Scholar

[13] G. Wang, et al.., “Estimation of the dissipation rate of turbulent kinetic energy: a review,” Chem. Eng. Sci., vol. 229, p. 116133, 2021, https://doi.org/10.1016/j.ces.2020.116133.Suche in Google Scholar

[14] J. Jimenez, “Small scale vortices in turbulent flows,” in New Approaches and Concepts in Turbulence, Basel, Birkhauser Basel, 1993, pp. 95–110.10.1007/978-3-0348-8585-0_7Suche in Google Scholar

[15] J. Jzhang, S. Xu, and W. Li, “High shear mixers: a review of typical applications and studies on power draw, flow pattern, energy dissipation and transfer properties,” Chem. Eng. Process. Process Intensif., vols. 57-58, pp. 25–41, 2012, https://doi.org/10.1016/j.cep.2012.04.004.Suche in Google Scholar

[16] M. Hamlehdar, A. Kasaeian, and M. R. Safaei, “Energy harvesting from fluid flow using piezoelectrics: a critical review,” Renewable Energy, vol. 143, pp. 1826–1838, 2019, https://doi.org/10.1016/j.renene.2019.05.078.Suche in Google Scholar

[17] M. M. Bernitsas, “Harvesting energy by flow included motions,” in Springer Handbook of Ocean Engineering, Cham, Springer, 2016, pp. 1163–1244.10.1007/978-3-319-16649-0_47Suche in Google Scholar

[18] H. Kong, Energy Harvesting from Natural Water Flow, Master’s thesis (Electronic Theses and Dissertations), Canada, University of Windsor, 2019. https://scholar.uwindsor.ca/etd/7715.Suche in Google Scholar

[19] A. Naqvi, A. Ali, W. A. Altabey, and S. A. Kouritem, “Energy harvesting from fluid flow using piezoelectric materials: a review,” Energies, vol. 15, no. 19, p. 7424, 2022, https://doi.org/10.3390/en15197424.Suche in Google Scholar

[20] L. Ding, L. Zhang, M. M. Bernitsas, and C. C. Chang, “Numerical simulation and experimental validation for energy harvesting of single-cylinder VIVACE converter with passive turbulence control,” Renewable Energy, vol. 85, pp. 1246–1259, 2016, https://doi.org/10.1016/j.renene.2015.07.088.Suche in Google Scholar

[21] W. Sun, T. Tan, Z. Yan, D. Zhao, X. Luo, and W. Huang, “Energy harvesting from water flow in open channel with macro fiber composite,” AIP Adv., vol. 8, no. 9, p. 095107, 2018, https://doi.org/10.1063/1.5035383.Suche in Google Scholar

[22] W. Sun, D. Zhao, T. Tan, Z. Yan, P. Guo, and X. Luo, “Low velocity water flow energy harvesting using vortex induced vibration and galloping,” Appl. Energy, vol. 251, p. 113392, 2019, https://doi.org/10.1016/j.apenergy.2019.113392.Suche in Google Scholar

[23] H. Park, A. P. Mentzelopoulos, and M. M. Bernitsas, “Hydrokinetic energy harvesting from slow currents using flow-induced oscillations,” Renewable Energy, vol. 214, pp. 242–254, 2023, https://doi.org/10.1016/j.renene.2023.05.110.Suche in Google Scholar

[24] S. Harikrishnan and S. Tiwari, “Simulation of fully developed flow and heat transfer in wavy channels using OpenFOAM,” in Advances in Mechanical Engineering: Select Proceedings of ICRIDME 2018, Singapore, Springer, 2020, pp. 869–877.10.1007/978-981-15-0124-1_78Suche in Google Scholar

[25] S. T. Hsu and J. F. Kennedy, “Turbulent flow in wavy pipes,” J. Fluid Mech., vol. 47, no. 3, pp. 481–502, 1971.10.1017/S0022112071001186Suche in Google Scholar

[26] M. Rokni and T. B. Gatski, “Predicting turbulent convective heat transfer in fully developed duct flows,” Int. J. Heat Fluid Flow, vol. 22, no. 4, pp. 381–392, 2001.10.1016/S0142-727X(01)00104-7Suche in Google Scholar

[27] S. Mahmud, A. S. Islam, and M. A. H. Mamun, “Separation characteristics of fluid flow inside two parallel plates with wavy surface,” Int. J. Eng. Sci., vol. 40, no. 13, pp. 1495–1509, 2002, https://doi.org/10.1016/S0020-72250200029-0.Suche in Google Scholar

