International Journal of Nanoscience and Nanotechnology

International Journal of Nanoscience and Nanotechnology

Magnetohydrodynamic Flow and Heat Transfer Enhancement with Al2O3-Cu Hybrid Ionanofluids over an Exponentially Stretching/Shrinking Permeable Sheet with Heat Generation and Slip Effects

Document Type : Research Paper

Authors
1 Department of Mechanical Engineering, Institute of Engineering and Management, School of University of Engineering and Management (UEM), Kolkata, Saltlake Sector V, Kolkata – 700 091, India
2 Department of Mechanical Engineering, Dr. B. C. Roy Engineering College, Durgapur- 713206, India
3 Department of Mechanical Engineering, Gandhi Academy of Technology and Engineering, Brahmapur, Odisha,761008, India
10.22034/ijnn.2025.2066935.2685
Abstract
Efficient heat transfer fluids are pivotal for high-performance thermal management systems. Although Conventional nanofluids exhibit improved thermal properties, their practical applications are often hindered by agglomeration and flow instability. To overcome these challenges, this study investigates a hybrid ionanofluid, comprising Al2O3 and Cu nanoparticles dispersed in a water–[C2mim] [CH3SO3] ionic liquid mixture under magnetohydrodynamic (MHD) boundary-layer (BL) flow conditions. The study focuses on analyzing how magnetic field strength, heat generation, suction, velocity and thermal slip influence the flow and heat transfer characteristics over an exponentially stretching or shrinking permeable surface. The governing partial differential equations are transformed via similarity variables and solved numerically using MATLAB’s bvp4c solver. A linear stability analysis is further performed to distinguish the physically realizable solution branch in cases of dual solutions. The results demonstrate that the hybrid ionanofluid substantially enhances both skin friction and heat transfer rates compared to conventional hybrid nanofluids, due to the combined effects of ionic liquid properties and nanoparticle synergy. Quantitatively, increasing Cu fraction (from 0.001 to 0.01) raises the local Nusselt number by ~1.7% and skin-friction coefficient by ~2.7%, while delaying bifurcation onset by ~5.4% and lowering suction threshold by ~2.3%. The findings highlight the superior heat transfer capability of hybrid ionanofluids and establish their potential as next-generation working fluids in advanced thermal systems.
Keywords
Subjects

1. Sidik NAC, Adamu IM, Jamil MM, Kefayati GHR, Mamat R, Najafi G. Recent progress on hybrid nanofluids in heat transfer applications: A comprehensive review. Int Commun Heat Mass Transf. 2016;78:68-79. https://doi.org/10.1016/j.icheatmasstransfer.2016.08.019 
2. Huminic G, Huminic A. Hybrid nanofluids for heat transfer applications - A state-of-the-art review. Int J Heat Mass Transf. 2018;125:82-103. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.059 
3. Maxwell JC. A Treatise on Electricity and Magnetism. Oxford: University of Oxford; 1873.
4. Hamilton RL, Crosser OK. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fund. 1962;1(3):187191. https://doi.org/10.1021/i160003a005
5. Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div. 1995;231:99-106. https://doi.org/10.1115/IMECE1995-0926
6. Sarkar J, Ghosh P, Adil A. A review on hybrid nanofluids: Recent research, development and applications. Renew Sustain Energy Rev. 2015;43:164-177. https://doi.org/10.1016/j.rser.2014.11.023 
7. Sundar LS, Sharma KV, Singh MK, Sousa ACM. Hybrid nanofluids preparation, thermal properties, heat transfer and friction factor-A review. Renew Sustain Energy Rev. 2017;68:185-198. https://doi.org/10.1016/j.rser.2016.09.108
