The current study provides a comprehensive analysis of MHD hybrid nanofluids and stagnation point flow toward a porous stretched cylinder in the presence of thermal radiation. Here, alumina (Al₂O₃) and copper (Cu) are considered the hybrid nanoparticles, while water (H₂O) is the base fluid. To begin, the required similarity transformations are applied to transform the nonlinear coupled PDEs into nonlinear coupled ODEs. The obtained highly nonlinear sets of ODEs are then solved analytically by using the HAM procedure. The calculations of the thermal radiation term in the energy equation are done based on the Roseland approximation. The result of various embedded variables on temperature and velocity profiles is drawn and explained briefly. Aside from that, the numerical solution of well-known physical quantities, like skin friction and the Nusselt number, is computed by means of tables for the modification of the relevant parameter. The analysis shows that the magnetic field has opposite behavior on θ(η) and f'(η) profiles. It is seen that more magnetic factors M decline f'(η) and upsurge θ(η). Moreover, the behavior of skin friction and the Nusselt number are the same for the magnetic parameter M. Meanwhile, a higher Reynolds number R_e declines temperature profile and skin friction while upsurging the local Nusselt number. There are many applications of this study that are not limited to engineering and manufacturing, such as polymer industry, crystal growth, tumor therapy, plasma, fusing metal in electric heaters, nuclear reactors, asthma treatment, gastric medication, cooling of atomic systems, electrolytic biomedicine, helical coil heat exchangers, axial fan design, polymer industry, plane counter jets, and solar collectors.

1. Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. In: Proceedings of the 1995 International Mechanical Engineering Congress and Exhibition; 12–17 November 1995; San Francisco, CA, United States. pp. 99–105.

2. Sheikholeslami M, Soleimani S, Ganji DD. Effect of electric field on hydrothermal behavior of nanofluid in a complex geometry. Journal of Molecular Liquids 2016; 213: 153–161. doi: 10.1016/j.molliq.2015.11.015

3. Hamad MAA, Pop I, Md Ismail AI. Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate. Nonlinear Analysis: Real World Applications 2011; 12(3): 1338–1346. doi: 10.1016/j.nonrwa.2010.09.014

4. Khan Z, Srivastava HM, Mohammed PO, et al. Thermal boundary layer analysis of MHD nanofluids across a thin needle using non-linear thermal radiation. Mathematical Biosciences and Engineering 2022; 19(12): 14116–41141. doi: 10.3934/mbe.2022658

5. Huminic G, Huminic A. Hybrid nanofluids for heat transfer applications—A state-of-the-art review. International Journal of Heat and Mass Transfer 2018; 125: 82–103. doi: 10.1016/j.ijheatmasstransfer.2018.04.059

6. Gabli A, Kezzar M, Zighed L, et al. Simultaneous impacts of Fe3O4 particles and thermal radiation on natural convection of non-Newtonian Flow between two vertical flat plates using ADM. Journal of Non-Equilibrium Thermodynamics 2020; 45(2): 173–189. doi: 10.1515/jnet-2019-0083

7. Sundar LS, Singh MK, Sousa ACM. Enhanced heat transfer and friction factor of MWCNT–Fe3O4/water hybrid nanofluids. International Communications in Heat and Mass Transfer 2014; 52: 73–83. doi: 10.1016/j.icheatmasstransfer.2014.01.012

8. Momin GG. Experimental investigation of mixed convection with water-Al2O3 & hybrid nanofluid in inclined tube for laminar flow. International Journal of Scientific & Technology Research 2013; 12(2): 195–202.

9. Bachok N, Ishak A, Pop I. Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid. International Journal of Heat and Mass Transfer 2012; 55(25–26): 8122–8128. doi: 10.1016/j.ijheatmasstransfer.2012.08.051

10. Merkin JH, Najib N, Bachok N, et al. Stagnation-point flow and heat transfer over an exponentially stretching/shrinking cylinder. Journal of the Taiwan Institute of Chemical Engineers 2017; 74: 65–72. doi: 10.1016/j.jtice.2017.02.008

11. Hussain S, Ahmed SE, Akbar T. Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle. International Journal of Heat and Mass Transfer 2017; 114: 1054–1066. doi: 10.1016/j.ijheatmasstransfer.2017.06.135

