Innovative semi-analytical approaches to micropolar MHD fluid flow between stretching disks under radiant heat flux

  • Ali Ahmadi Azar Department of Mechanical Engineering, NT.C., Islamic Azad University, Tehran, Iran
Article ID: 2838
Keywords: MHD flow; semi-analytical methods; stretchable disks; modified AGM; HAN-method

Abstract

This study investigates the viscous, incompressible, laminar, time-independent micropolar MHD fluid flow between two stretching disks under radiant heat flux, with applications in industrial systems like turbines and nuclear reactors. Using suitable similarity transformations, the nonlinear constitutive equations are reduced to coupled ODEs and solved through two novel semi-analytical approaches: the Hybrid Analytical-Numerical method (HAN method), which constructs analytical solutions from numerical data, and the modified Akbari-Ganji Method (modified AGM) that operates independently of numerical solutions. Results demonstrate that stretching Reynolds number, magnetic parameter, and three micropolar parameters significantly affect all five dimensionless quantities (axial/radial velocity, microrotation, temperature, and concentration), while Eckert number variations cause a 16.5% maximum temperature increase when doubled from 1 to 2. A 429% temperature surge occurs as the Prandtl number rises from 3 to 22, whereas the Schmidt number (0.1–1.5) only modifies the concentration profile shape without changing extrema. The radiation parameter (0–8) alters temperature distribution between disks without affecting maxima/minima. Three validation methods confirm solution accuracy: graphical verification, comparison with existing analytical results, and cross-method consistency between HAN and modified AGM outputs. The study’s innovative dual-method approach coupled with 3D contour visualizations provides unprecedented semi-analytical solutions for this classical problem, offering both theoretical advancement and practical industrial insights.

Published
2025-06-26
How to Cite
Ahmadi Azar, A. (2025). Innovative semi-analytical approaches to micropolar MHD fluid flow between stretching disks under radiant heat flux. Mechanical Engineering Advances, 3(2), 2838. https://doi.org/10.59400/mea2838
Section
Article

References

[1]Agarwal R. Heat and mass transfer in electrically conducting micropolar fluid flow between two stretchable disks. Materials Today: Proceedings. 2021; 46: 10227-10238. doi: 10.1016/j.matpr.2020.11.614

[2]Jalili P, Ahmadi Azar A, Jalili B, et al. Heat transfer analysis in cylindrical polar system with magnetic field: A novel Hybrid Analytical and Numerical Technique. Case Studies in Thermal Engineering. 2022; 40: 102524. doi: 10.1016/j.csite.2022.102524

[3]Eringen AC. Simple microfluids. International Journal of Engineering Science. 1964; 2(2): 205-217. doi: 10.1016/0020-7225(64)90005-9

[4]Eringen AC. Theory of Micropolar Fluids. Indiana University Mathematics Journal. 1966; 16(1): 1-18. doi: 10.1512/iumj.1967.16.16001

[5]Eringen AC. Microcontinuum Field Theories: I. Foundations and Solids. Springer New York; 2012.

[6]Lukaszewicz G. Micropolar Fluids: Theory and Applications. Birkhäuser Boston; 2012.

[7]Turkyilmazoglu M. Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform suction or injection. International Journal of Mechanical Sciences. 2010; 52(12): 1735-1744. doi: 10.1016/j.ijmecsci.2010.09.007

[8]Turkyilmazoglu M. Purely analytic solutions of magnetohydrodynamic swirling boundary layer flow over a porous rotating disk. Computers & Fluids. 2010; 39(5): 793-799. doi: 10.1016/j.compfluid.2009.12.007

[9]Turkyilmazoglu M. Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform vertical magnetic field. Acta Mechanica. 2010; 218(3-4): 237-245. doi: 10.1007/s00707-010-0416-4

[10]Sahoo B, Van Gorder RA, Andersson HI. Steady revolving flow and heat transfer of a non-Newtonian Reiner–Rivlin fluid. International Communications in Heat and Mass Transfer. 2012; 39(3): 336-342. doi: 10.1016/j.icheatmasstransfer.2011.12.007