[28] M. Rahimi-Esbo, A. A. Ranjbar, A. Ramiar, A. Arya, and M. Rahgoshay, “Numerical study of turbulent forced convection jet flow in a converging sinusoidal channel,” Int. J. Therm. Sci., vol. 59, pp. 176–185, 2012, https://doi.org/10.1016/j.ijthermalsci.2012.03.016.Suche in Google Scholar

[29] A. G. Ramgadia and A. K. Saha, “Three-dimensional numerical study of turbulent flow and heat transfer in a wavy-walled duct,” Int. J. Heat Mass Transfer, vol. 67, pp. 98–117, 2013, https://doi.org/10.1016/j.ijheatmasstransfer.2013.07.081.Suche in Google Scholar

[30] A. G. Ramgadia and A. K. Saha, “Study of fully-developed turbulent flow and heat transfer in a rotating wavy-walled duct,” Int. J. Heat Mass Transfer, vol. 144, p. 118578, 2019, https://doi.org/10.1016/j.ijheatmasstransfer.2019.118578.Suche in Google Scholar

[31] M. Sarkar, S. B. Paramane, and A. Sharma, “Periodically fully developed heat and fluid flow characteristics in a furrowed wavy channel,” Heat Transfer Eng., vol. 38, no. 2, pp. 278–288, 2016, https://doi.org/10.1080/01457632.2016.1177434.Suche in Google Scholar

[32] D. S. Toghraie, O. A. Akbari, A. Koveiti, and R. Mashayekhi, “Numerical investigation of turbulent nanofluid flow and two-dimensional forced-convection heat transfer in a sinusoidal converging-diverging channel,” Heat Tran. Res., vol. 50, no. 7, pp. 671–695, 2019, https://doi.org/10.1615/heattransres.2018025937.Suche in Google Scholar

[33] D. M. Ferley and S. J. Ormiston, “Numerical analysis of laminar forced convection in corrugated-plate channels with sinusoidal, ellipse, and rounded-vee wall shapes,” Numer. Heat Transf. A Appl., vol. 63, no. 8, pp. 563–589, 2013, https://doi.org/10.1115/ihtc14-22082.Suche in Google Scholar

[34] A. Kumar, S. K. Mehta, S. Pati, and M. Murugesan, “Analysis of thermal and hydraulic performances for flow in a wavy channel with varying amplitude,” J. Therm. Anal. Calorim., vol. 148, no. 2, pp. 517–531, 2023, https://doi.org/10.1007/s10973-022-11784-9.Suche in Google Scholar

[35] E. M. Sparrow and N. Cur, “Maldistributed inlet flow effects on turbulent heat transfer and pressure drop in a flat rectangular duct,” J. Heat Transfer, vol. 105, no. 3, pp. 527–536, 1983, https://doi.org/10.1115/1.3245617.Suche in Google Scholar

[36] T. M. Liou, S. M. Wu, and Y. H. Hwang, “Experimental and theoretical investigations of turbulent flow in a side-inlet rectangular conbustor,” J. Propul. Power, vol. 6, no. 2, pp. 131–138, 1990, https://doi.org/10.2514/3.23234.Suche in Google Scholar

[37] J. C. Misra and S. K. Ghosh, “Flow of a Casson fluid in a narrow tube with a side branch,” Int. J. Eng. Sci., vol. 38, no. 18, pp. 2045–2077, 2000, https://doi.org/10.1016/s0020-72250000008-2.Suche in Google Scholar

[38] T. H. Ko, “A numerical study on the effects of side-inlet angle on the mixing phenomena in a three-dimensional side-dump combustor,” Int. Commun. Heat Mass Tran., vol. 33, no. 7, pp. 853–862, 2006, https://doi.org/10.1016/j.icheatmasstransfer.2006.04.010.Suche in Google Scholar

[39] X. P. Du, M. Zeng, Z. Y. Dong, and Q. W. Wang, “Experimental study of the effect of air inlet angle on the air-side performance for cross-flow finned oval-tube heat exchangers,” Exp. Therm. Fluid Sci., vol. 52, pp. 146–155, 2014, https://doi.org/10.1016/j.expthermflusci.2013.09.005.Suche in Google Scholar

[40] Z. Liu, H. Li, L. Shi, and Y. Zhang, “Numerical study of the air inlet angle influence on the air-side performance of plate-fin heat exchangers,” Appl. Therm. Eng., vol. 89, pp. 356–364, 2015, https://doi.org/10.1016/j.applthermaleng.2015.06.032.Suche in Google Scholar