12. Dhinesh Kumar D, Valan Arasu A. A comprehensive review of preparation, characterization, properties and stability of hybrid nanofluids. Renewable and Sustainable Energy Reviews 2018; 81: 1669–1689. doi: 10.1016/j.rser.2017.05.257

13. Sajid MU, Ali HM. Thermal conductivity of hybrid nanofluids: A critical review. International Journal of Heat and Mass Transfer 2018; 126: 211–234. doi: 10.1016/j.ijheatmasstransfer.2018.05.021

14. Hemmat Esfe M, Wongwises S, Naderi A, et al. Thermal conductivity of Cu/TiO2–water/EG hybrid nanofluid: Experimental data and modeling using artificial neural network and correlation. International Communications in Heat and Mass Transfer 2015; 66: 100–104. doi: 10.1016/j.icheatmasstransfer.2015.05.014

15. Zadkhast M, Toghraie D, Karimipour A. Developing a new correlation to estimate the thermal conductivity of MWCNT-CuO/water hybrid nanofluid via an experimental investigation. Journal of Thermal Analysis and Calorimetry 2017; 129(2): 859–867. doi: 10.1007/s10973-017-6213-8

16. Pourrajab R, Noghrehabadi A, Behbahani M, Hajidavalloo E. An efficient enhancement in thermal conductivity of water-based hybrid nanofluid containing MWCNTs-COOH and Ag nanoparticles: Experimental study. Journal of Thermal Analysis and Calorimetry 2021; 143(5): 3331–3343. doi: 10.1007/s10973-020-09300-y

17. Oztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow 2008; 29(5): 1326–1336. doi: 10.1016/j.ijheatfluidflow.2008.04.009

18. Homann F. The need for high speed in the flow around the cylinder and around the sphere (German). Zeitschrift fur Angewandte Mathematik und Mechanik 1936; 16: 153–164. doi: 10.1002/zamm.19360160304

19. Weidman PD. Non-axisymmetric Homann stagnation-point flows. Journal of Fluid Mechanics 2012; 702: 460–469. doi: 10.1017/jfm.2012.197

20. Jawad M, Khan Z, Bonyah E, Jan R. Analysis of hybrid nanofluid stagnation point flow over a stretching surface with melting heat transfer. Mathematical Problems in Engineering 2022; 2022: 1–12. doi: 10.1155/2022/9469164

21. Khan Z, Jawad M, Bonyah E, et al. Magnetohydrodynamic thin film flow through a porous stretching sheet with the impact of thermal radiation and viscous dissipation. Mathematical Problems in Engineering 2022; 2022: 1–10. doi: 10.1155/2022/1086847

22. Borrelli A, Giantesio G, Patria MC. Numerical simulations of three-dimensional MHD stagnation-point flow of a micropolar fluid. Computers & Mathematics with Applications 2013; 66(4): 472–489. doi: 10.1016/j.camwa.2013.05.023

23. Grosan T, Pop I, Revnic C, Ingham DB. Magnetohydrodynamic oblique stagnation-point flow. Meccanica 2009; 44(5): 565–572. doi: 10.1007/s11012-009-9196-0

24. Wang CY. Stagnation flow on a plate with anisotropic slip. European Journal of Mechanics—B/Fluids 2013; 38: 73–77. doi: 10.1016/j.euromechflu.2012.10.005

25. Wang CY. Off-centered stagnation flow towards a rotating disc. International Journal of Engineering Science 2008; 46(4): 391–396. doi: 10.1016/j.ijengsci.2008.01.014

26. Wang CY. Stagnation flow towards a shrinking sheet. International Journal of Non-Linear Mechanics 2008; 43(5): 377–382. doi: 10.1016/j.ijnonlinmec.2007.12.021

27. Ahmed J, Shahzad A, Farooq A, et al. Radiative heat transfer in Homann stagnation-point flow of hybrid nanofluid. Applied Nanoscience 2020; 10(12): 5305–5314. doi: 10.1007/s13204-020-01464-1

28. Anuar NS, Bachok N, Pop I. Cu-Al2O3/water hybrid nanofluid stagnation point flow past MHD stretching/shrinking sheet in presence of homogeneous-heterogeneous and convective boundary conditions. Mathematics 2020; 8(8): 1237. doi: 10.3390/math8081237

29. Sreekala B, Janardhan K, Ramya D, Shravani I. MHD boundary layer nanofluid flow of heat transfer over a nonlinear stretching sheet presence of thermal radiation and partial slip with suction. Global Journal of Pure and Applied Mathematics 2017; 13(9): 4927–4941.