[11]Srivastava N. MHD Flow of the Micropolar Fluid between Eccentrically Rotating Disks. International Scholarly Research Notices. 2014; 2014: 1-7. doi: 10.1155/2014/317075

[12]Iqbal MF, Ali K, Ashraf M. Heat and mass transfer analysis in unsteady titanium dioxide nanofluid between two orthogonally moving porous coaxial disks: a numerical study. Canadian Journal of Physics. 2015; 93(3): 290-299. doi: 10.1139/cjp-2014-0243

[13]Kocic M, Stamenkovic Z, Petrovic J, et al. Heat transfer in micropolar fluid flow under the influence of magnetic field. Thermal Science. 2016; 20(suppl. 5): 1391-1404. doi: 10.2298/tsci16s5391k

[14]Turkyilmazoglu M. Flow and heat simultaneously induced by two stretchable rotating disks. Physics of Fluids. 2016; 28(4). doi: 10.1063/1.4945651

[15]Akhter S, Ashraf M, Ali K. MHD flow and heat transfer analysis of micropolar fluid through a porous medium between two stretchable disks using quasi-linearization method. Iran. J. Chem. Chem. Eng. 2017; 36(4).

[16]Doh DH, Muthtamilselvan M. Thermophoretic particle deposition on magnetohydrodynamic flow of micropolar fluid due to a rotating disk. International Journal of Mechanical Sciences. 2017; 130: 350-359. doi: 10.1016/j.ijmecsci.2017.06.029

[17]Hayat T, Javed M, Imtiaz M, et al. Convective flow of Jeffrey nanofluid due to two stretchable rotating disks. Journal of Molecular Liquids. 2017; 240: 291-302. doi: 10.1016/j.molliq.2017.05.024

[18]Das A, Sahoo B. Flow of a Reiner‐Rivlin fluid between two infinite coaxial rotating disks. Mathematical Methods in the Applied Sciences. 2018; 41(14): 5602-5618. doi: 10.1002/mma.5103

[19]Tabassum M, Mustafa M. A numerical treatment for partial slip flow and heat transfer of non-Newtonian Reiner-Rivlin fluid due to rotating disk. International Journal of Heat and Mass Transfer. 2018; 123: 979-987. doi: 10.1016/j.ijheatmasstransfer.2018.03.040

[20]Yao B, Lian L. A new analysis of the rotationally symmetric flow in the presence of an infinite rotating disk. International Journal of Mechanical Sciences. 2018; 136: 106-111. doi: 10.1016/j.ijmecsci.2017.12.023

[21]Sahoo B, Shevchuk IV. Heat transfer due to revolving flow of Reiner-Rivlin fluid over a stretchable surface. Thermal Science and Engineering Progress. 2019; 10: 327-336. doi: 10.1016/j.tsep.2019.03.004

[22]Yao B, Lian L. Series solution of the rotationally symmetric flow in the presence of an infinite rotating disk with uniform suction. European Journal of Mechanics - B/Fluids. 2019; 74: 159-166. doi: 10.1016/j.euromechflu.2018.11.012

[23]Zangooee MR, Hosseinzadeh Kh, Ganji DD. Hydrothermal analysis of MHD nanofluid (TiO2-GO) flow between two radiative stretchable rotating disks using AGM. Case Studies in Thermal Engineering. 2019; 14: 100460. doi: 10.1016/j.csite.2019.100460

[24]Das A, Sarkar S Flow analysis of Reiner-Rivlin fluid between two stretchable rotating disks. In: Recent Trends in Wave Mechanics and Vibrations: Select Proceedings of WMVC 2018 Springer Singapore; 2020. pp. 61-70. doi: 10.1007/978-981-15-0287-3_5

[25]Naqvi SMRS, Kim HM, Muhammad T, et al. Numerical study for slip flow of Reiner-Rivlin nanofluid due to a rotating disk. International Communications in Heat and Mass Transfer. 2020; 116: 104643. doi: 10.1016/j.icheatmasstransfer.2020.104643

