Analytical and Numerical Analyses of MHD Non-Newtonian Third-Grade Nanofluid in Couette and Poiseuille Flows Using AGM

Abstract:

In the present study, an analytical solution for MHD flow-heat transfer highly non-linear equations of non-Newtonian third-grade nanofluid is established using the AGM method while considering the effect of the magnetic field, the radiation heat transfer, the inclination and the nanoparticles fraction. From dimensionless analysis, the main characteristic parameters are identified, specifically the viscoelastic parameter, the magnetic parameter, the gravitational parameter, the generalized pressure gradient, the thermal radiation parameter, the Brinkman number and the Hamilton number. Two classes of problems, namely, plane Couette flow and plane Poiseuille flow, are considered. Validation was conducted using results from established numerical methods, including Mathematica software, the Adomian Decomposition Method (ADM), and BVP4C solver to benchmark our findings derived via the Akbari Gangi Method. The comparative analysis reveals the reliability and accuracy of the established analytical solutions. The effect of the main parameters of water-SWCNT nanofluid on velocity and temperature profiles are graphically illustrated and discussed. The main results reveal that increasing a magnetic parameter results in a significant drop in the velocity. Furthermore, the rise in Brinkman's number and the radiation parameter affect the temperature differently. Additionally, the viscoelastic and gravitational parameters have opposite velocity and temperature effects. The results demonstrate the complex interaction between several physical characteristic parameters in the fluid dynamics and heat transfer processes. The efficient and highly accurate series-based analytical solutions for flow velocity and temperature obtained through the Akbari-Ganji Method provide valuable insights and are a powerful tool for addressing similar problems in fluid dynamics and heat transfer.

• Periodical: Defect and Diffusion Forum (Volume 444)
• Pages: 57-81
• DOI: https://doi.org/10.4028/p-25jGsj
• Online since: October 2025
• Authors: Karima Azri, Mourad Mecili, El Hacene Mezaache*
• Keywords: Akbari-Ganji Method, Analytical Solution, Couette Flow, Non-Newtonian Fluid, Poiseuille Flow, Third-Grade Fluid

References

[1] S. M. Venthan, P. S. Kumar, S. S. Kumar, S. Sudarsan, and G. Rangasamy, A computational study of the impact of fluid flow characteristics on convective heat transfer with Hall current using the MHD non-Newtonian fluid model, Chemical Engineering Research and Design, 203, 789-799 (2024)

DOI: 10.1016/j.cherd.2024.02.013

[2] M. Shaheen, A. Raza, H. Khursheed, M. Jameel, I. Tlili, S. U. Khan, S. A. Althobaiti, M. Gupta, and M. I. Khan, Applications of magnetic field and porous medium for Jeffrey (non-Newtonian) fluid by using Laplace simulations, Journal of Radiation Research and Applied Sciences, 17(4), 101176 (2024).

DOI: 10.1016/j.jrras.2024.101176

[3] A. D. Ohaegbue, S. O. Salawu, R. A. Oderinu, A. A. Oyewumi, A. O. Akindele, and J. A. Owolabi, Thermal criticality and two-step diffusion-reaction of electromagnetic Casson-Williamson fluid flow along a vertical channel with convective cooling under bimolecular kinetic, Chemical Physics, 587, 112411 (2024). https://doi.org/10.1016/j.chemphys. 2024.112411

DOI: 10.1016/j.chemphys.2024.112411

[4] R. Fathollahi, A. Alizadeh, P. Kamaribidkorpeh, A. M. Abed, and P. Pasha, Analyzing the effect of radiation on the unsteady 2D MHD Al2O3-water flow through parallel squeezing sheets by AGM and HPM, Alexandria Engineering Journal, 69, 207-219 (2023)

DOI: 10.1016/j.aej.2022.11.035

[5] P. M. Zar, B. Jalili, P. Jalili, and D. D. Ganji, Thermal study of magnetohydrodynamic nanofluid flow and brownian motion between parallel sheets, International Journal of Thermofluids, 23, 100806 (2024)

DOI: 10.1016/j.ijft.2024.100806

[6] B. Jalili, P. M. Zar, D. Liu, C.-H. Ji, P. Jalili, M. A. H. Abdelmohimen, and D. D. Ganji, Thermal study of MHD hybrid nano fluids confined between two parallel sheets: Shape factors analysis, Case Studies in Thermal Engineering, 63, 105229 (2024)

DOI: 10.1016/j.csite.2024.105229

[7] Y. M. Aiyesimi, G. T. Okedayo, and O. W. Lawal, Effects of Magnetic Field on the MHD Flow of a Third Grade Fluid through Inclined Channel with Ohmic Heating, Journal of Applied & Computational Mathematics, 3(2), 1000153 (2014)

