ORIGINAL PAPER
Three-dimensional boundary layer dynamics of couple-stress non-Newtonian fluids: MHD effects and generalized flux analysis via OHAM
Muhammad Sohail,
Muhammad Awais Sherani,
Kamaleldin Abodayeh,
Syed Tehseen Abbas,
Corresponding Author
Muhammad Sohail
Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
Composite Materials Scientific Research Center of Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan
Correspondence
Muhammad Sohail, Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, 64200, Pakistan.
Email: [email protected]
Search for more papers by this authorMuhammad Awais Sherani
Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan
Search for more papers by this authorKamaleldin Abodayeh
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
Search for more papers by this authorSyed Tehseen Abbas
Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan
Search for more papers by this authorMuhammad Sohail,
Muhammad Awais Sherani,
Kamaleldin Abodayeh,
Syed Tehseen Abbas,
Corresponding Author
Muhammad Sohail
Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
Composite Materials Scientific Research Center of Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan
Correspondence
Muhammad Sohail, Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, 64200, Pakistan.
Email: [email protected]
Search for more papers by this authorMuhammad Awais Sherani
Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan
Search for more papers by this authorKamaleldin Abodayeh
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
Search for more papers by this authorSyed Tehseen Abbas
Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan
Search for more papers by this authorFirst published: 19 April 2025
Abstract
This paper presents an investigation of the three-dimensional boundary layer dynamics of couple-stress non-Newtonian fluids under MHD effects. The generalized heat and mass flux models are formulated based on the non-Fourier (Cattaneo-Christov) and non-Fick theories. With the application of the Optimal Homotopy Analysis Method (OHAM), the governing equations, developed from momentum, energy, and mass conservation laws, are solved to analyze the intricate interplay between thermal, solutal, and fluid dynamic parameters. The methodology takes into account factors such as rotation, magnetic fields, and others: chemical reactions, thermal radiation, and Brownian motion. The results are extremely insightful: rotational forces retard linear velocity due to increased friction, while magnetic fields reduce flow dynamics. Thermal radiation increases fluid temperature, and increased Prandtl number and relaxation parameters reduce the rates of thermal transmission. Concentration profiles respond dynamically to chemical reaction rates and Brownian motion, and higher reactions enhance delays in particle diffusion. Numerical findings supported by Mathematica reveal that Nusselt and Sherwood numbers increase with thermal and mass transport parameters, confirming enhanced heat and mass transfer under specific conditions.
REFERENCES
- 1Ramzan, M., Farooq, M., Alsaedi, A., Hayat, T.: MHD three-dimensional flow of couple stress fluid with Newtonian heating. Eur. Phys. J. Plus. 128, 1–15 (2013)
- 2Ellahi, R., Zeeshan, A., Shehzad, N., Hussain, A., Sait, S.M.: Mixed convection of two layers with radiative electro-magnetohydrodynamics nanofluid flow in vertical enclosure. Nanotechnology. 35(9), 095402 (2023)
10.1088/1361-6528/ad115b Google Scholar
- 3Zeeshan, A., Ahmad, M., Ellahi, R., Sait, S.M., Shehzad, N.: Hydromagnetic flow of two immiscible nanofluids under the combined effects of Ohmic and viscous dissipation between two parallel moving plates. J. Magn. Magn. Mater. 575, 170741 (2023)
- 4Bhatti, M.M., Bég, O.A., Ellahi, R., Doranehgard, M.H., Rabiei, F.: Electro-magnetohydrodynamics hybrid nanofluid flow with gold and magnesium oxide nanoparticles through vertical parallel plates. J. Magn. Magn. Mater. 564, 170136 (2022)
- 5Awan, F.J., Maqbool, K., Sait, S.M., Ellahi, R.: Buoyancy effect on the unsteady diffusive convective flow of a Carreau fluid passed over a coated disk with energy loss. Coatings. 12(10), 1510 (2022)
