Deep learning–driven investigations of thermal performance in GO–SWCNT–MWCNT/H 2 O-based ternary nanofluids flow over a stretching sheet: a comparative analysis of steady and unsteady states using Levenberg–Marquardt neural network model
Source abstract
Abstract
Abstract This paper explores the thermal and hydrodynamic characteristics of a GO–SWCNT–MWCNT/H 2 O ternary nanofluid when passing through a stretching sheet under steady and unsteady flow with the consideration of magnetic field and thermal radiations. Similarity variables are used to transform the governing nonlinear partial differential equations, which are solved in the finite element method (FEM). The effect on the velocity, temperature, concentration, and skin-friction coefficient, Nusselt number, and Sherwood number of nanoparticle volume fractions, magnetic parameter, Prandtl number, and Schmidt number is examined. It has been found that when nanoparticle volume fractions are increased, thermal performance is greatly increased, and that the thermal boundary layer is observably thickening. Growth of the magnetic parameter decreases velocity owing to the effects of Lorentz forces and increases temperature owing to the improvements in Joule heating. With increasing Prandtl number, the thickness of the thermal boundary layer is decreased and the rate of convective heat transfer is enhanced. The models of artificial neural network (ANN) are applied to gain better predictive power through the Levenberg–Marquardt (LM) and Bayesian Regularization (BR) algorithms on FEM-generated data. BR model has a higher predictive accuracy as its overall regression coefficient is R = 0.92195 than the LM model with regression coefficient R = 0.61285. The results give a quantitative understanding of how ternary nanofluid systems may be optimized to serve advanced thermal management systems in industrial cooling systems and energy systems.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Nanofluid Flow and Heat Transfer · Fluid Dynamics and Vibration Analysis · Phase Change Materials Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Humanities and Basic Sciences , G Pulla Reddy Engineering College , Kurnool , 518007 , Andhra Pradesh , India
Department of Mechanical Engineering , RGM College of Engineering and Technology , Nandyala , Andhra Pradesh , 518501 , India
Future Interdisciplinary Research of Science and Technology, Institute of Innovative Research , Tokyo Institute of Technology , 4259-R2-23 Nagatsutacho, Midoriku , Yokohamashi , Kanagawa , 226-8503 Japan
Department of Mechanical Engineering , Sreyas Institute of Engineering and Technology , Hyderabad , 500068 , Telangana , India
Department of Mathematics , Koneru Lakshmaiah Education Foundation , Vaddeswaram , Guntur , 522302 , Andhra Pradesh , India
Department of Mechanical Engineering , Lloyd Institute of Engineering & Technology , Knowledge Park II , Greater Noida , Uttar Pradesh , 201306 , India
Jadara University Research Center , Jadara University , Jordan
Departamento de Ciencias de la Construcción, Facultad de Ciencias de la Construcción Ordenamiento Territorial , Universidad Tecnológica Metropolitana , Santiago , 8330383 , Chile
Faculty of Educational Sciences , Al-Ahliyya Amman University , Amman , 19328 , Jordan
Department of Biosciences, Saveetha School of Engineering , Saveetha Institute of Medical and Technical Sciences , Chennai , 602105 , India
