journal article·2026-01-23Open access

Comparative RSM-based study of nano, hybrid, and ternary nanofluid heat transfer with Cattaneo–Christov flux in porous media

Usman Afzal, Khalid Masood, Azhar Ali Zafar, Rizwan A. Farade, Nehad Ali Shah, Jae Dong Chung

Nanotechnology Reviews· Volume 15· Issue 1

Abstract

Abstract This study conducts a comparative analysis of nano, hybrid, and ternary nanofluids in an Oldroyd-B fluid model within a Darcy–Forchheimer porous medium, focusing on heat transfer efficiency. It examines the effects of thermal radiation, heat source/sink, viscous dissipation, relaxation, and retardation time under different thermophysical conditions. Nanofluids are widely used in medicine, electronic cooling, heat exchangers, and renewable energy systems. However, the comparative performance of nano, hybrid, and ternary nanofluids in an Oldroyd-B framework remains unexplored. This study fills this gap by evaluating TiO 2 , Fe 3 O 4 , and CoFe 3 O 4 nanoparticles and optimizing their thermal efficiency using numerical and statistical modeling. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity variables and solved with the BVP4C method. Response surface methodology (RSM) is applied for parameter optimization, while multilinear regression analysis provides further insights. Graphical and tabulated results show that nano nanofluids achieve the highest heat transfer, followed by hybrid, while ternary nanofluids perform the lowest due to increased resistance. Thermal radiation improves heat transfer, whereas the Forchheimer number reduces it. The obtained findings can guide the selection of nanofluids for high-performance heat exchangers, magnetohydrodynamic (MHD) cooling systems, solar-thermal collectors, nuclear and industrial cooling, and biomedical thermal regulation technologies. The integration of RSM further provides a practical optimization framework for engineering design and performance improvement in energy-efficient systems. These findings offer valuable insights into optimizing nanofluid-based thermal systems, aiding advancements in heat exchangers, MHD cooling, and energy-efficient technologies.
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Research context

OpenAlex topics: Nanofluid Flow and Heat Transfer · Solar Thermal and Photovoltaic Systems · Solar Energy Systems and Technologies

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Mechanical Engineering , Sejong University , Seoul , 05006 , Republic of Korea

Department of Mathematics and Statistics , College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU) , Riyadh , 11623 , Saudi Arabia

Department of Mathematics , Government College University , Lahore , 54000 , Pakistan

Department of Electrical and Electronic Engineering, Faculty of Engineering , Advanced Lighting, ALPER, University Putra Malaysia , 43400 , Serdang , Malaysia

References (40)

