COMPARATIVE STUDY ON FREE VERSUS MIXED CONVECTION IN MHD BOUNDARY LAYER FLOW OF VISCOELASTIC MICROPOLAR FLUID OVER A SPHERE

DOI: https://doi.org/10.30598/barekengvol20iss4pp2997-3010
Keywords: Keller-Box Method, Magnetohydrodynamic Convection, Viscoelastic Micropolar

Abstract

This study presents a numerical investigation comparing free and mixed convection in boundary layer flow of viscoelastic micropolar fluid over a sphere under magnetohydrodynamic (MHD) effects. A mathematical framework was formulated that consists of the continuity equation, momentum conservation, energy balance, and micropolar constitutive relations. They are expressed as a coupled system of partial differential equations (PDEs). These equations were simplified into ordinary differential equations (ODEs) through similarity transformations and then solved numerically using the Keller-box method in Fortran. The comparative analysis focuses on the distinct characteristics of free and mixed convection regimes, examining the effects of various parameters on skin friction coefficients and heat transfer. Results reveal that viscoelastic and micropolar parameters significantly dictate skin friction and heat transfer, while the magnetic parameter exhibits contrasting impacts depending on the convection regime. Furthermore, boundary layer separation is found to be sensitive to parameter variations only under mixed convection, where increased magnetic and assisting flow effects provide a stabilizing delay. This comparative framework offers a deeper understanding of the fundamental mechanisms governing these convection regimes and their practical implications in engineering applications.

Downloads

Download data is not yet available.

References

H. A. Nabwey, M. Ashraf, and A. Rashad, "A COMPREHENSIVE REVIEW OF CONVECTIVE HEAT TRANSFER IN HUMID AIR AND ITS PHYSICAL PERSPECTIVES IN CLIMATE CHANGE," AIP Advances, vol. 15, no. 5, 2025, doi: https://doi.org/10.1063/5.0270951.

Y. Huang, J. Ge, Y. Chen, and C. Zhang, "NATURAL AND FORCED CONVECTION HEAT TRANSFER CHARACTERISTICS OF SINGLE-PHASE IMMERSION COOLING SYSTEMS FOR DATA CENTERS," International Journal of Heat and Mass Transfer, vol. 207, p. 124023, 2023, doi: https://doi.org/10.1016/j.ijheatmasstransfer.2023.124023.

E. Salzer, Z. Gorgin Karaji, M. van Doeselaar, M. A. Tryfonidou, and K. Ito, "THE ROLE OF LOADING-INDUCED CONVECTION VERSUS DIFFUSION ON THE TRANSPORT OF SMALL MOLECULES INTO THE INTERVERTEBRAL DISC," (in eng), Eur Spine J, vol. 34, no. 1, pp. 326-337, Jan 2025, doi: https://doi.org/10.1007/s00586-024-08589-9.

R. Henniche and A. Korichi, "MIXED AND FORCED CONVECTION HEAT TRANSFER IN BAFFLED CHANNELS: A BRIEF REVIEW," Journal of Heat and Mass Transfer Research, vol. 12, no. 1, pp. 15-28, 2025, doi: https://doi.org/10.22075/JHMTR.2024.34280.1565.

W. Sun et al., "STUDY ON INTERACTION MECHANISM BETWEEN NATURAL CONVECTION AND FORCED CONVECTION DURING STORAGE AND TEMPERATURE RISE OF WAXY CRUDE OIL TANK," Engineering Applications of Computational Fluid Mechanics, vol. 19, no. 1, p. 2498354, 2025, doi: https://doi.org/10.1080/19942060.2025.2498354.

T. L. Bergman and A. S. Lavine, FUNDAMENTALS OF HEAT AND MASS TRANSFER. 8 ED. HOBOKEN, NJ: John Wiley & Sons, 2017.

Y. Cengel and A. J. Ghajar, HEAT AND MASS TRANSFER: FUNDAMENTALS AND APPLICATIONS. MCGRAW-HILL EDUCATION, 2020.

E. R. G. Eckert, "A PIONEERING ERA IN CONVECTIVE HEAT TRANSFER RESEARCH," in International Heat Transfer Conference Digital Library, pp. 1-8, Sept. 6-10, 1982.doi:http://dx.doi.org/10.1615/IHTC7.4180.

J. D. Anderson, "LUDWIG PRANDTL’S BOUNDARY LAYER," Physics Today, vol. 58, no. 12, pp. 42-48, 2005, doi: https://doi.org/10.1063/1.2169443.

A. Lévêque, "LES LOIS DE LA TRANSMISSION DE CHALEUR PAR CONVECTION," Annales des Mines, vol. 13, pp. 201–299, 1930.

E. Pohlhausen, "DER WÄRMEAUSTAUSCH ZWISCHEN FESTEN KÖRPERN UND FLÜSSIGKEITEN MIT KLEINER REIBUNG UND KLEINER WÄRMELEITUNG," ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol. 1, no. 2, pp. 115-121, 1921, doi: https://doi.org/10.1002/zamm.19210010205.

V. M. Falkner, "SOLUTIONS OF THE BOUNDARY LAYER EQUATIONS," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 12, pp. 865-896, 1931, doi: https://doi.org/10.1080/14786443109461870.