Electrical Engineering Department, College of Engineering , King Khalid University , Abha , 61421 , Saudi Arabia
Queen’s University Belfast , 19 Chlorine Gardens , Belfast , Northern Ireland , BT9 5DL , UK
References (34)
Show source-provided references
1. Atofarati, EO, Sharifpur, M, Huan, Z. Nanofluids for heat transfer enhancement: a holistic analysis of research advances, technological progress, and regulations for health and safety. Cogent Eng 2024;11:2434623. https://doi.org/10.1080/23311916.2024.2434623.10.1080/23311916.2024.2434623 ↗
2. Fatunmbi, EO, Obalalu, AM, Khan, U, Hussain, SM, Muhammad, T. Model development and heat transfer characteristics in renewable energy systems conveying hybrid nanofluids subject to nonlinear thermal radiation. Multidiscip Model Mater Struct 2024;20:1328–42. https://doi.org/10.1108/MMMS-05-2024-0128.10.1108/MMMS-05-2024-0128 ↗
3. Galal, AM, Alharbi, FM, Arshad, M, Alam, MM, Abdeljawad, T. Convective heat transfer analysis of hybrid nanofluid over shrinking/stretching surfaces with velocity slip. J Therm Anal Calorim 2024;150:22215–26. https://doi.org/10.1007/s10973-024-13725-0.10.1007/s10973-024-13725-0 ↗
4. Wang, J, Yang, X, Klemeš, JJ, Tian, K, Ma, T, Sunden, B. A review on nanofluid stability: preparation and application. Renew Sustain Energy Rev 2023;188:113854. https://doi.org/10.1016/j.rser.2023.113854.10.1016/j.rser.2023.113854 ↗
5. Afzal, F, Kamran, T. Advanced heat transfer analysis of 3D magnetohydrodynamic nanofluid flow over an extending sheet with thermal radiation and internal heat generation/absorption. Multiscale Multidiscip Model Exp Des 2025;8:113. https://doi.org/10.1007/s41939-024-00693-z.10.1007/s41939-024-00693-z ↗
6. Kumar, K, Singh, B, Kumar, P, Nisar, KS, Abdel-Aty, AH, Alkhazaleh, S, et al.. Heat and mass transfer effect in stagnation point flow of MHD Jeffery nanofluid flow over a porous stretching sheet with thermal radiation. Int J Thin Films Sci Technol 2024;13:47–58. https://doi.org/10.18576/ijtfst/130106.10.18576/ijtfst/130106 ↗
7. Kodi, R, Ganteda, C, Dasore, A, Kumar, ML, Laxmaiah, G, Hasan, MA, et al.. Influence of MHD mixed convection flow for Maxwell nanofluid through a vertical cone with porous material in the existence of variable heat conductivity and diffusion. Case Stud Therm Eng 2023;44:102875. https://doi.org/10.1016/j.csite.2023.102875.10.1016/j.csite.2023.102875 ↗
8. Shree, SU, Hanumagowda, BN, Saini, G, Singh, K, Kulshreshta, A, Varma, SVK, et al.. Heat and mass transfer in electrically conducting hybrid nanofluid flow between two rotating parallel stretching surfaces: an entropy analysis. Multiscale Multidiscip Model Exp Des 2025;8:18. https://doi.org/10.1007/s41939-024-00635-9.10.1007/s41939-024-00635-9 ↗
9. Konda, JR, NP, MR, Konijeti, R, Dasore, A. Effect of non-uniform heat source/sink on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium. Multidiscip Model Mater Struct 2019;15:452–72. https://doi.org/10.1108/MMMS-01-2018-0011.10.1108/MMMS-01-2018-0011 ↗
10. Haider, S, Syed Muhammad, I, Li, YZ, Butt, AS. Numerical study of unsteady boundary layer flow and heat transmission of a nanofluid past a continuously stretching sheet immersed in porous media. Int J Numer Methods Heat Fluid Flow 2020;30:1589–602. https://doi.org/10.1108/HFF-11-2018-0664.10.1108/HFF-11-2018-0664 ↗
11. Imoro, I, Etwire, CJ, Musah, R. MHD flow of blood-based hybrid nanofluid through a stenosed artery with thermal radiation effect. Case Stud Therm Eng 2024;59:104418. https://doi.org/10.1016/j.csite.2024.104418.10.1016/j.csite.2024.104418 ↗