DOI: 10.4172/2168-9679.1000153

[8] M. Nadeem, I. Siddique, F. Jarad, and R. N. Jamil, Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment, Mathematical Problems in Engineering, (1), 9137479 (2021)

DOI: 10.1155/2021/9137479

[9] I. Khan, T. Chinyoka, E. A. A. Ismail, F. A. Awwad, and Z. Ahmad, MHD flow of third-grade fluid through a vertical micro-channel filled with porous media using semi implicit finite difference method, Alexandria Engineering Journal, 86, 513-524 (2024)

DOI: 10.1016/j.aej.2023.11.070

[10] A. Rauf, F. Batool, N. A. Shah, and J. Chung, The influence of fractional time-derivative on the helical flows of generalized multi-layer immiscible second grade fluids in a cylindrical domain, Ain Shams Engineering Journal, 14, 102145 (2023)

DOI: 10.1016/j.asej.2023.102145

[11] K. Ali, Y.R. Reddy, and B.C. Shekar, Thermo-fluidic transport process in magnetohydrodynamic Couette channel containing hybrid nanofluid, Partial Differential Equations in Applied Mathematics, 7, 100468 (2023). https://doi.org/10.1016/j.padiff.2022. 100468

DOI: 10.1016/j.padiff.2022.100468

[12] R. Derakhshan, A. Shojaei, K. Hosseinzadeh, M. Nimafar, and D. D. Ganji, Hydrothermal analysis of magneto-hydrodynamic nanofluid flow between two parallel by AGM, Case Studies in Thermal Engineering, 14, 100439 (2019). https://doi.org/10.1016/j.csite.2019. 100439

DOI: 10.1016/j.csite.2019.100439

[13] B. Jalili, M. Emad, P. Jalili, D. Domiri Ganji, S. Saleem, and E.M. Tag-eldin, Thermal analysis of boundary layer nanofluid flow over the movable plate with internal heat generation, radiation, and viscous dissipation, Case Studies in Thermal Engineering, 49, 103203 (2023)

DOI: 10.1016/j.csite.2023.103203

[14] L. Ali, B. Ali, A.A.A. Mousa, Z. Hammouch, S. Hussain, I. Siddique, and Y. Huang, Insight into significance of thermal stratification and radiation on dynamics of micropolar water based TiO2 nanoparticle via finite element simulation, Journal of Materials Research and Technology, 19, 4209-4219 (2022)

DOI: 10.1016/j.jmrt.2022.06.043

[15] S. Gouran, S. Mohsenian, and S. E. Ghasemi, Theoretical analysis on MHD nanofluid flow between two concentric cylinders using efficient computational techniques, Alexandria Engineering Journal, 61(4), 3237-3248 (2022).

DOI: 10.1016/j.aej.2021.08.047

[16] I. Siddique, R. M. Zulqarnain, M. Nadeem, and F. Jarad, Numerical Simulation of MHD Couette Flow of a Fuzzy Nanofluid through an Inclined Channel with Thermal Radiation Effect, Computational Intelligence and Neuroscience, 2021(1), 6608684 (2021)

DOI: 10.1155/2021/6608684

[17] D. Gurram, O. Makinde, and K. Balamurugan, Influence of Magneto Hydro Dynamics (MHD) Nonlinear Radiation on Micropolar Nanofluid Flow Over a Stretching Surface: Revised Buongiorno's Nanofluid Model, Journal of Nanofluids, 11, 1009-1022 (2022)

DOI: 10.1166/jon.2022.1890

[18] M. Usman, Y. Hou, F. Ali, M. Zahid, and M. A. Rana, Unveiling the role of MHD forces in Oldroyd 8-constant fluid during Forward roll-coating: Comparing numerical and analytical computations, Results in Physics, 58, 107492 (2024)

DOI: 10.1016/j.rinp.2024.107492

[19] P. A. Bello, K. S. Adegbie, and A. Adewole, Non-adiabatic Couette-Poiseuille flow along catalytic surface reactions with variable properties and thermal radiation, Results in Engineering, 21, 101855 (2024)

DOI: 10.1016/j.rineng.2024.101855

[20] S. S. Ardahaie, A. J. Amiri, A. Amouei, K. Hosseinzadeh, and D. D. Ganji, Investigating the effect of adding nanoparticles to the blood flow in presence of magnetic field in a porous blood arterial, Informatics in Medicine Unlocked, 10, 71-81 (2018)

DOI: 10.1016/j.imu.2017.10.007

[21] N. C. Roy, and I. Pop, Flow and heat transfer of a second-grade hybrid nanofluid over a permeable stretching/shrinking sheet, The European Physical Journal Plus, 135(9), 768 (2020)