- 6Riaz, A., Ellahi, R., Sait, S.M., Muhammad, T.: Magnetized Jeffrey nanofluid with energy loss in between an annular part of two micro non-concentric pipes. Energy Sources A: Recovery Util. Environ. Eff. 44(3), 8314–8333 (2022)
- 7Goodarzi, M., Tlili, I., Moria, H., Alkanhal, T.A., Ellahi, R., Anqi, A.E., Safaei, M.R.: Boiling heat transfer characteristics of graphene oxide nanoplatelets nano-suspensions of water-perfluorohexane (C6F14) and water-n-pentane. Alex. Eng. J. 59(6), 4511–4521. (2020)
- 8Majeed, A., Amin, N., Zeeshan, A., Ellahi, R., Sait, S.M., Vafai, K.: Numerical investigation on activation energy of chemically reactive heat transfer unsteady flow with multiple slips. Int. J. Numer. Methods Heat Fluid Flow. 30(11), 4955–4977 (2020)
- 9Akbar, S., Sohail, M.: Three dimensional MHD viscous flow under the influence of thermal radiation and viscous dissipation. Int. J. Emerg. Multidiscip. Math. 1(3), 106–117 (2022)
- 10Naz, R., Sohail, M., Hayat, T.: Numerical exploration of heat and mass transport for the flow of nanofluid subject to Hall and ion slip effects. Multidiscip. Mod. Mater. Struct. 16(5), 951–965 (2020)
- 11Waseem, F., Sohail, M., Lone, S.A., Chambashi, G.: Numerical simulations of heat generation, thermal radiation and thermal transport in water-based nanoparticles: OHAM study. Sci. Rep. 13(1), 15650 (2023)
- 12Alhazmi, S.E., Wang, F., Nazir, U., Sohail, M., Ali, U., Thounthong, P., Jamshed, W.: Utilization of modified fluxes on thermal and mass transportation in Williamson material. Adv. Mech. Eng. 14(1), 16878140221075874 (2022)
- 13Sarafraz, M.M., Pourmehran, O., Yang, B., Arjomandi, M., Ellahi, R.: Pool boiling heat transfer characteristics of iron oxide nano-suspension under constant magnetic field. Int. J. Therm. Sci. 147, 106131 (2020)
- 14Haider, J.A., Gul, S., Nadeem, S.: Numerical investigation of the heat transfer and peristaltic flow through a asymmetric channel having variable viscosity and electric conductivity. Scientia Iranica. (2023)
10.24200/sci.2023.60404.6783 Google Scholar
- 15Nadeem, S., Ishtiaq, B., Alzabut, J., Ghazwani, H.A., Hassan, A.M.: Unsteady magnetized flow of micropolar fluid with prescribed thermal conditions subject to different geometries. Results Phys. 53, 106946 (2023)
- 16Ishtiaq, B., Nadeem, S., Alzabut, J.: Effects of variable magnetic field and partial slips on the dynamics of Sutterby nanofluid due to biaxially exponential and nonlinear stretchable sheets. Heliyon. 9(7) (2023)
- 17Shahzad, M.H., Nadeem, S., Awan, A.U., Allahyani, S.A., Ahammad, N.A., Eldin, S.M.: On the steady flow of non-Newtonian fluid through multi-stenosed elliptical artery: a theoretical model. Ain Shams Eng. J. 15(1), 102262 (2024)
- 18Baig, M.N.J., Salamat, N., Duraihem, F.Z., Akhtar, S., Nadeem, S., Alzabut, J., Saleem, S.: Exact analytical solutions of stagnation point flow over a heated stretching cylinder: A phase flow nanofluid model. Chin. J. Phys. 86, 1–11 (2023)
- 19Ali, R., Farooq, A., Shahzad, A., Benim, A.C., Iqbal, A., Razzaq, M.: Computational approach on three-dimensional flow of couple-stress fluid with convective boundary conditions. Phys. A. 553, 124056 (2020)
- 20Hayat, T., Muhammad, T., Shehzad, S.A., Alsaedi, A.: Simultaneous effects of magnetic field and convective condition in three-dimensional flow of couple stress nanofluid with heat generation/absorption. J. Braz. Soc. Mech. Sci. Eng. 39, 1165–1176 (2017)
- 21Ullah, A., Ikramullah Selim, M.M., Abdeljawad, T., Ayaz, M., Mlaiki, N., Ghafoor, A.: A magnetite–water-based nanofluid three-dimensional thin film flow on an inclined rotating surface with non-linear thermal radiations and couple stress effects. Energies. 14(17), 5531 (2021)
- 22Rao, T.V.V.L.N., Sufian, S., Mohamed, N.M.: Analysis of nanoparticle additive couple stress fluids in three-layered journal bearing. J. Phys.: Conf. Ser. 431(1), 012023 (2013)
- 23Ibrahim, W., Gamachu, D., Bedada, B.: Entropy generation analysis of three dimensional mixed convection flow of couple stress nanofluid with non-Fourier's heat and non-Fick's mass flux model. Alex. Eng. J. 61(11), 8843–8857 (2022)
