In this paper, the modified q-Homotopy analysis method (q-HAM) is employed to study the problem of magne tohydrodynamic (MHD) flow of nanofluid under buoyancy effects semi-analytically. The approximate analytic expressions of dimensionless velocity, dimensionless angular velocity, dimensionless temperature and dimension less concentration profiles are given explicitly. We can also derive the approximate analytical expressions for skin friction coefficient, Nusselt Number, and sherwood number. The graphical representation for numerous physical factors involved in the model are provided. This method is also extended to resolve various nonlinear problems in the applied sciences.
[1] V. Ananthaswamy, T. Nithya, and V. K. Santhi, Mathematical analysis of the Navier-stokes equations for steady Magnetohydrodynamic flow, Journal of information and computational science, 10(3) (2020), 989-1003.
[2] K. Bhattacharyya, S. Mukhopadhyay, G. C. Layek, and I. Pop, Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet, Int. J. Heat Mass Transf., 55(11-12) (2012), 2945-2952.
[3] J. Buongiorno, Convective transport in nanofluids, J. Heat Transf., 128(3) (2006), 240-250.
[4] P. Carragher and L. J. Crane, Heat transfer on a continuous stretching sheet, ZAMM-J. Appl. Math. Mech./Zeitschrift fu¨r Angewandte Mathematik und Mechanik, 62(10) (1982), 564-565.
[5] A. J. Chamkha, A. M. Rashad, T. Armaghani, and M. A. Mansour, Effects of partial slip on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu–water nanofluid, J. Therm. Anal. Calorim, 132(2) (2018), 1291-1306.
[6] A. J. Chamkha, R. A. Mohamed, and S. E. Ahmed, Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects, Meccanica, 46(2) (2011), 399-411.
[7] A. J. Chamkha, S. Abbasbandy, A. M. Rashad, and K. Vajravelu, Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid, Meccanica, 48(2) (2013), 275-285.
[8] S. U. Choi and J. A. Eastman, Enhancing thermal Conductivity of Fluids with Nanoparticles (No. ANL/MSD/CP84938; CONF-951135-29), Argonne National Lab., IL (United States), (1995).
[9] L. J. Crane, Flow past a stretching plate, ZAMP (Z. Angew. Math. Phys.), 21 (1970), 645-647.
[10] M. E. M. Khedr, A. J. Chamkha, and M. Bayomi, Combined effect of heat generation or absorption and firstorder chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface., Int. J. Therm. Sci, 48(8) (2009), 1658-1663.
[11] A. C. Eringen, Simple micropolar fluids, Int. J. Eng. Sci., 2 (1964).
[12] A. C. Eringen, Theory of micropolar fluids, J. Math. Mech, 16 (1966), 1-18.
[13] R. S. R. Gorla and A. Chamkha, Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid, Nanoscale Microscale Thermophysem, 15(2) (2011), 81-94.
[14] R. U. Haq, S. Nadeem, N. S. Akbar, and Z. H. Khan, Buoyancy and radiation effect on stagnation point flow of micropolar nanofluid along a vertically convective stretching surface, IEEE Trans. Nanotechnol, 14(1) (2015), 42-50.
[15] T. Hayat, M. I. Khan, M. Waqas, A. Alsaedi, and M. I. Khan, Radiative flow of micro polar Nanofluid accounting thermophoresis and Brownian momen, Int. J. Hydrogen Energy, 42(26) (2017), 16821-16833.
[16] M. E. M. Khedr, A. J. Chamkha, and M. Bayomi, MHD flow of a micropolar fluid past a stretched permeable surface with heat generation or absorption, Nonlinear Anal. Model Control, 14(1) (2009), 27-40.
[17] S. J. Liao, Proposed homotopy analysis techniques for the solution of non-linear Problems, Ph.D. dissertation, Shanghai Jiao Tong University, Shanghai, (1992).
[18] S. J. Liao, An approximate solution technique which does not depend upon small Parameters: a special example, International Journal of Non-linear Mechanics, 30 (1995), 371-380.
[19] S. J. Liao, An approximate solution technique which does not depend upon small Parameters (Part 2): an application in fluid mechanics, International Journal of Non-linear Mechanics., 32 (1997), 815-822.
[20] S. J. Liao, An explicit, totally analytic approximation of Blasius viscous flow problem, International Journal of Non-Linear Mechanics, 385 (1999), 385.
[21] S. J. Liao, A uniformly valid analytic solution of 2D viscous flow past a semi-infinite Flat plate, Journal of Fluid, 385 (1999), 101-128.
[22] S. J. Liao and A. Campo Journal of Fluid MechAnalytic solutions of the temperature distribution in Blasius Viscous flow problems, 453 (2019), 411-425.
[23] L. Ali Lund, Z. Omar, and I. Khan, Mathematical analysis of Magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface, Journal heliyon, (2019), e02432.
[24] G. Lukaszewicz, Micropolar Fluids: Theory and Applications, Brikhauser Basel, (1999).
[25] L. A. Lund, Z. Omar, and I. Khan, Analysis of dual solution for MHD flow of Williamson Fluid with slippage, Heliyon, 5(3) (2019), e01345.