[26]Usman M, Mehmood A, Weigand B. Heat transfer from a non-isothermal rotating rough disk subjected to forced flow. International Communications in Heat and Mass Transfer. 2020; 110: 104395. doi: 10.1016/j.icheatmasstransfer.2019.104395

[27]Faraz N, Khan Y. Analytical solution of electrically conducted rotating flow of a second grade fluid over a shrinking surface. Ain Shams Engineering Journal. 2011; 2(3-4): 221-226. doi: 10.1016/j.asej.2011.10.001

[28]Zhang X, Li M. Analysis of a semi-implicit and structure-preserving finite element method for the incompressible MHD equations with magnetic-current formulation. Communications in Nonlinear Science and Numerical Simulation. 2024; 128: 107677. doi: 10.1016/j.cnsns.2023.107677

[29]Jalaal M, Nejad MG, Jalili P, et al. Homotopy perturbation method for motion of a spherical solid particle in plane couette fluid flow. Computers & Mathematics with Applications. 2011; 61(8): 2267-2270. doi: 10.1016/j.camwa.2010.09.042

[30]Abdelmoneim M, Eldabe NT, Abouzeid MY, et al. Modified Darcy’s law and couple stress effects on electro-osmotic flow of non-Newtonian nanofluid with peristalsis. International Journal of Applied Electromagnetics and Mechanics. 2023; 72(3): 253-277. doi: 10.3233/jae-220287

[31]Hamad MAA. Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. International Communications in Heat and Mass Transfer. 2011; 38(4): 487-492. doi: 10.1016/j.icheatmasstransfer.2010.12.042

[32]Bejan A. A synthesis of analytical results for natural convection heat transfer across rectangular enclosures. International Journal of Heat and Mass Transfer. 1980; 23(5): 723-726. doi: 10.1016/0017-9310(80)90017-4

[33]Ndlovu PL, Moitsheki RJ. Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with Temperature-Dependent Properties. Mathematical Problems in Engineering. 2013; 2013: 1-14. doi: 10.1155/2013/273052

[34]Mabood F, Khan WA, Ismail AIMd. MHD flow over exponential radiating stretching sheet using homotopy analysis method. Journal of King Saud University - Engineering Sciences. 2017; 29(1): 68-74. doi: 10.1016/j.jksues.2014.06.001

[35]Talarposhti RA, Jalili P, Rezazadeh H, et al. Optical soliton solutions to the (2+1)-dimensional Kundu–Mukherjee–Naskar equation. International Journal of Modern Physics B. 2020; 34(11): 2050102. doi: 10.1142/s0217979220501027

[36]Jalili B, Jalili P, Sadighi S, et al. Effect of magnetic and boundary parameters on flow characteristics analysis of micropolar ferrofluid through the shrinking sheet with effective thermal conductivity. Chinese Journal of Physics. 2021; 71: 136-150. doi: 10.1016/j.cjph.2020.02.034

[37]Mahabaleshwar US, Maranna T, Pérez LM, et al. An effect of magnetohydrodynamic and radiation on axisymmetric flow of non-Newtonian fluid past a porous shrinking/stretching surface. Journal of Magnetism and Magnetic Materials. 2023; 571: 170538. doi: 10.1016/j.jmmm.2023.170538

[38]Khan Y. A series solution of the boundary value problem arising in the application of fluid mechanics. International Journal of Numerical Methods for Heat & Fluid Flow. 2018; 28(10): 2480-2490. doi: 10.1108/hff-11-2017-0474

[39]Ahmad A, Ishaq A, Khan Y. Influence of FENE-P fluid on drag reduction and heat transfer past a magnetized surface. International Journal of Modern Physics B. 2022; 36(23). doi: 10.1142/s0217979222501454

[40]Khan Y, Majeed AH, Rasheed MA, et al. Dual solutions for double diffusion and MHD flow analysis of micropolar nanofluids with slip boundary condition. Frontiers in Physics. 2022; 10. doi: 10.3389/fphy.2022.956737

[41]Khan Y. Magnetohydrodynamic flow of linear visco-elastic fluid model above a shrinking/stretching sheet: A series solution. Scientia Iranica. 2017. doi: 10.24200/sci.2017.4305