- 24Ramzan, M.: Influence of Newtonian heating on three dimensional MHD flow of couple stress nanofluid with viscous dissipation and joule heating. PLoS One. 10(4), e0124699 (2015)
- 25Akram, S., Saleem, N., Umair, M.Y., Munawar, S.: Impact of partial slip and lateral walls on peristaltic transport of a couple stress fluid in a rectangular duct. Sci. Prog. 104(2), 00368504211013632 (2021)
- 26Mahariq, I., Astratov, V., Kurt, H.: Persistence of photonic nanojet formation under the deformation of circular boundary. J. Opt. Soc. Am. B. 33(4), 535–542 (2016)
- 27Mahariq, I., Beryozkina, S., Mohammed, H., Kurt, H.: On the Eddy current losses in metallic towers. Int. J. Renew. Energy Devel. 9(1) (2020)
- 28Mahariq, I., Abdeljawad, T., Karar, A.S., Alboon, S.A., Kurt, H., Maslov, A.V.: Photonic nanojets and whispering gallery modes in smooth and corrugated micro-cylinders under point-source illumination. Photonics. 7(3), 50 (2020)
- 29Mahariq, I., Giden, I.H., Alboon, S., Aly, W.H.F., Youssef, A., Kurt, H.: Investigation and analysis of Acoustojets by spectral element method. Mathematics. 10(17), 3145 (2022)
- 30Mahariq, I.: Reply to Minin, I.V., Minin, O.V. Comment on “Mahariq et al. Investigation and analysis of Acoustojets by spectral element method”. Mathematics. 10(23), 3145 (2022)
10.3390/math10173145 Google Scholar
- 31Mahariq, I., Beryozkina, S.: Experimental realization of electromigration at high power for copper wires. J. Energy Syst. 3(4), 158–167 (2019)
10.30521/jes.616982 Google Scholar
- 32Mahariq, I., Giden, I.H., Kurt, H., Minin, O.V., Minin, I.V.: Strong electromagnetic field localization near the surface of hemicylindrical particles. Opt. Quantum Electron. 50, 423 (2018)
- 33Mahariq, I., Arpaci, I., Kuzuoğlu, M.: Analysis of scattering from perfect electric conducting cylinders by spectral element method. In: Computational Electromagnetics International Workshop (CEM). IEEE, Izmir, Turkey (2015)
- 34Mahariq, I., Eti, N., Kurt, H.: Engineering photonic nano-jet generation. In: Computational Electromagnetics International Workshop. IEEE, Izmir, Turkey (2015)
- 35Li, X., Nutakki, T.U.K., Abdullaev, S., Alzubaidi, L.H., Mahariq, I.: Pollutant removal from aqueous solutions and effective photocatalytic H2 generation by enhanced visible-light-driven S-scheme composite: Response surface methodology optimization and electron transfer pathways. J. Mol. Liq. 411, 125709 (2024)
- 36Zhou, X.,Ding, C., Abed, A.M., Dahari, M., Mahariq, I.: Techno-economic assessment and transient modeling of a solar-based multi-generation system for sustainable/clean coastal urban development. Renew. Energy 233, 121119 (2024)
- 37Zheng, S., Abed, A.M., Chaturvedi, R., Fouad, Y., Mahariq, I.: Energetic/economic/scalability assessment of active solar energy and waste heat utilization in urban environments for H2/freshwater production: A CSP-centered multigeneration system with dual-loop power generation. Process Saf. Environ. Prot. 190, 495–511 (2024)
- 38Lin, H., Zhao, J., Abdulwahab, A., Lin, Z., Mahariq, I.: Development of a comprehensive environmental guidance and sustainability assessment for different organic fraction of municipal solid waste-to-biofuel scenarios based on life cycle analysis. Energy. 304 132073 (2024)
- 39Yan, C., Basem, A., Al-Asadi, H.A., Alhadrawi, M., Mahariq, I.: Novel Fe2O3/Bi2O3/CeO2 heterojunction photocatalyst for wastewater treatment: Characterization, photocatalytic performance and mechanism study. J. Mol. Liq. 410, 125580 (2024)
- 40Rehman, A., Khan, D.,Jan, R., Mahariq, I.: The impact of marangoni convection on carbon nanotube blood base hybrid nanofluid with thermal radiation viscous dissipation and couple stress. BioNanoScience. 14, 814–823 (2024)
- 41Abed, A.M., Chauhan, B.S., Ayed, H., Deifalla, A., Mahariq, I.: Hydrothermal performance analyses of an isothermal tube with punched twisted tape turbulator (PTT). Case Stud. Thermal Eng. 57, 104308 (2024)
- 42Ishaque, M., Laghari, J.A., Bhayo, M.A., Chandio, S., Mahariq, I.: Hybrid ANFIS-PI-based robust control of wind turbine power generation system. Int. Trans. Elect. Energy Syst. (2024). https://doi.org/10.1155/2024/2389751