[26] L. A. Lund, Z. Omar, I. Khan, J. Raza, M. Bakouri, and I. Tlili, Stability analysis of Darcy-Forchheimer flow of casson type nanofluid over an exponential sheet: investigation of critical points, Symmetry, 11(3) (2019), 412.
[27] E. Magyari and A. J. Chamkha, Combined effect of heat generation or absorption and First-order chemical reaction on micropolar fluid flows over a uniformly stretched Permeable surface: the full analytical solution, Int. J. Therm. Sci., 49(9) (2010), 1821-1828.
[28] E. Magyari and A. J. Chamkha, Exact analytical results for the thermosolutal MHD Marangoni boundary layers, International Journal of Thermal Sciences, 47(7) (2008), 848-857.
[29] O. Mahian, L. Kolsi, M. Amani, P. Estelle, G. Ahmadi, and C. Kleinstreuer, Recent Advances in Modelling and Simulation of Nanofluid Flows-Part I: Fundamental and theory, Physics Reports, (2018).
[30] M. Miklav and C. Y. Wang, Viscous flow due to a shrinking sheet, Q. Appl. Math., 64 (2006), 283-290.
[31] A. Mudhaf AI and A. J. Chamkha, Similarity solutions for MHD thermosolutal Maranon convection over a flat surface in the presence of heat generation or absorption effects, Heat Mass Transf., 42(2) (2005), 112-121.
[32] N. F. M. Noor, R. U. Haq, S. Nadeem, and I. Hashim, Mixed convection stagnation flow of a micropolar nanofluid along a vertically stretching surface with slip effects, Meccanica, 50(8) (2015), 2007-2022.
[33] C. RamReddy, P. V. S. N. Murthy, A. J. Chamkha, and A. M. Rashad, Soret effect on mixed convection flow in a nanofluid under convective boundary condition, Int. J. Heat Mass Transf., 64 (2013), 384-392.
[34] M. M. Rashidi, M. Reza, and S. Gupta, MHD stagnation point flow of micropolar nanofluid between parallel porous plates with uniform blowing, Powder Technol., 301 (2016), 876-885.
[35] P. S. Reddy and A. J. Chamkha, Soret and Dufour effects on MHD convective flow of Al2O3–water and TiO2–water nanofluids past a stretching sheet in porous media with heat generation/absorption, Adv. Powder Technol, 27(4) (2016), 1207-1218.
[36] P. S. Reddy, P. Sreedevi, and A. J. Chamkha, MHD boundary layer flow, heat and mass transfer analysis over a rotating disk through porous medium saturated by Cu-water and Ag-water nanofluid with chemical reaction, Powder Technol., 307 (2017), 46-55.
[37] B. Seethalakshmi, V. Ananthaswamy, and V. K. Santhi, Mathematical study on non-Linear boundary value problem of boundary layer separation in circular diffuser flows, Journal of Xidian University, 14(7) (2020), 128-147.
[38] D. Sumera, J. Uddin, and A. Rohni, Stefan blowing and slip effects on unsteady nanofluid transport past a shrinking sheet: multiple solutions, Journal of Information and Computational Science, Heat Transf. Asian Res., (2019).
[39] R. K. Tiwari and M. K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transf., 50(9-10) (2007), 2002-2018.
[40] M. Turkyilmazoglu, A note on micropolar fluid flow and heat transfer over a porous shrinking sheet, Int. J. Heat Mass Transf, 72 (2014), 388-391.
[41] M. Turkyilmazoglu, Flow of a micropolar fluid due to a porous stretching sheet and heat transfer, Int. J. NonLinear Mech., 83 (2016), 59-64.
[42] M. Turkyilmazoglu, Free and circular jets cooled by single phase nanofluids, Eur. J. Mech. B Fluid., 76 (2019), 1-6.
[43] M. Turkyilmazoglu, Buongiorno model in a nanofluid filled asymmetric channel Fulfilling zero net particle flux at the walls, Int. J. Heat Mass Transf, 126 (2018), 974-979.
Ananthaswamy, V. and Punitha, S. (2026). A mathematical study on infinite boundary value problem for MHD flow of a micropolar nanofluid. Computational Methods for Differential Equations, 14(2), 701-720. doi: 10.22034/cmde.2025.55531.2311
MLA
Ananthaswamy, V. , and Punitha, S. . "A mathematical study on infinite boundary value problem for MHD flow of a micropolar nanofluid", Computational Methods for Differential Equations, 14, 2, 2026, 701-720. doi: 10.22034/cmde.2025.55531.2311
HARVARD
Ananthaswamy, V., Punitha, S. (2026). 'A mathematical study on infinite boundary value problem for MHD flow of a micropolar nanofluid', Computational Methods for Differential Equations, 14(2), pp. 701-720. doi: 10.22034/cmde.2025.55531.2311
CHICAGO
V. Ananthaswamy and S. Punitha, "A mathematical study on infinite boundary value problem for MHD flow of a micropolar nanofluid," Computational Methods for Differential Equations, 14 2 (2026): 701-720, doi: 10.22034/cmde.2025.55531.2311
VANCOUVER
Ananthaswamy, V., Punitha, S. A mathematical study on infinite boundary value problem for MHD flow of a micropolar nanofluid. Computational Methods for Differential Equations, 2026; 14(2): 701-720. doi: 10.22034/cmde.2025.55531.2311
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