12. Jyothi, K, Reddy, PS, Reddy, MS. Carreau nanofluid heat and mass transfer flow through wedge with slip conditions and nonlinear thermal radiation. J Braz Soc Mech Sci Eng 2019;41:415. https://doi.org/10.1007/s40430-019-1904-7.10.1007/s40430-019-1904-7 ↗
13. Waqas, H, Farooq, U, Liu, D, Abid, M, Imran, M, Muhammad, T. Heat transfer analysis of hybrid nanofluid flow with thermal radiation through a stretching sheet: a comparative study. Int Commun Heat Mass Transf 2022;138:106303. https://doi.org/10.1016/j.icheatmasstransfer.2022.106303.10.1016/j.icheatmasstransfer.2022.106303 ↗
14. Gupta, R. Modeling of artificial neural network to analyze heat and mass transfer of ternary hybrid nanofluid between two parallel plates with inclined magnetic field. Numer Heat Transf A Appl 2026;87:2366445. https://doi.org/10.1080/10407782.2024.2366445.10.1080/10407782.2024.2366445 ↗
15. Jyothi, K, Dasore, A, Ganapati, R, Shareef, SM, Chamkha, AJ, Prasad, VR. Comparative numerical analysis of heat and mass transfer characteristics in Sisko Al2O3-EG and TiO2-EG fluids on a stretched surface. Front Heat Mass Transf 2024;22:79–105. https://doi.org/10.32604/fhmt.2024.046891.10.32604/fhmt.2024.046891 ↗
16. Mahmood, Z, Duraihem, FZ, Adnan, Khan, U, Hassan, AM. Model-based comparative analysis of MHD stagnation point flow of hybrid nanofluid over a stretching sheet with suction and viscous dissipation. Numer Heat Transf B Fundam 2025;86:1639–60. https://doi.org/10.1080/10407790.2024.2318457.10.1080/10407790.2024.2318457 ↗
17. Kotike, J, Beedalannagari, O, Rekapalli, L, Usman, M, Kadavakollu, KR. Neural network modeling of CuO/Au hybrid nanofluid thermal performance with slip effects for advanced process applications. Processes 2025;13:516. https://doi.org/10.3390/pr13020516.10.3390/pr13020516 ↗
18. Arshad, S, Hussain, A, Hassan, A, Wróblewski, P, Elfasakhany, A, Elkotb, MA, et al.. Thermal energy investigation of magneto-hydrodynamic nano-material liquid flow over a stretching sheet: comparison of single and composite particles. Alexandria Eng J 2022;61:10453–62. https://doi.org/10.1016/j.aej.2022.03.069.10.1016/j.aej.2022.03.069 ↗
19. Majeed, A, Amanat, A, Rosalind Mary, GL, Altohamy, AA, Alsayegh, R, Khan, SU, et al.. Thermally developed radiated flow of single and multiple carbon nanotubes with variable thermal conductivity. J Radiat Res Appl Sci 2025;18:101244. https://doi.org/10.1016/j.jrras.2024.101244.10.1016/j.jrras.2024.101244 ↗
20. Jiang, X, Hatami, M, Abderrahmane, A, Younis, O, Makhdoum, BM, Guedri, K. Mixed convection heat transfer and entropy generation of MHD hybrid nanofluid in a cubic porous cavity with wavy wall and rotating cylinders. Appl Therm Eng 2023;226:120302. https://doi.org/10.1016/j.applthermaleng.2023.120302.10.1016/j.applthermaleng.2023.120302 ↗
21. Returi, MC, Konijeti, R, Dasore, A. Heat transfer enhancement using hybrid nanofluids in spiral plate heat exchangers. Heat Transf Asian Res 2019;48:3128–43. https://doi.org/10.1002/htj.21534.10.1002/htj.21534 ↗
22. Mliki, E, Hamdi, R, Jaffali, S, Al-Ohali, M. Statistical comparison of models and machine learning for predicting Arrhenius parameters in ternary liquid mixtures. J Mol Liq 2025;421:126933. https://doi.org/10.1016/j.molliq.2025.126933.10.1016/j.molliq.2025.126933 ↗