[42]Anusha T, Mahabaleshwar US, Hatami M. Navier slip effect on the thermal-flow of Walters’ liquid B flow due to porous stretching/shrinking with heat and mass transfer. Case Studies in Thermal Engineering. 2021; 28: 101691. doi: 10.1016/j.csite.2021.101691

[43]Ghadikolaei SS, Hosseinzadeh KH, Hatami M, et al. Investigation for squeezing flow of ethylene glycol (C2H6O2) carbon nanotubes (CNTs) in rotating stretching channel with nonlinear thermal radiation. Journal of Molecular Liquids. 2018; 263: 10-21. doi: 10.1016/j.molliq.2018.04.141

[44]Ghasemi SE, Hatami M, Sarokolaie AK, et al. Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods. Physica E: Low-dimensional Systems and Nanostructures. 2015; 70: 146-156. doi: 10.1016/j.physe.2015.03.002

[45]Fakour M, Vahabzadeh A, Ganji DD, et al. Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls. Journal of Molecular Liquids. 2015; 204: 198-204. doi: 10.1016/j.molliq.2015.01.040

[46]Rashad A, Nafe M, Eisa D. 2D Radiative Casson-Carreau Hybrid Nanofluid Flow through a Circular Cylinder in a Darcy-Forchheimer Porous Medium. New Valley University Journal of Basic and Applied Sciences. 2023; 1(1): 1-19. doi: 10.21608/nujbas.2023.218751.1012

[47]Rashad AM, Nafe MA, Eisa DA. Yield Stress Impact on Magnetohydrodynamic Jeffery Hybrid Nanofluid Flow Over a Moving Porous Surface: Buongiorno’s Model. Journal of Nanofluids. 2023; 12(7): 1729-1738. doi: 10.1166/jon.2023.2057

[48]Abdelhafez MA, Awad AA, Nafe MA, et al. Time-dependent viscous flow of higher-order reactive MHD Maxwell nanofluid with Joule heating in a porous regime. Waves in Random and Complex Media. 2021; 34(3): 1041-1061. doi: 10.1080/17455030.2021.1927237

[49]Turkyilmazoglu M. Evidence of stretching/moving sheet-triggered nonlinear similarity flows: atomization and electrospinning with/without air resistance. International Journal of Numerical Methods for Heat & Fluid Flow. 2024; 34(9): 3598-3614. doi: 10.1108/hff-04-2024-0254

[50]Turkyilmazoglu M. Two Models on the Unsteady Heat and Fluid Flow Induced by Stretching or Shrinking Sheets and Novel Time-Dependent Solutions. ASME Journal of Heat and Mass Transfer. 2024; 146(10). doi: 10.1115/1.4065674

[51]Enamul, S. and Ontela, S., 2025. Entropy Analysis of Hall-Effect-Driven Ti− CoFe2O4/Engine Oil-Based Hybrid Nanofluid Flow Between Spinning Porous Disks with Thermal Convective Boundaries. JCIS Open, p.100134. https://doi.org/10.1016/j.jciso.2025.100134

[52]Hussain, M., Shahid, S., Akbar, N.S. and Alaoui, M.K., 2025. Unsteady Flow and Heat Transfer Optimization of Viscous Fluid with Bioconvection over a Rotating Stretchable Disk and Gyrotactic Motile Microorganisms. Case Studies in Thermal Engineering, p.105796. https://doi.org/10.1016/j.csite.2025.105796

[53]Lone, S.A., Bossly, R., Alduais, F.S., Al-Bossly, A., Khan, A. and Saeed, A., 2025. Thermal investigation of magnetized Casson hybrid nanofluid flow through two stretchable angular rotating disks with variable porosity and Cattaneo-Christov heat flux model: a numerical approach. Colloid and Polymer Science, 303(3), pp.529-546. https://doi.org/10.1007/s00396-024-05363-7

[54]Mandal, S., Mukherjee, S., Shit, G.C. and Vajravelu, K., 2025. Entropy analysis of MHD flow in hybrid nanofluid over a rotating disk with variable viscosity and nonlinear thermal radiation. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 105(2), p.e202301027. https://doi.org/10.1002/zamm.202301027