Show source-provided references
1. Cengel, YA, Cimbala, JM. Fluid mechanics fundamentals and applications, 3rd ed. New York: Mc Graw Hill; 2013.
2. White, FM. Viscous fluid flow. New York: McGraw-Hill Education, third; 2005:656 p.
3. Lin, W, Zhang, P, Lin, J. Flow and heat transfer property of Oldroyd-B-Fluid-Based nanofluids containing cylindrical particles in a pipe. Processes (MDPI) 2021;9:647. https://doi.org/10.3390/pr9040647.10.3390/pr9040647 ↗
4. Fetecau, C, Imran, M, Fetecau, C, Burdujan, I. Helical flow of an Oldroyd-B fluid due to a circular cylinder. Z Angew Math Phys 2010;61:959–69. https://doi.org/10.1007/s00033-009-0038-7.10.1007/s00033-009-0038-7 ↗
5. Kamran, M, Athar, M, Imran, M. Critical study on rotational flow of a fractional Oldroyd-B fluid through an infinite circular cylinder. Int Scholarly Res Network 2012 (2011):1–15. https://doi.org/10.5402/2012/835398.10.5402/2012/835398 ↗
6. Sanchez, HAC, Jovanovic, MR, Kumar, S, Morozov, A, Shankar, V, Subramanian, G, et al.. Understanding viscoelastic flow instabilities: Oldroyd-B fluids. J Non-Newtonian Fluid Mech 2022;302:1047425. https://doi.org/10.1016/j.jnnfm.2022.104742.10.1016/j.jnnfm.2022.104742 ↗
7. Shakeel, A, Ahmad, S, Khan, H, Shah, NA, Haq, SU. Flows with slip of Oldroyd-B fluids over a moving plate. Adv Mathematic Phys 2016:1–9. https://doi.org/10.1155/2016/8619634.10.1155/2016/8619634 ↗
8. Jamil, M, Khan, NA, Imran, MA. New exact solutions for an Oldroyd-B fluid with fractional derivatives: Stokes’ first problem. Int J Nonlinear Sci Numer Simulation 2014;14:7–8. https://doi.org/10.1515/ijnsns-2011-024.10.1515/ijnsns-2011-024 ↗
9. Si, X, Lei, X, Xu, B, Li, B, Zhu, J, Cao, L. The periodic secondary flow of Oldroyd-B fluids driven by direct electric field in a rectangular curved channel. Phys Fluids 2023;35:032005. https://doi.org/10.1063/5.0138394.10.1063/5.0138394 ↗
10. Ganji, DD, Malvandi, A. Heat transfer enhancement using nanofluid flow in microchannels: simulation of heat and mass transfer. Oxford, UK: William Andrew; 2016.10.1016/B978-0-323-43139-2.00004-6 ↗
11. Ghassemi, M, Shahidian, A. Nano and bio heat transfer and fluid flow. London, UK: Academic Press; 2017.
12. Priyadharshini, P, Archana, MV, Shah, NA, Alsheri, MH. Ternary hybrid nanofluid flow emerging on a symmetrically. Symmetry 2023;15:1225. https://doi.org/10.3390/sym15061225.10.3390/sym15061225 ↗
13. Abrar, MN. Thermal investigation of casson hybrid nanoparticles over a porous stretchable plate: a Cattaneo–Christov heat flux model. J Therm Anal Calorim 2024;150:1–12. https://doi.org/10.1007/s10973-024-13279-1.10.1007/s10973-024-13279-1 ↗
14. Rehman, M, Turkyilmazoglu, M, Mushtaq, Z. Effects of multiple shapes for steady flow with transformer oil+Fe3O4+TiO2 nanofluids. Appl Math Mech 2024;45:373–88. https://doi.org/10.1007/s10483-024-3088-7.10.1007/s10483-024-3088-7 ↗
15. Revathi, G, Rao, DP, Rao, SR, Babu, KS, Prasad, TV, Babu, MJ. Entropy generation optimization in a ree-eyring ternary hybrid nanofluid flow over an elastic surface with non-fourier heat flux. East Eur J Phys 2024:122–33. https://doi.org/10.26565/2312-4334-2024-4-11.10.26565/2312-4334-2024-4-11 ↗
16. Narayana Naik, R, Suneetha, S, Srinivasa Babu, KS, Jayachandra Babu, M. Entropy optimization in ternary hybrid nanofluid flow over a convectively heated bidirectional stretching sheet with Lorentz forces and viscous dissipation: a Cattaneo–Christov heat flux model. Proc Inst Mech Eng Part E J Process Mech Eng 2024:09544089241275779.10.1177/09544089241275779 ↗
17. Naik, RN, Suneetha, S, Babu, KS, Babu, MJ. Impact of exponential heat source and thermal radiation on the flow of hybrid nanofluid across a bi-directional stretching surface with activation energy J Phys Conf 2024;2765:012003.10.1088/1742-6596/2765/1/012003 ↗
18. Acharya, N, Maity, S, Kundu, PK. Framing the hydrothermal features of magnetized TiO2–CoFe2O4 water-based steady hybrid nanofluid flow over a radiative revolving disk. Multidiscip Model Mater Struct 2020;16:765–90. https://doi.org/10.1108/MMMS-08-2019-0151.10.1108/MMMS-08-2019-0151 ↗
19. Nasir, S, Sirisubtawee, S, Juntharee, P, Berrouk, AS, Mukhtar, S, Gul, T. Heat transport study of ternary hybrid nanofluid flow under magnetic dipole effect. Appl Nanosci 2022;12:2777–88. https://doi.org/10.1007/s13204-022-02583-7.10.1007/s13204-022-02583-7 ↗
20. Guedri, K, Khan, A, Sene, N, Raizah, Z, Saeed, A, Galal, AM. Thermal flow for radiative ternary hybrid nanofluid over nonlinear stretching sheet subject to darcy–forchheimer phenomenon. Math Probl Eng 2022;2022:14. https://doi.org/10.1155/2022/3429439.10.1155/2022/3429439 ↗
21. Adun, H, Kavaz, D, Dagbasi, M. Review of ternary hybrid nanofluid: synthesis, stability, thermophysical properties, heat transfer applications, and environmental effects. J Clean Prod 2021;328:129525. https://doi.org/10.1016/j.jclepro.2021.129525.10.1016/j.jclepro.2021.129525 ↗