30. Jawad M, Shah Z, Islam S, et al. Impact of nonlinear thermal radiation and the viscous dissipation effect on the unsteady three-dimensional rotating flow of single-wall carbon nanotubes with aqueous suspensions. Symmetry 2019; 11(2): 207. doi: 10.3390/sym11020207

31. Jawad M, Saeed A, Kumam P, et al. Analysis of boundary layer MHD Darcy-Forchheimer radiative nanofluid flow with Soret and Dufour effects by means of Marangoni convection. Case Studies in Thermal Engineering 2021; 23: 100792. doi: 10.1016/j.csite.2020.100792

32. Khashi’ie NS, Arifin NM, Rashidi MM, et al. Magnetohydrodynamics (MHD) stagnation point flow past a shrinking/stretching surface with double stratification effect in a porous medium. Journal of Thermal Analysis and Calorimetry 2020; 139(6): 3635–3648. doi: 10.1007/s10973-019-08713-8

33. Mohd Nasir NAA, Ishak A, Pop I. Stagnation-point flow and heat transfer past a permeable quadratically stretching/shrinking sheet. Chinese Journal of Physics 2017; 55(5): 2081–2091. doi: 10.1016/j.cjph.2017.08.023

34. Kamal F, Zaimi K, Ishak A, Pop I. Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect. International Journal of Numerical Methods for Heat & Fluid Flow 2018; 28(11): 2650–2663. doi: 10.1108/HFF-01-2018-0031

35. Kamal F, Zaimi K, Ishak A, Pop I. Stability analysis of MHD stagnation-point flow towards a permeable stretching/shrinking sheet in a nanofluid with chemical reactions effect. Sains Malaysiana 2019; 48(1): 243–250. doi: 10.17576/jsm-2019-4801-28

36. Khashi’ie NS, Md Arifin N, Nazar R, et al. A stability analysis for magnetohydrodynamics stagnation point flow with zero nanoparticles flux condition and anisotropic slip. Energies 2019; 12(7): 1268. doi: 10.3390/en12071268

37. Khashi’ie NS, Arifin NM, Pop I, et al. Non-axisymmetric Homann stagnation point flow and heat transfer past a stretching/shrinking sheet using hybrid nanofluid. International Journal of Numerical Methods for Heat & Fluid Flow 2020; 30(10): 4583–4606. doi: 10.1108/hff-11-2019-0824

38. Khashi’ie NS, Arifin NM, Nazar R, et al. Magnetohydrodynamics (MHD) axisymmetric flow and heat transfer of a hybrid nanofluid past a radially permeable stretching/shrinking sheet with Joule heating. Chinese Journal of Physics 2020; 64: 251–263. doi: 10.1016/j.cjph.2019.11.008

39. Srivastava HM, Khan Z, Mohammed PO, et al. Heat transfer of buoyancy and radiation on the free convection boundary layer MHD flow across a stretchable porous sheet. Energies 2022; 16(1): 58. doi: 10.3390/en16010058

40. Wang CY. Fluid flow due to a stretching cylinder. The Physics of Fluids 1988; 31(3): 466–468. doi: 10.1063/1.866827

41. Butt AS, Ali A, Mehmood A. Numerical investigation of magnetic field effects on entropy generation in viscous flow over a stretching cylinder embedded in a porous medium. Energy 2016; 99: 237–249. doi: 10.1016/j.energy.2016.01.067

42. Rehman KU, Al-Mdallal QM, Qaiser A, et al. Finite element examination of hydrodynamic forces in grooved channel having two partially heated circular cylinders. Case Studies in Thermal Engineering 2020; 18: 100600. doi: 10.1016/j.csite.2020.100600