DOI: 10.1140/epjp/s13360-020-00788-9

[22] A. Laouer, E. H. Mezaache, and S. Laouar, Influence of surface mass transfer on the stability of forced convection flow over a horizontal flat plate, Computational Thermal Sciences, 8(4), 355-369 (2016)

DOI: 10.1615/ComputThermalScien.2016016415

[23] A. Laouer, E. H. Mezaache, and S. Laouar, Stability Analysis of MHD Fluid Flow over a Moving Plate with Pressure Gradient Using the Chebyshev Spectral Method, International Journal of Engineering Research in Africa, 49, 29-38 (2020). 10.4028/www.scientific.net/ JERA.49.29

DOI: 10.4028/www.scientific.net/jera.49.29

[24] J. Báez-Amador, R. Baños, J. Arcos, F. Méndez, and O. Bautista, Flow enhancement produced by a pulsatile flow of shear-thinning fluids in circular and concentric annular tubes, Journal of Non-Newtonian Fluid Mechanics, 334, 105346 (2024).

DOI: 10.1016/j.jnnfm.2024.105346

[25] P. Jalili, A. Ahmadi Azar, B. Jalili, Z. Asadi, and D. Domiri Ganji, Heat transfer analysis in cylindrical polar system with magnetic field: A novel Hybrid Analytical and Numerical Technique, Case Studies in Thermal Engineering, 40, 102524 (2022)

DOI: 10.1016/j.csite.2022.102524

[26] R. Iranmanesh, S. F. S. Takami, Z. Helforoush, N. Muhammad Diaa, Y. Safari, P. Pasha, A. a. Alizadeh, and H. Zekri, Using analytical methods for finding the approximate solutions to fractional differential equations, International Journal of Thermofluids, 20, 100462 (2023)

DOI: 10.1016/j.ijft.2023.100462

[27] M. Mecili, and E. H. Mezaache, Slug Flow-Heat Transfer in Parallel Plate Microchannel Including Slip Effects and Axial Conduction, Energy Procedia, 36, 268-277 (2013)

DOI: 10.1016/j.egypro.2013.07.031

[28] M. Mecili, and E. Mezaache, Analytical solution for slip flow-heat transfer in microtubes including viscous dissipation and axial heat conduction, International Journal of Heat and Technology, 31, 27-36 (2013)

DOI: 10.18280/ijht.310204

[29] M.M. Mohseni, and F.P. Shariati, First and second laws analysis of viscoelastic fluid with temperature dependent properties for Couette-Poiseuille flow, Propulsion and Power Research, 12(3), 380-396 (2023)

DOI: 10.1016/j.jppr.2023.04.002

[30] M. S. Alqurashi, F. S. Bayones, S. M. Abo-Dahab, A. M. Abd-Alla, and M. S. Soliman, Mixed convection effect on MHD Oldroyd-B nanofluid flow over a stretching sheet through a porous medium with viscous dissipation-chemical engineering applications, Alexandria Engineering Journal, 125, 507–525 (2025)

DOI: 10.1016/j.aej.2025.04.056

[31] S. Daoudi, M. R. Sari, F. L. Rashid, H. Dhahri, A. Mhimid, M. Kezzar, K. Ilyas, K. S. Muhammad, and A.A.Y. Badria, Thermally radiative MHD Jeffery-Hamel flow in a convergent-divergent conduit: A hybrid nanofluid fluid model under nanoparticles shape factor impact, Journal of Radiation Research and Applied Sciences, 18(1):101314 (2025)

DOI: 10.1016/j.jrras.2025.101314

[32] S. Aziz, S. U. Khan, D. H. Qureshi, N. Abdullah, K. Ghachem, A. Eladeb, and L. Kolsi, Nonlinear effects in bioconvective flow of third-grade nanomaterial over stretched Riga plate with modified diffusion, Journal of Radiation Research and Applied Sciences, 18(2):101467 (2025)

DOI: 10.1016/j.jrras.2025.101467

[33] A. A. Aldhafeeri, A numerical analysis of the radiative blood-based hybrid nanofluid flow over an exponentially extending heated surface using a porous medium, Journal of Radiation Research and Applied Sciences, 18(2):101503 (2025)

DOI: 10.1016/j.jrras.2025.101503

[34] J. Shah, M. U. Rehman, I. L. Popa, E. A. A. Ismail, F. A.  Awwad, M. Alqurashi, M. Alqurashi, A. Kumar, and U. Ishtiaq, Radiation effects on heat and mass transfer in porous media using Casson nanofluids: Fractional model with nanoparticles in vegetable oil, Journal of Radiation Research and Applied Sciences, 18 (2): 101505 (2025)