22. Rasheed, T, Hussain, T, Anwar, MT, Ali, J, Rizwan, K, Bilal, M, et al.. Hybrid nanofluids as renewable and sustainable colloidal suspensions for potential photovoltaic/thermal and solar energy applications. Front Chem 2021;9:737033. https://doi.org/10.3389/fchem.2021.737033.10.3389/fchem.2021.737033 ↗
23. Yasmin, H, Giwa, So., Noor, S, Sharifpur, M. Experimental exploration of hybrid nanofluids as energy-efficient fluids in solar and thermal energy storage applications. Nanomaterials 2023;13:278. https://doi.org/10.3390/nano13020278.10.3390/nano13020278 ↗
24. Soudagar, MEM, Ramesh, S, Khan, TMU, Almakayeel, N, Ramesh, R, Ghazali, NNN, et al.. An overview of the existing and future state of the art advancement of hybrid energy systems based on PV-solar and wind. Int J Low Carbon Technol 2024;19:207–16. https://doi.org/10.1093/ijlct/ctad123.10.1093/ijlct/ctad123 ↗
25. Mukhtar, S, Gul, T. Solar radiation and thermal convection of hybrid nanofluids for the optimization of solar collector. Mathematics 2023;11:11758 75. https://doi.org/10.3390/math11051175.10.3390/math11051175 ↗
26. Freedman, JP, Wang, H, Prasher, RS. Analysis of nanofluid-based parabolic trough collectors for solar thermal applications. J Sol Energy Eng 2018;140:051008–1. https://doi.org/10.1115/1.4039988.10.1115/1.4039988 ↗
27. Abrar, MN, Kosar, S, Razzaq, R. Thermal investigation of micro-polar tangent hyperbolic flow using a hybrid nanofluid approach. J Appl Phys 2025;137:034302. https://doi.org/10.1063/5.0243611.10.1063/5.0243611 ↗
28. Razzaq, R, Khan, Z, Abrar, MN, Almohsen, B, Farooq, U. Chemical reaction and radiation analysis for the MHD casson nanofluid fluid flow using artificial intelligence. Chaos Solitons Fractals 2025;190:115756. https://doi.org/10.1016/j.chaos.2024.115756.10.1016/j.chaos.2024.115756 ↗
29. Menni, Y, Chamkha, AJ, Lorenzini, G, Kaid, N, Ameur, H, Bensafi, M. Advances of nanofluids in solar collectors - a review of numerical studies. Mathematic Modell Eng Problems 2019;6:415–27. https://doi.org/10.18280/mmep.060313.10.18280/mmep.060313 ↗
30. Abdelrazik, AS, Osama, A, Allam, AN, Shboul, B, Sharafedin, MA, Elwardany, M, et al.. ANSYS-fluent numerical modeling of the solar thermal and hybrid photovoltaic-based solar harvesting systems. J Therm Anal Calorim 2023;148:11373–424. https://doi.org/10.1007/s10973-023-12509-2.10.1007/s10973-023-12509-2 ↗
31. Jamshed, W, Sirin, C, Selimefendigil, F, Shamshuddin, MD, Altowairqi, Y, Eid, MR. Thermal characterization of coolant maxwell type nanofluid flowing in parabolic trough solar collector (PTSC) used inside solar powered ship application. Coatings 2021;11:1552. https://doi.org/10.3390/coatings11121552.10.3390/coatings11121552 ↗
32. Reddy, MG, Sandeep, N. Enhanced heat transfer in hydrodynamic non-Newtonian film flows past an extending cylinder: a hydrogen energy application. Waves Random Complex Media 2022;35:1–14. https://doi.org/10.1080/17455030.2022.2086322.10.1080/17455030.2022.2086322 ↗
33. Khuri, AI, Mukhopadhyay, S. Response surface methodology. Wiley Interdiscip Rev: Comput Stat 2010;2:128–49. https://doi.org/10.1002/wics.73.10.1002/wics.73 ↗
34. Maddina, DK, Díaz Palencia, JL. Response surface optimisation on non-uniform shapes ternary hybrid nanofluid flow in stenosis artery with motile gyrotactic microorganisms. Chem Phys 2024;590. http://hdl.handle.net/20.500.12226/2592.10.1016/j.chemphys.2024.112539 ↗
35. Yasir, M, Ahmed, A, Khan, M, Alzahrani, AK, Malik, ZU, Alshehri, AM. Mathematical modelling of unsteady Oldroyd-B fluid flow due to stretchable cylindrical surface with energy transport. Ain Shams Eng J 2023;14:101825. https://doi.org/10.1016/j.asej.2022.101825.10.1016/j.asej.2022.101825 ↗
36. Lu, D, Li, Z, Ramzan, M, Shafee, A, Chung, JD. Unsteady squeezing carbon nanotubes-based nano-liquid flow with Cattaneo–Christov heat flux and homogeneous–heterogeneous reactions. Appl Nanosci 2019;9:169–78. https://doi.org/10.1007/s13204-018-0899-1.10.1007/s13204-018-0899-1 ↗
37. Khan, NS, Gul, T, Islam, S, Khan, I, Alqahtani, AM, Alshomrani, AS. Magnetohydrodynamic nano liquid thin film sprayed on a stretching cylinder with heat transfer. Appl Sci 2017;7:271. https://doi.org/10.3390/app7030271.10.3390/app7030271 ↗
38. Kumar, J, Sandeep, N. Computational analysis to examine the role of nanoparticle shape on operative usage of solar energy. Int J Hydrogen Energy 2024;56:937–48. https://doi.org/10.1016/j.ijhydene.2023.12.228.10.1016/j.ijhydene.2023.12.228 ↗
39. Negi, AS, Kumar, B. Nano-ferrofluid (Mn–Zn, CoFe2O4, Fe3O4) flow in a permeable channel with induced magnetic field. Waves Random Complex Media 2023:1–28. https://doi.org/10.1080/17455030.2023.2165193.10.1080/17455030.2023.2165193 ↗
40. Jan, A, Mushtaq, M, Hussain, M. Heat transfer enhancement of forced convection magnetized cross model ternary hybrid nanofluid flow over a stretching cylinder: non-similar analysis. Int J Heat Fluid Flow 2024;106:109302. https://doi.org/10.1016/j.ijheatfluidflow.2024.109302.10.1016/j.ijheatfluidflow.2024.109302 ↗