8. Babu JR, Kumar KK, Rao SS. State-of-art review on hybrid nanofluids. Renew Sustain Energy Rev. 2017;77:551-565. https://doi.org/10.1016/j.rser.2017.04.040
9. Rohni AM, Ahmad S, Ismail AIM, Pop I. Boundary layer flow and heat transfer over an exponentially shrinking vertical sheet with suction. Int J Therm Sci. 2013;64:264-272. https://doi.org/10.1016/j.ijthermalsci.2012.08.016 
10. Sathish Kumar M, Sandeep N, Rushi Kumar B, Dinesh PA. A comparative analysis of magnetohydrodynamic nonNewtonian fluids flow over an exponential stretched sheet. Alex Eng J. 2018;57(3):2093-2100. https://doi.org/10.1016/j.aej.2017.06.002 
11. Merkin JH, Najib N, Bachok N, Ishak A, Pop I. Stagnationpoint flow and heat transfer over an exponentially stretching/shrinking cylinder. J Taiwan Inst Chem Eng. 2017;74:65-72. https://doi.org/10.1016/j.jtice.2017.02.008
12. Ur Rehman F, Nadeem S, Ur Rehman H, Ul Haq R. Thermophysical analysis for three-dimensional MHD stagnation-point flow of nanomaterial influenced by an exponential stretching surface. Results Phys. 2018;8:316-323. https://doi.org/10.1016/j.rinp.2017.12.026
13. Ghosh S, Mukhopadhyay S. Flow and heat transfer of nanofluid over an exponentially shrinking porous sheet with heat and mass fluxes. Propuls Power Res. 2018;7(3):268-275. https://doi.org/10.1016/j.jppr.2018.07.004 
14. Lund LA, Omar Z, Khan I. Quadruple solutions of mixed convection flow of magnetohydrodynamic nanofluid over exponentially vertical shrinking and stretching surfaces: Stability analysis. Comput Methods Programs Biomed. 2019;182:105044. https://doi.org/10.1016/j.cmpb.2019.105044 
15. Manjunatha S, AmmaniKuttan B, Jayanthi S, Chamkha A, Gireesha BJ. Heat transfer enhancement in the boundary layer flow of hybrid nanofluids due to variable viscosity and natural convection. Heliyon. 2019;5(4):e01469. https://doi.org/10.1016/j.heliyon.2019.e01469 
16. Bumataria RK, Chavda NK, Panchal H. Current research aspects in mono and hybrid nanofluid based heat pipe technologies. Heliyon. 2019;5(5):e01627. https://doi.org/10.1016/j.heliyon.2019.e01627
17. Huminic G, Huminic A, Dumitrache F, Fleaca C, Morjan I. Study of the thermal conductivity of hybrid nanofluids: Recent research and experimental study. Powder Technol. 2020;367:347-357. https://doi.org/10.1016/j.powtec.2020.03.052
18. Bhattacharyya K. Boundary layer flow and heat transfer over an exponentially shrinking sheet. Chin Phys Lett. 2011;28(7):074701. https://doi.org/10.1088/0256307X/28/7/074701 
19. Waini I, Ishak A, Pop I. Mixed convection flow over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid. Alex Eng J. 2020;59(3):1881-1891. https://doi.org/10.1016/j.aej.2020.05.030 
20. Dero S, Rohni AM, Saaban A. Stability analysis of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids with effect of viscous dissipation over stretching and shrinking surfaces using a single-phase model. Heliyon. 2020;6(4):e03510.
21. Khashi’ie NS, Arifin NM, Pop I, Nazar R, Hafidzuddin EH, Wahi N. Flow and heat transfer past a permeable power-law deformable plate with orthogonal shear in a hybrid nanofluid. Alex Eng J. 2020;59(3):1869-1879. https://doi.org/10.1016/j.aej.2020.05.029 
22. Zainal NA, Nazar R, Naganthran K, Pop I. Heat generation/absorption effect on MHD flow of hybrid nanofluid over bidirectional exponential stretching/shrinking sheet. Chin J Phys. 2021;69:118-133. https://doi.org/10.1016/j.cjph.2020.12.002
23. Rao Y. Nanofluids: Stability, phase diagram, rheology and applications. Particuology. 2010;8(6):549-555. https://doi.org/10.1016/j.partic.2010.08.004 
24. Ribeiro APC, Lourenço MJV, Nieto de Castro C, Hardacre C. Thermal conductivity of ‘Bucky Gels’. In: Proceedings of the Conference on Molten Salts and Ionic Liquids (EUCHEM2008). Copenhagen; 2008:24-29.