[41] Z. L. Chiam, P. S. Lee, P. K. Singh, and N. Mou, “Investigation of fluid flow and heat transfer in wavy micro-channels with alternating secondary branches,” Int. J. Heat Mass Transfer, vol. 101, pp. 1316–1330, 2016, https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.097.Suche in Google Scholar

[42] F. Wang, I. L. Animasaun, Q. M. Al-Mdallal, S. Saranya, and T. Muhammad, “Dynamics through three-inlets of t-shaped ducts: significance of inlet velocity on transient air and water experiencing cold fronts subject to turbulence,” Int. Commun. Heat Mass Tran., vol. 148, p. 107034, 2023, https://doi.org/10.1016/j.icheatmasstransfer.2023.10703.Suche in Google Scholar

[43] F. Wang, I. L. Animasaun, D. M. Al Shamsi, T. Muhammad, and A. Ali, “Transient cold-front-water through y-shaped aluminium ducts: nature of turbulence, non-equilibrium thermodynamics, and velocity at the converged and diverged outlets,” J. Non-Equilibrium Thermodyn., vol. 49, no. 4, pp. 485–512, 2024, https://doi.org/10.1515/jnet-2024-0011.Suche in Google Scholar

[44] L. Sun, et al.., “Effect of vane angle on turbulence-chemistry interactions, temperature, flow field, burnout, and NOx emissions in swirling flames fueled by semicoke mixtures,” Environ. Sci. Pollut. Res., vol. 31, no. 3, pp. 3828–3852, 2023, https://doi.org/10.1007/s11356-023-30977-9.Suche in Google Scholar PubMed

[45] L. Dong, K.-S. Choi, and X. Mao, “Interplay of the leading-edge vortex and the tip vortex of a low-aspect-ratio thin wing,” Exp. Fluid, vol. 61, no. 9, 2020, Art. no. 200.10.1007/s00348-020-03023-4Suche in Google Scholar

[46] T. Kajishima, K. Taira, T. Kajishima, and K. Taira, “Reynolds-averaged Navier-Stokes equations,” Comput. Fluid Dynam: Incomp. Turbul. Flow., pp. 237–268, 2017.10.1007/978-3-319-45304-0_7Suche in Google Scholar

[47] M. M. Gibson and B. E. Launder, “Ground effects on pressure fluctuations in the atmospheric boundary layer,” J. Fluid Mech., vol. 86, no. 3, pp. 491–511, 1978, https://doi.org/10.1017/s0022112078001251.Suche in Google Scholar

[48] B. E. Launder, “Second-moment closure: present and future?” Int. J. Heat Fluid Flow, vol. 10, no. 4, pp. 282–300, 1989, https://doi.org/10.1016/0142-727x8990017-9.Suche in Google Scholar

[49] B. E. Launder, G. J. Reece, and W. Rodi, “Progress in the development of a Reynolds-stress turbulence closure,” J. Fluid Mech., vol. 68, no. 3, pp. 537–566, 1975, https://doi.org/10.1017/s0022112075001814.Suche in Google Scholar

[50] P. Joshi, X. Liu, and J. Katz, “Effect of mean and fluctuating pressure gradients on boundary layer turbulence,” J. Fluid Mech., vol. 748, pp. 36–84, 2014, https://doi.org/10.1017/jfm.2014.147.Suche in Google Scholar

[51] D. J. Fritsch, V. Vishwanathan, K. Todd Lowe, and W. J. Devenport, “Fluctuating pressure beneath smooth wall boundary layers in non-equilibrium pressure gradients,” AIAA J., vol. 60, no. 8, pp. 4725–4743, 2022, https://doi.org/10.2514/1.j061431.Suche in Google Scholar

[52] D. Lakehal and F. Thiele, “Sensitivity of turbulent shedding flows to non-linear stress-strain relations and Reynolds stress models,” Comput. Fluid, vol. 30, no. 1, pp. 1–35, 2000, https://doi.org/10.1016/S0045-79300000003-7.Suche in Google Scholar

[53] S. Heinz, R. Mokhtarpoor, and M. Stoellinger, “Theory-based Reynolds-averaged Navier-Stokes equations with large eddy simulation capability for separated turbulent flow simulations,” Phys. Fluids, vol. 32, no. 6, p. 065102, 2020, https://doi.org/10.1063/5.0006660.Suche in Google Scholar