23. Winklbauer, L, Burger, J. Chemical equilibrium and liquid-liquid equilibrium in ternary mixtures of formaldehyde, water, and isobutanol/n-butanol between 295 K and 348 K. Fluid Phase Equilib 2025;594:114364. https://doi.org/10.1016/j.fluid.2025.114364.10.1016/j.fluid.2025.114364 ↗
24. Sadrmousavi-Dizaj, A, Xu, D, Zhang, L, Gao, J, Ma, Y, Wang, Y. Liquid-liquid equilibria and intermolecular interactions for extraction of 2-methyl phenol, 3-methyl phenol, and phenol from water by a ternary hydrophobic deep eutectic solvent. J Taiwan Inst Chem Eng 2025;167:105845. https://doi.org/10.1016/j.jtice.2024.105845.10.1016/j.jtice.2024.105845 ↗
25. Generous, MM, Abu-Nada, E, Alazzam, A. Exploring the potential of hybrid nanofluids for enhanced heat transfer in a duct: a comprehensive study utilizing a phases-interaction driven multiphase mixture model. Int J Thermofluids 2023;20:100453. https://doi.org/10.1016/j.ijft.2023.100453.10.1016/j.ijft.2023.100453 ↗
26. Adnan, W, Abbas, W, Alqahtani, AM, Mahmood, Z, Beinane, SAO, Bilal, M. Numerical heat featuring in radiative convective ternary nanofluid under induced magnetic field and heat generating source. Int J Mod Phys B 2025;39:2550044. https://doi.org/10.1142/S0217979225500444.10.1142/S0217979225500444 ↗
27. Alqawasmi, K, Alharbi, KAM, Farooq, U, Noreen, S, Imran, M, Akgül, A, et al.. Numerical approach toward ternary hybrid nanofluid flow with nonlinear heat source-sink and Fourier heat flux model passing through a disk. Int J Thermofluids 2023;18:100367. https://doi.org/10.1016/j.ijft.2023.100367.10.1016/j.ijft.2023.100367 ↗
28. MathWorks. MATLAB & Simulink: regression [Internet]. 2023 [cited 2026 May 11]. Available from: https://www.mathworks.com/help/stats/regression-and-anova.html.
29. Mishra, A, Rawat, SK, Yaseen, M, Pant, M. Development of machine learning algorithm for assessment of heat transfer of ternary hybrid nanofluid flow towards three different geometries: case of artificial neural network. Heliyon 2023;9:e21453. https://doi.org/10.1016/j.heliyon.2023.e21453.10.1016/j.heliyon.2023.e21453 ↗
30. Shatnawi, TAM, Abbas, N, Shatanawi, W. Comparative study of Casson hybrid nanofluid models with induced magnetic radiative flow over a vertical permeable exponentially stretching sheet. AIMS Mathematics 2022;7:20545–64. https://doi.org/10.3934/math.20221126.10.3934/math.20221126 ↗
31. Mishra, A. Performance analysis of the radiative Reiner-Philippoff hybrid nanofluid flow over a stretching/shrinking sheet under the effect of suction. Pramana 2025;99:1–15. https://doi.org/10.1007/s12043-025-02952-1.10.1007/s12043-025-02952-1 ↗
32. Mishra, A, Gunjan, P. Thermal-flow characteristics of an Ellis hybrid nanofluid containing polytetrafluoroethylene-SWCNTs over a stretching/shrinking cylinder with slip effect. Nano-Structures & Nano-Objects 2025;43:1–17. https://doi.org/10.1016/j.nanoso.2025.101515.10.1016/j.nanoso.2025.101515 ↗
33. Mishra, A. Hydrothermal performance of hybrid nanofluid flow over an exponentially stretching sheet influenced by gyrotactic microorganisms: a comparative evaluation of Yamada-Ota and Xue models. Numerical Heat Transfer, Part A: Applications 2025;86:8817–46. https://doi.org/10.1080/10407782.2024.2363496.10.1080/10407782.2024.2363496 ↗
34. Mishra, A. Thompson and Troian slip effects on ternary hybrid nanofluid flow over a permeable plate with chemical reaction. Numerical Heat Transfer, Part B: Fundamentals 2025;86:2640–68. https://doi.org/10.1080/10407790.2024.2346929.10.1080/10407790.2024.2346929 ↗