43. Abbas Z, Rasool S, Rashidi MM. Heat transfer analysis due to an unsteady stretching/shrinking cylinder with partial slip condition and suction. Ain Shams Engineering Journal 2015; 6(3): 939–945. doi: 10.1016/j.asej.2015.01.004

44. Abaszadeh M, Safavinejad A, Amiri H, Amiri Delouei A. A direct-forcing IB-LBM implementation for thermal radiation in irregular geometries. Journal of Thermal Analysis and Calorimetry 2022; 147(20): 11169–11181. doi: 10.1007/s10973-022-11328-1

45. Abaszadeh M, Safavinejad A, Amiri Delouei A, Amiri H. Analysis of radiative heat transfer in two-dimensional irregular geometries by developed immersed boundary-lattice Boltzmann method. Journal of Quantitative Spectroscopy and Radiative Transfer 2022; 280: 108086. doi: 10.1016/j.jqsrt.2022.108086

46. Atashafrooz M, Sajjadi H, Amiri Delouei A. Simulation of combined convective-radiative heat transfer of hybrid nanofluid flow inside an open trapezoidal enclosure considering the magnetic force impacts. Journal of Magnetism and Magnetic Materials 2023; 567: 170354. doi: 10.1016/j.jmmm.2023.170354

47. Al Sakkaf LY, Al-Mdallal QM, Al Khawaja U. A numerical algorithm for solving higher-order nonlinear BVPs with an application on fluid flow over a shrinking permeable infinite long cylinder. Complexity 2018; 2018: 1–11. doi: 10.1155/2018/8269541

48. Cunning GM, Davis AMJ, Weidman PD. Radial stagnation flow on a rotating circular cylinder with uniform transpiration. Journal of Engineering Mathematics 1998; 33(2): 113–128. doi: 10.1023/A:1004243728777

49. Wan Zaimi WMKA, Ishak A, Pop I. Unsteady viscous flow over a shrinking cylinder. Journal of King Saud University-Science 2013; 25(2): 143–148. doi: 10.1016/j.jksus.2012.11.005

50. Waini I, Ishak A, Pop I. Hybrid nanofluid flow towards a stagnation point on a stretching/shrinking cylinder. Scientific Reports 2020; 10(1): 9296. doi: 10.1038/s41598-020-66126-2

51. Devi SPA, Devi SSU. Numerical investigation of hydromagnetic hybrid Cu–Al2O3/water nanofluid flow over a permeable stretching sheet with suction. International Journal of Nonlinear Sciences and Numerical Simulation 2016; 17(5): 249–257. doi: 10.1515/ijnsns-2016-0037

52. Waini I, Ishak A, Pop I. Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid. International Journal of Heat and Mass Transfer 2019; 136: 288–297. doi: 10.1016/j.ijheatmasstransfer.2019.02.101

53. Oztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow 2008; 29(5): 1326–1336. doi: 10.1016/j.ijheatfluidflow.2008.04.009

54. Liao S. The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems [PhD thesis]. Shanghai Jiao Tong University; 1992.

55. Li Y, Nohara BT, Liao S. Series solutions of coupled Van der Pol equation by means of homotopy analysis method. Journal of Mathematical Physics 2010; 51(6): 063517. doi: 10.1063/1.3445770

56. Liao S. A kind of approximate solution technique which does not depend upon small parameters—II. An application in fluid mechanics. International Journal of Non-Linear Mechanics 1997; 32(5): 815–822. doi: 10.1016/S0020-7462(96)00101-1

57. Liao S. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. Journal of Fluid Mechanics 2003; 488: 189–212. doi: 10.1017/S0022112003004865

58. S. Liao, A new branch of solutions of boundary-layer flows over an impermeable stretched plate. International Journal of Heat and Mass Transfer 2005; 48(12): 2529–2539. doi: 10.1016/j.ijheatmasstransfer.2005.01.005

59. Liao S. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical 2010; 15(8): 2003–2016. doi: 10.1016/j.cnsns.2009.09.002

60. Liao S, Tan Y. A general approach to obtain series solutions of nonlinear differential equations. Studies in Applied Mathematics 2007; 119(4): 297–354. doi: 10.1111/j.1467-9590.2007.00387.x