[54] A. Patsekha, R. Wei, and R. Galler, “Comparative analysis of numerical methods regarding the backflow investigation in tunnels of zentrum am berg,” BHM Berg- Hüttenmännische Monatsh., vol. 167, no. 12, pp. 566–577, 2022, https://doi.org/10.1007/s00501-022-01304-5.Suche in Google Scholar

[55] F. Wang, I. L. Animasaun, Q. M. Al-Mdallal, S. Saranya, and T. Muhammad, “Dynamics through three-inlets of t-shaped ducts: significance of inlet velocity on transient air and water experiencing cold fronts subject to turbulence,” Int. Commun. Heat Mass Tran., vol. 148, p. 107034, 2023, https://doi.org/10.1016/j.icheatmasstransfer.2023.107034.Suche in Google Scholar

[56] B. Fleischli, L. Mangani, A. Del Rio, and E. Casartelli, “A discrete adjoint method for pressure-based algorithms,” Comput. Fluid, vol. 227, p. 105037, 2021, https://doi.org/10.1016/j.compfluid.2021.105037.Suche in Google Scholar

[57] J. Qin, H. Pan, M. M. Rahman, X. Tian, and Z. Zhu, “Introducing compressibility with SIMPLE algorithm,” Math. Comput. Simulat., vol. 180, pp. 328–353, 2021, https://doi.org/10.1016/j.matcom.2020.09.010.Suche in Google Scholar

[58] P. Wu, F. Chao, D. Wu, J. Shan, and J. Gou, “Implementation and comparison of high-resolution spatial discretization schemes for solving two-fluid seven-equation two-pressure model,” Sci. Technol. Nuc. Inst., vol. 2017, no. 1, pp. 4252975–14, 2017, https://doi.org/10.1155/2017/4252975.Suche in Google Scholar

[59] G. T. Carroll, P. D. Devereux, D. N. Ku, T. M. McGloughlin, and M. T. Walsh, “Experimental validation of convection-diffusion discretisation scheme employed for computational modelling of biological mass transport,” Biomed. Eng. Online, vol. 9, pp. 1–13, 2010, https://doi.org/10.1186/1475-925x-9-34.Suche in Google Scholar

[60] L. Freret, M. Williamschen, and C. P. Groth, “Enhanced anisotropic block-based adaptive mesh refinement for three-dimensional inviscid and viscous compressible flows,” J. Comput. Phys., vol. 458, p. 111092, 2022, https://doi.org/10.1016/j.jcp.2022.111092.Suche in Google Scholar

[61] M. El Rafei, L. Konozsy, and Z. Rana, “Investigation of numerical dissipation in classical and implicit large eddy simulations,” Aerospace, vol. 4, no. 4, p. 59, 2017, https://doi.org/10.3390/aerospace4040059.Suche in Google Scholar

[62] C. Zhang, et al.., “Accelerating flow simulations in the built environment by using the fast fluid dynamics initializer,” Build. Environ., vol. 253, p. 111274, 2024, https://doi.org/10.1016/j.buildenv.2024.111274.Suche in Google Scholar

[63] K. M. Almohammadi, D. B. Ingham, L. Ma, and M. Pourkashan, “Computational fluid dynamics (CFD) mesh independency techniques for a straight blade vertical axis wind turbine,” Energy, vol. 58, pp. 483–493, 2013, https://doi.org/10.1016/j.energy.2013.06.012.Suche in Google Scholar

[64] V. A. F. Costa, “On the stability and convergence of numerical solutions,” Numer. Heat Transf. B: Fundam., vol. 79, no. 2, pp. 55–69, 2020, https://doi.org/10.1080/10407790.2020.1803602.Suche in Google Scholar

[65] A. Yusuf, M. M. Bhatti, and R. Ellahi, “Study of ionic water/graphene nanofluids in solar panels under the effects of thermal radiation and slip conditions using experimental data,” Int. Commun. Heat Mass Tran., vol. 164, p. 108845, 2025, https://doi.org/10.1016/j.icheatmasstransfer.2025.108845.Suche in Google Scholar

[66] J. K. Madhukesh, B. C. Prasannakumara, S. A. Shehzad, M. I. Anwar, and S. Nasir, “Endothermic and exothermic chemical reactions’ influences on a nanofluid flow across a permeable microchannel with a porous medium,” Int. J. Ambient Energy, vol. 45, no. 1, p. 2325515, 2024, https://doi.org/10.1080/01430750.2024.2325515.Suche in Google Scholar