25. Nieto de Castro C. Thermophysical properties of ionic liquids: Do we know how to measure them accurately? J Mol Liq. 2010;156(1):10-17. https://doi.org/10.1016/j.molliq.2010.06.007 
26. Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf. 1998;11(2):151-170. https://doi.org/10.1080/08916159808946559
27. Xuan Y, Roetzel W. Conceptions for heat transfer correlation of nanofluids. Int J Heat Mass Transf. 2000;43(19):3701-3707. https://doi.org/10.1016/S0017-9310(99)00369-5
28. Titan CP, Morshed AKMM, Fox E, Khan AJ. Enhanced thermophysical properties of NEILs as heat transfer fluids for solar thermal applications. Appl Therm Eng. 2017;110:19. https://doi.org/10.1016/j.applthermaleng.2016.08.004
29. Minea AA, El-Maghlany WM. Influence of hybrid nanofluids on the performance of parabolic trough collectors in solar thermal systems: Recent findings and numerical comparison. Renew Energy. 2018;120:350-364. https://doi.org/10.1016/j.renene.2017.12.09330. Chereches EI, Viswanatha Sharma K, Minea AA. A numerical approach in describing ionanofluids behavior in laminar and turbulent flow. Continuum Mech Thermodyn. 2018;31(2):497506. https://doi.org/10.1007/s00161-018-0634-x
31. Minea AA, El-Maghlany WM. Natural convection heat transfer utilizing ionic nanofluids with temperature-dependent thermophysical properties. Chem Eng Sci. 2017;174:1324. https://doi.org/10.1016/j.ces.2017.08.028
32. Minea AA, Moldoveanu MG, Dodun O. Thermal conductivity enhancement by adding nanoparticles to ionic liquids. Solid State Phenom. 2017;261:121-126. https://doi.org/10.4028/www.scientific.net/SSP.261.121
33. Asghar A, Dero S, Lund LA, Shah Z, Alshehri MH, Vrinceanu N. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface. Open Phys. 2024;22:20240052. https://doi.org/10.1515/phys2024-0052 
34. Asghar A, Teh YY, Javed Iqbal M, Ali L. Thermal characterization of hybrid nanofluid with impact of convective boundary layer flow and Joule heating law: Dual solutions case study. Mod Phys Lett B. 2024;38:2450158. https://doi.org/10.1142/S0217984924501586 
35. Soomro AM, Lund LA, Asghar A, Bonyah E, Shah Z, Garalleh HA. Magnetized Casson SA-hybrid nanofluid flow over a permeable moving surface with stability analysis. Int J Thermofluids. 2024;21:100555. https://doi.org/10.1016/j.ijft.2023.100555 
36. Asghar A, Hanafy H, Fadhel MA, Lund LA, Khan SU, Tlili I. DarcyForchheimer radiative flow of a hybrid nanofluid with velocity mass flux and thermal stability. J Porous Media. 2025;28(5):7187. https://doi.org/10.1615/JPorMedia.2024051851 
37. Asghar A, Nangraj AR, Dero S, Shah NA, Lund LA. Dual solutions for the Darcy-Forchheimer porous medium with convective heat transfer effect on rotating hybrid nanofluid. Z Angew Math Mech. 2025;105:e70046. https://doi.org/10.1002/zamm.70046
38. Asghar A, Ying TY, Lund LA, Shah Z, Vrinceanu N, Islam S. Radiative porosity sodium alginate hybrid nanofluid flow over an exponential stretching/shrinking surface: Dual solutions. Nano-Struct Nano-Objects. 2025;42:101463. https://doi.org/10.1016/j.nanoso.2025.101463 
39. Asghar A, Govindarajoo MV, Ara H, Zaimi K, Ying TY, Lund LA. Effect of water-based alumina-copper MHD hybrid nanofluid on a power-law form stretching/shrinking sheet with Joule heating and slip condition: Dual solutions study. CFD Lett. 2024;17(3):119-135. https://doi.org/10.37934/cfdl.17.4.119135 
40. Fadhel MA, Asghar A, Lund LA, Shah Z, Vrinceanu N, Tirth V. Dual numerical solutions of Casson SA-hybrid nanofluid toward a stagnation point flow over stretching/shrinking cylinder. Nanotechnol Rev. 2024;13:20230191. https://doi.org/10.1515/ntrev-2023-0191 
41. Ramya D, Rao JA, Shravani I. Numerical Simulation of MHD Boundary Layer Stagnation Flow of Nanofluid over a Stretching Sheet with Slip and Convective Boundary Conditions. Int J Nanosci Nanotechnol. 2020;16(2):103-115.