DOI: 10.1016/j.jrras.2025.101505

[35] Adnan, A. Rasheed, K. Alnamasi, A.M.A. Alsharif, and M.N. Bashir, Transport phenomena in Blasius nanofluid model motivated by radiations and dissipation Energy: Investigation for convective surface case, Journal of Radiation Research and Applied Sciences, 18(3):101689 (2025)

DOI: 10.1016/j.jrras.2025.101689

[36] A. Hasibi, A. Gholami, Z. Asadi, and D.D. Ganji, Importance of induced magnetic field and exponential heat source on convective flow of Casson fluid in a micro-channel via AGM, Theoretical and Applied Mechanics Letters, 12(3), 100342 (2022)

DOI: 10.1016/j.taml.2022.100342

[37] B. Jalili, H. Roshani, P. Jalili, M. Jalili, P. Pasha, and D. D. Ganji, The magnetohydrodynamic flow of viscous fluid and heat transfer examination between permeable disks by AGM and FEM, Case Studies in Thermal Engineering, 45, 102961 (2023)

DOI: 10.1016/j.csite.2023.102961

[38] M.R. Akbari, D.D. Ganji, A. Majidian, and A.R. Ahmadi, Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM, Frontiers of Mechanical Engineering, 9 (2), 177-190 (2014)

DOI: 10.1007/s11465-014-0288-8

[39] H. Mirgolbabaee, S. T. Ledari, and D. D. Ganji, Semi-analytical investigation on micropolar fluid flow and heat transfer in a permeable channel using AGM, Journal of the Association of Arab Universities for Basic and Applied Sciences, 24(1), 213-222 (2017)

DOI: 10.1016/j.jaubas.2017.01.002

[40] A.A. Alizadeh, F. Sabet Sarvestani, H. Zekri, M.O. Al-Khafaji, H. Mahmood Salman, D. Domiri Ganji, and P. Pasha, The novelty of using the AGM and FEM for solutions of partial differential and ordinary equations along a stretchable straight cylinder, Case Studies in Thermal Engineering, 45, 102946 (2023)

DOI: 10.1016/j.csite.2023.102946

[41] A. M. Siddiqui, A. Zeb, Q. K. Ghori, and A. M. Benharbit, Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates, Chaos, Solitons & Fractals, 36(1), 182-192 (2008)

DOI: 10.1016/j.chaos.2006.06.037

[42] Javanmard, M., M.H. Taheri, and S.M. Ebrahimi, Heat transfer of third-grade fluid flow in a pipe under an externally applied magnetic field with convection on wall. Applied Rheology, 28, 56023 (2018)

DOI: 10.1016/j.ijmecsci.2017.05.012

[43] M. K. Nayak, G. C. Dash, and L. P. Singh, Steady MHD flow and heat transfer of a third grade fluid in wire coating analysis with temperature dependent viscosity, International Journal of Heat and Mass Transfer, 79, 1087–1095 (2014). https://doi.org/10.1016/j.ijheatmasstransfer. 2014.08.057

DOI: 10.1016/j.ijheatmasstransfer.2014.08.057

[44] T. Hayat, A. Shafiq, and A. Alsaedi, A. (2014). Effect of Joule heating and thermal radiation in flow of third-grade fluid over a radiative surface. PLOS ONE, 9(1), e83153

DOI: 10.1371/journal.pone.0083153

[45] A. Hiremath, G. J. Reddy, M. Kumar, and O. A. Bég, Unsteady free convective heat transfer in third-grade fluid flow from an isothermal vertical plate: A thermodynamic analysis, International Journal of Modern Physics B, 33(8), 1950060 (2019)

DOI: 10.1142/S0217979219500607

[46] E. Pop, D. Mann, Q. Wang, K. Goodson, and H. Dai, Thermal conductance of an individual single-wall carbon nanotube above room temperature, Nano Letters, 6(1), 96-100 (2006)

DOI: 10.1021/nl052145f

[47] D. Hecht, L. Hu, and G. Grüner, Conductivity scaling with bundle length and diameter in single walled carbon nanotube networks, Applied Physics Letters, 89, 133112 (2006)

DOI: 10.1063/1.2356999

[48] F. Du, R. C Scogna, W. Zhou, S. Brand, J. E. Fischer, and K. I. Winey, Nanotube networks in polymer nanocomposites: Rheology and electrical conductivity, Macromolecules, 37(24), 9048–9055 (2004)

DOI: 10.1021/ma049164g

[49] J. Glory, M. Bonetti, M. Helezen, M. Mayne-L'Hermite, C. Reynaud. Thermal and electrical conductivities of water-based nanofluids prepared with long multiwalled carbon nanotubes. Journal of Applied Physics, 103(9), 094309 (2008)

DOI: 10.1063/1.2908229