- 43Channa, I.A., Li, D., Koondhar, M.A., Dahri, F.H., Mahariq, I.: An improved machine learning-based model for detecting and classifying PQDs with high noise immunity in renewable-integrated microgrids. Int. Trans. Elect. Energy Syst. (2024). https://doi.org/10.1155/2024/9118811
- 44Mahariq, I., Saeed, N., Khalil, A., Ijaz, M.: Classes of ordinary differential equations for the alpha power lomax distribution. Contemp. Mathematics. 5(3), 3426–3433 (2025)
- 45Bdaiwi, M., Akroot, A., Wahhab, H.A.A., Mahariq, I.: Numerical analysis of the steam turbine performance in power station with a low power cycle. J. Eng. Sci. Technol. 18, 163–177 (2023)
- 46Al-Meshal, L., Al-Kandari, J., Al-Othman, D., Murshid, N., Mahariq, I.: A possible technique for sea waves energy extraction in Kuwait. In: International Conference on Electrical, Computer, Communications and Mechatronics Engineering. IEEE, Mauritius (2021)
- 47Javed, T., Ali, N., Abbas, Z., Sajid, M.: Flow of an Eyring-Powell non-Newtonian fluid over a stretching sheet. Chem. Eng. Commun. 200(3), 327–336 (2013)
- 48Hayat, T., Aziz, A., Muhammad, T., Ahmad, B.: Influence of magnetic field in three-dimensional flow of couple stress nanofluid over a nonlinearly stretching surface with convective condition. PLoS One. 10(12), e0145332 (2015)
- 49Ibrahim, W.: Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory. Results Phys. 8, 569–577 (2018)
- 50Hayat, T., Muhammad, T., Alsaedi, A., Ahmad, B.: Three-dimensional flow of nanofluid with Cattaneo–Christov double diffusion. Results Phys. 6, 897–903. (2016)
- 51Mabood, F., Yusuf, T.A., Bognár, G.: Features of entropy optimization on MHD couple stress nanofluid slip flow with melting heat transfer and nonlinear thermal radiation. Sci. Rep. 10(1), 19163 (2020)
- 52Sohail, M., Abbas, S.T.: Utilization of variable thermal conductivity and diffusion coefficient on non-Newtonian Prandtl model with modified heat and mass fluxes. Multidiscip. Mod. Mater. Struct. 20(2), 317–340 (2024)
- 53Ali, M.H., Abbas, S.T., Sohail, M., Singh, A.: Study of bioconvection phenomenon in Jefferey model in a Darcy-Forchheimer porous medium. BioNanoScience. 1–13 (2024)
- 54Sohail, M., Rafique, E., Singh, A., Tulu, A.: Engagement of modified heat and mass fluxes on thermally radiated boundary layer flow past over a stretched sheet via OHAM analysis. Discover Appl. Sci. 6(5), 240 (2024)
10.1007/s42452-024-05833-1 Google Scholar
- 55Sohail, M., Ilyas, K., Rafique, E., Singh, A., Jahan, S.: OHAM analysis on bio-convective flow of partial differential equations of casson nanofluid under thermal radiation impact past over a stretching sheet. BioNanoScience. 14, 1572–1582 (2024)
- 56Kavitha, L., Rehman, K.U., Varma, S.V.K., Shatanawi, W., Kumar, G.V., Asghar, Z.: Parametric analysis for Thermally Magnetized Hybrid Ternary (TMHT) nanofluid flow on thin film with temperature stratification. Int. J. Thermofluids. 101089 (2025)
- 57Rehman, K.U., Shatanawi, W., Yian, L.Y.: On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning. Partial Differ. Equ. Appl. Math. 101078 (2025)
10.1016/j.padiff.2025.101078 Google Scholar
- 58Abbas, N., Shatanawi, W., Rehman, K.U. and Shatnawi, T.A.: Velocity and thermal slips impact on boundary layer flow of micropolar nanofluid over a vertical nonlinear stretched Riga sheet. Proc. Inst. Mech. Eng., Part N. 238(3-4), 107–117 (2024)
- 59Prasad, K.V., Mebarek-Oudina, F., Vaidya, H., Choudhari, R., Karanth, S., Tripathi, D.: Tangent hyperbolic MHD nanoliquids on non-isothermal stretched sheets: Analyzing the impact of transport parameters, variable fluid properties and convective boundary conditions. Results Phys. 66, 108008 (2024)
10.1016/j.rinp.2024.108008 Google Scholar
- 60Mebarek-Oudina, F., Dharmaiah, G., Prasad, J.R., Vaidya, H., Kumari, M.A.: Thermal and flow dynamics of magnetohydrodynamic burgers' fluid induced by a stretching cylinder with internal heat generation and absorption. Int. J. Thermofluids. 25, 100986 (2025)
10.1016/j.ijft.2024.100986 Google Scholar
- 61Kazmi, S.N., Hussain, A., Rehman, K.U., Shatanawi, W.: Thermal analysis of hybrid nanoliquid contains iron-oxide (Fe3O4) and copper (Cu) nanoparticles in an enclosure. Alex. Eng. J. 101, 176–185 (2024)
10.1016/j.aej.2024.05.098 Google Scholar