[55]Naveed Khan, M., Ahmad, S., Ahammad, N.A., Alqahtani, T. and Algarni, S., 2025. Numerical investigation of hybrid nanofluid with gyrotactic microorganism and multiple slip conditions through a porous rotating disk. Waves in Random and Complex Media, 35(2), pp.3789-3804. https://doi.org/10.1080/17455030.2022.2055205

[56]Rauf, A., Ramesh, G.K., Fatima, S., Shehzad, S.A., Madhukesh, J.K. and Siddiq, M.K., 2025. Horizontal Magnetic Field Influence on Fluid Flow Across a Variable Thickness Rotating Disk With Stretching and Melting Phenomenon. Heat Transfer. https://doi.org/10.1002/htj.23285

[57]Senbagaraja, P. and De, P., 2025. Sensitivity analysis on electro-osmotic flow of EMHD tangent hyperbolic nanofluid through porous rotating disk with variable thermal conductivity, Stefan blowing and thermal radiation. Multiscale and Multidisciplinary Modeling, Experiments and Design, 8(1), p.65. https://doi.org/10.1007/s41939-024-00648-4

[58]Sultana, U., Mushtaq, M., Ahmad, I. and Muhammad, T., 2025. Porosity and heat transfer analysis of nanofluids due to rotating-stretching disk with Joule heating. Modern Physics Letters B, 39(01), p.2450404. https://doi.org/10.1142/S0217984924504049

[59]Turkyilmazoglu, M. and Pop, I., 2025. Rheology of Bingham viscoplastic flow triggered by a rotating and radially stretching disk. International Journal of Numerical Methods for Heat & Fluid Flow. https://doi.org/10.1108/HFF-11-2024-0845

[60]Usman, Kumar, R.V., Khan, W.A., AL‐lobani, E.M. and Massoud, E.E.S., 2025. Mathematical modeling and numerical simulations of convective heat transport in a stagnant flow of water‐based copper, aluminum oxide and MWCNTs nanofluid upon a stretching spinning disk. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 105(1), p.e202400476. https://doi.org/10.1002/zamm.202400476

[61]Zada, J., Khan, A., Farooq, M., Alsubaie, A.S., Rezapour, S. and Inc, M., 2025. Computation of stretching disks fluid flow of hybrid nanofluid under the effect of variable magnetic field. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 105(1), p.e202400114. https://doi.org/10.1002/zamm.202400114

[62]Azar, A.A., 2025. Semi-analytical solution for nonlinear Von Kármán swirling fluid flow via the hybrid analytical and numerical method. Mechanical Engineering Advances, 3(2), pp.2878-2878. https://doi.org/10.59400/mea2878

[63]Jalili P, Azar AA, Jalili B, et al. The HAN method for a thermal analysis of forced non-Newtonian MHD Reiner-Rivlin viscoelastic fluid motion between two disks. Heliyon. 2023; 9(6): e17535. doi: 10.1016/jheliyon2023.e17535

[64]Jalili B, Ahmadi Azar A, Esmaeili K, et al. A novel approach to micropolar fluid flow between a non-porous disk and a porous disk with slip. Chinese Journal of Physics. 2024; 87: 118-137. doi: 10.1016/j.cjph.2023.11.023

[65]Ahmadi Azar A, Jalili B, Jalili P, et al. Investigating the effect of structural changes of two stretching disks on the dynamics of the MHD model. Scientific Reports. 2023; 13(1). doi: 10.1038/s41598-023-48988-4

[66]Jalili P, Azar AA, Jalili B, et al. A Novel Analytical Investigation of a Swirling Fluid Flow and a Rotating Disk in the Presence of Uniform Suction. Arabian Journal for Science and Engineering. 2023; 49(8): 10453-10469. doi: 10.1007/s13369-023-08391-7

[67]Jalili P, Azar AA, Jalili B, et al. Study of nonlinear radiative heat transfer with magnetic field for non-Newtonian Casson fluid flow in a porous medium. Results in Physics. 2023; 48: 106371. doi: 10.1016/j.rinp.2023.106371