[67] K. Vinutha, B. C. Prasannakumara, J. K. Madhukesh, U. Khan, A. Ishak, and R. Kumar, “Computational analysis of ternary hybrid nanofluids mass transport and Bodewadt flow across a rotating disk driven by waste discharge concentration,” Proc. Inst. Mech. Eng., N: J. Nanomater. Nanoeng. Nanosyst., 2024, 23977914241304625, https://doi.org/10.1177/23977914241304625.Suche in Google Scholar

[68] B. K. Sharma, C. Kumawat, and M. M. Bhatti, “Optimizing energy generation in power-law nanofluid flow through curved arteries with gold nanoparticles,” Numer. Heat Transf. A Appl., vol. 85, no. 18, pp. 3058–3090, 2024, https://doi.org/10.1080/10407782.2023.2232123.Suche in Google Scholar

[69] S. Li, et al.., “Aspects of an induced magnetic field utilization for heat and mass transfer ferromagnetic hybrid nanofluid flow driven by pollutant concentration,” Case Stud. Therm. Eng., vol. 53, p. 103892, 2024, https://doi.org/10.1016/j.csite.2023.103892.Suche in Google Scholar

[70] I. L. Animasaun, T. K. Kumar, F. A. Noah, S. S. Okoya, Q. M. Al-Mdallal, and M. M. Bhatti, “Insight into Darcy flow of ternary-hybrid nanofluid on horizontal surfaces: exploration of the effects of convective and unsteady acceleration,” ZAMM - J. Appl. Math. Mech. Z. Angew. Math. Mech., vol. 103, no. 5, p. e202200197, 2022, https://doi.org/10.1002/zamm.202200197.Suche in Google Scholar

[71] S. U. Khan, K. Ramesh, A. Riaz, M. Awais, and M. M. Bhatti, “Insights into the impact of Cattaneo-Christov heat flux on bioconvective flow in magnetized Reiner-Rivlin nanofluids,” Sep. Sci. Technol., vol. 59, nos. 10-14, pp. 1172–1182, 2024, https://doi.org/10.1080/01496395.2024.2366889.AdnanSuche in Google Scholar

[72] B. C. Prasannakumara, J. K. Madhukesh, and G. K. Ramesh, “Bioconvective nanofluid flow over an exponential stretched sheet with thermophoretic particle deposition,” Propuls. Power Res., vol. 12, no. 2, pp. 284–296, 2023, https://doi.org/10.1016/j.jppr.2023.05.004.Suche in Google Scholar

[73] G. E. Karniadakis, B. B. Mikic, and A. T. Patera, “Minimum-dissipation transport enhancement by flow destabilization: Reynolds’ analogy revisited,” J. Fluid Mech., vol. 192, pp. 365–391, 1988, https://doi.org/10.1017/s0022112088001909.Suche in Google Scholar

[74] F. Sotiropoulos and V. C. Patel, “Turbulence anisotropy and near-wall modeling in predicting three-dimensional shear-flows,” AIAA J., vol. 33, no. 3, pp. 504–514, 1995, https://doi.org/10.2514/3.12605.Suche in Google Scholar

[75] P. S. Bernard, J. M. Thomas, and R. A. Handler, “Vortex dynamics and the production of Reynolds stress,” J. Fluid Mech., vol. 253, pp. 385–419, 1993, https://doi.org/10.1017/s0022112093001843.Suche in Google Scholar

[76] D. Borello, A. Salvagni, and K. Hanjalic, “Effects of rotation on flow in an asymmetric rib-roughened duct: LES study,” Int. J. Heat Fluid Flow, vol. 55, pp. 104–119, 2015, https://doi.org/10.1016/j.ijheatfluidflow.2015.07.012.Suche in Google Scholar

[77] W. W. Willmarth and S. S. Lu, “Structure of the Reynolds stress near the wall,” J. Fluid Mech., vol. 55, no. 1, pp. 65–92, 1972, https://doi.org/10.1017/s002211207200165x.Suche in Google Scholar

[78] J. Sun, D. Kuhn, and G. Naterer, “Eddy viscosity and Reynolds stress models of entropy generation in turbulent channel flows,” J. Fluid Eng., vol. 139, no. 3, p. 034501, 2017, https://doi.org/10.1115/1.4035138.Suche in Google Scholar

Received: 2025-04-30
Accepted: 2025-06-16
Published Online: 2025-07-01
Published in Print: 2025-10-27

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 27.3.2026 von https://www.degruyterbrill.com/document/doi/10.1515/jnet-2025-0046/html
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