42. Peiravi MM, Ashabi A. Magneto Effects on Fe3O4 Nanoparticles through the Triangular and Rectangular Baffles on Thread Stretching Surface for Rotary Seals in Computer Hardware. Int J Nanosci Nanotechnol. 2022;18(3):143-156.
43. Devi SSU, Devi SPA. Numerical investigation of three-dimensional hybrid Cu-Al₂O₃/water nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heating. Can J Phys. 2016;94(5):490-496. https://doi.org/10.1139/cjp-20150799 
44. Waini I, Ishak A, Pop I. Hybrid nanofluid flow induced by an exponentially shrinking sheet. Chin J Phys. 2019;60:125-133.
45. Ghosh S, Mukhopadhyay S. Stability analysis for model based study of nanofluid flow over an exponentially shrinking permeable sheet in presence of slip. Neural Comput Appl. 2020;32(11):7201-7211. https://doi.org/10.1007/s00521-01904221-w 
46. Mukhopadhyay S, Andersson HI. Effects of slip and heat transfer analysis of flow over an unsteady stretching surface. Heat Mass Transf. 2009;45(11):1447-1452. https://doi.org/10.1007/s00231-009-0516-7 
47. Eid MR, Nafe MA. Thermal conductivity variation and heat generation effects on magneto-hybrid nanofluid flow in a porous medium with slip condition. Waves Random Complex Media. 2020;32(6):2835-2859. https://doi.org/10.1080/17455030.2020.1810365 
48. Hayat T, Nadeem S. Heat transfer enhancement with Ag-CuO/water hybrid nanofluid. Results Phys. 2017;7:2317-2324. https://doi.org/10.1016/j.rinp.2017.06.034
49. Merkin JH. On dual solutions occurring in mixed convection in a porous medium. J Eng Math. 1986;20(2):171-179. https://doi.org/10.1007/BF00042775 
50. Weidman PD, Kubitschek DG, Davis AMJ. The effect of transpiration on self-similar boundary layer flow over moving surfaces. Int J Eng Sci. 2006;44(11-12):730-737. https://doi.org/10.1016/j.ijengsci.2006.04.005 
51. Yan L, Dero S, Khan I, Mari IA, Baleanu D, Nisar KS, et al. Dual solutions and stability analysis of magnetized hybrid nanofluid with Joule heating and multiple slip conditions. Processes. 2020;8(3):332. https://doi.org/10.3390/pr8030332
52. Chereches EI, Minea AA. Experimental evaluation of electrical conductivity of ionanofluids based on water-[C₂mim][CH₃SO₃] ionic liquids mixtures and alumina nanoparticles. J Therm Anal Calorim. 2021;145(6):3151-3157. https://doi.org/10.1007/s10973-020-09925-z 
53. Datta A, Kumar S, Halder P. Heat transfer and thermal characteristics effects on moving plate impinging from Cu water nanofluid jet. J Therm Sci. 2020;29(1):182-193. https://doi.org/10.1007/s11630-019-1107-7 
54. Datta A, Halder P. Thermal efficiency and hydraulic performance evaluation on Ag-Al₂O₃ and SiC-Al₂O₃ hybrid nanofluid for circular jet impingement. Arch Thermodyn. 2021;42(1):163182. https://doi.org/10.24425/ather.2021.136953
55. Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20(4):571-581. https://doi.org/10.1063/1.1700493 
56. Kierzenka J, Shampine LF. A BVP solver based on residual control and the MATLAB PSE. ACM Trans Math Softw. 2001;27(3):299316. https://doi.org/10.1145/502800.502801
57. Hafidzuddin MEH, Nazar R, Arifin NM, Pop I. Boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity. J Appl Fluid Mech. 2016;9(4):2025-2036. https://doi.org/10.18869/acadpub.jafm.68.235.24834 
58. Ishak A. MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malays. 2011;40(4):391-395.
59. Magyari E, Keller B. Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J Phys D Appl Phys. 1999;32(5):577-585. https://doi.org/10.1088/00223727/32/5/012 
60. Bidin B, Nazar R. Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. Eur J Sci Res. 2009;33(4):710-717.
61. Tiwari RK, Das MK. Heat transfer augmentation in a two sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf. 2007;50(9-10):2002-2018. https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.034