[68]Jalili B, Azar AA, Jalili P, et al. Analytical approach for micropolar fluid flow in a channel with porous walls. Alexandria Engineering Journal. 2023; 79: 196-226. doi: 10.1016/j.aej.2023.08.015

[69]Jalili B, Ahmadi Azar A, Jalili P, et al. Investigation of the unsteady MHD fluid flow and heat transfer through the porous medium asymmetric wavy channel. Case Studies in Thermal Engineering. 2024; 61: 104859. doi: 10.1016/j.csite.2024.104859

[70]Jalili P, Ahmadi Azar A, Jalili B, et al. A novel technique for solving unsteady three-dimensional brownian motion of a thin film nanofluid flow over a rotating surface. Scientific Reports. 2023; 13(1). doi: 10.1038/s41598-023-40410-3

[71]Azar EA, Jalili B, Azar AA, et al. An exact analytical solution of the Emden–Chandrasekhar equation for self-gravitating isothermal gas spheres in the theory of stellar structures. Physics of the Dark Universe. 2023; 42: 101309. doi: 10.1016/j.dark.2023.101309

[72]Jalili B, Azar AA, Liu D, et al. Analytical formulation of the steady-state planar Taylor–Couette flow constitutive equations with entropy considerations. Physics of Fluids. 2024; 36(11). doi: 10.1063/5.0239765

[73]Khan KA, Vivas-Cortez M, Ishfaq K, et al. Exploring the numerical simulation of Maxwell nanofluid flow over a stretching sheet with the influence of chemical reactions and thermal radiation. Results in Physics. 2024; 60: 107635. doi: 10.1016/j.rinp.2024.107635

[74]Basit MA, Imran M, Akgül A, et al. Mathematical analysis of heat and mass transfer efficiency of bioconvective Casson nanofluid flow through conical gap among the rotating surfaces under the influences of thermal radiation and activation energy. Results in Physics. 2024; 63: 107863. doi: 10.1016/j.rinp.2024.107863

[75]Alzabut J, Nadeem S, Noor S, et al. Numerical analysis of Magnetohydrodynamic convection heat flow in an enclosure. Results in Physics. 2023; 51: 106618. doi: 10.1016/j.rinp.2023.106618

[76]Gamachu D, Ibrahim W, Bijiga LK. Nonlinear convection unsteady flow of electro-magnetohydrodynamic Sutterby hybrid nanofluid in the stagnation zone of a spinning sphere. Results in Physics. 2023; 49: 106498. doi: 10.1016/j.rinp.2023.106498

[77]Tshivhi KS, Tshehla MS. Heat source and radiation effects on MHD flow of Copper-Water nanofluid over exponential stretching surface with slip. Results in Physics. 2024; 58: 107463. doi: 10.1016/j.rinp.2024.107463

[78]Leng Y, Li Y, Anwaar H, et al. Unraveling metachronal wave effects on heat and mass transfer in Non-Newtonian fluid. Case Studies in Thermal Engineering. 2024; 58: 104379. doi: 10.1016/j.csite.2024.104379

[79]McChesney M. A Textbook of Magnetohydrodynamics. J. A. Shercliff. Pergamon Press, Oxford. 1965. 265 pp. Diagrams. 21s. The Journal of the Royal Aeronautical Society. 1966; 70(663): 453-453. doi: 10.1017/s0001924000058607

[80]Devi SPAA, Devi RUU. On hydromagnetic flow due to a rotating disk with radiation effects. Nonlinear Analysis: Modelling and Control. 2011; 16(1): 17-29. doi: 10.15388/na.16.1.14112

[81]Pattnaik PK, Panda S, Baithalu R, et al. Darcy-Forchheimer inertial drag on micropolar hybrid nanofluid flow through a channel: Akbari-Ganji method. Chaos, Solitons & Fractals. 2025; 194: 116197. doi: 10.1016/j.chaos.2025.116197

[82]Mirgolbabaee H, Ledari ST, Ganji DD. 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. 2017; 24(1): 213-222. doi: 10.1016/j.jaubas.2017.01.002