D. A. S. Rees and I. Pop, "FREE CONVECTION BOUNDARY-LAYER FLOW OF A MICROPOLAR FLUID FROM A VERTICAL FLAT PLATE," IMA Journal of Applied Mathematics, vol. 61, no. 2, pp. 179-197, 1998, doi: https://doi.org/10.1093/imamat/61.2.179.

O. A. Bég, V. R. Prasad, B. Vasu, N. B. Reddy, Q. Li, and R. Bhargava, "FREE CONVECTION HEAT AND MASS TRANSFER FROM AN ISOTHERMAL SPHERE TO A MICROPOLAR REGIME WITH SORET/DUFOUR EFFECTS," International Journal of Heat and Mass Transfer, vol. 54, no. 1-3, pp. 9-18, 2011, doi: https://doi.org/10.1016/j.ijheatmasstransfer.2010.10.005.

T. Tayebi, A. Dogonchi, A. J. Chamkha, M. B. B. Hamida, S. El-Sapa, and A. M. Galal, "MICROPOLAR NANOFLUID THERMAL FREE CONVECTION AND ENTROPY GENERATION THROUGH AN INCLINED I-SHAPED ENCLOSURE WITH TWO HOT CYLINDERS," Case Studies in Thermal Engineering, vol. 31, 2022, doi: https://doi.org/10.1016/j.csite.2022.101813.

N. A. Rosaidi, N. H. Ab Raji, S. N. H. A. Ibrahim, and M. R. Ilias, "ALIGNED MAGNETOHYDRODYNAMICS FREE CONVECTION FLOW OF MAGNETIC NANOFLUID OVER A MOVING VERTICAL PLATE WITH CONVECTIVE BOUNDARY CONDITION," Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, vol. 93, no. 2, pp. 37-49, 2022, doi: https://doi.org/10.37934/arfmts.93.2.3749.

S. F. H. Mohd Kanafiah, A. R. M. Kasim, S. M. Zokri, N. S. Arifin, N. S. Nordin, and M. a. Mokhtar, "FREE CONVECTION BOUNDARY LAYER FLOW OF BRINKMAN-VISCOELASTIC FLUID OVER A HORIZONTAL CIRCULAR CYLINDER WITH CONSTANT WALL TEMPERATURE," CFD Letters, vol. 15, pp. 103-114, 2023, doi: https://doi.org/10.37934/cfdl.15.1.103114.

S. F. H. M. Kanafiah, A. R. M. Kasim, S. M. Zokri, and M. R. Ilias, "COMBINED CONVECTIVE TRANSPORT OF BRINKMAN-VISCOELASTIC FLUID ACROSS HORIZONTAL CIRCULAR CYLINDER WITH CONVECTIVE BOUNDARY CONDITION," Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, vol. 89, no. 2, pp. 15-24, 2022, doi: https://doi.org/10.37934/arfmts.89.2.1524.

M. Salleh, R. Nazar, and I. Pop, "MODELING OF FREE CONVECTION BOUNDARY LAYER FLOW ON A SOLID SPHERE WITH NEWTONIAN HEATING," Acta Applicandae Mathematicae, vol. 112, no. 3, pp. 263-274, 2010, doi: https://doi.org/10.1007/s10440-010-9567-5.

M. Salleh, R. Nazar, and I. Pop, "MIXED CONVECTION BOUNDARY LAYER FLOW ABOUT A SOLID SPHERE WITH NEWTONIAN HEATING," Archives of Mechanics, vol. 62, no. 4, pp. 283-303, 2010. https://doi.org/10.3814/2010/736039

R. Mahat, S. Shafie, and I. Ullah, "FREE CONVECTION OF VISCOELASTIC NANOFLUID FLOW ON A HORIZONTAL CIRCULAR CYLINDER WITH CONSTANT HEAT FLUX," Journal of Advanced Research in Applied Sciences and Engineering Technology, vol. 30, no. 3, pp. 1-8, 2023, doi: https://doi.org/10.37934/araset.30.3.18.

R. Mahat, M. Saqib, I. Ulah, S. Shafie, and S. M. Isa, "MHD MIXED CONVECTION OF VISCOELASTIC NANOFLUID FLOW DUE TO CONSTANT HEAT FLUX," Journal of Advanced Research in Numerical Heat Transfer, vol. 9, no. 1, pp. 19-25, 2024.

F. A. Alwawi, H. T. Alkasasbeh, A. M. Rashad, and R. Idris, "NATURAL CONVECTION FLOW OF SODIUM ALGINATE BASED CASSON NANOFLUID ABOUT A SOLID SPHERE IN THE PRESENCE OF A MAGNETIC FIELD WITH CONSTANT SURFACE HEAT FLUX," in Journal of Physics: Conference Series, 13-25 July, 2019.doi:https://doi.org/10.1088/1742-6596/1366/1/012005.

F. A. Alwawi, A. S. Hamarsheh, H. T. Alkasasbeh, and R. Idris, "MIXED CONVECTION FLOW OF MAGNETIZED CASSON NANOFLUID OVER A CYLINDRICAL SURFACE," Coatings, vol. 12, no. 3, p. 296, 2022, doi: https://doi.org/10.3390/coatings12030296.

L. A. Aziz, A. R. M. Kasim, M. Z. Salleh, and S. Shafie, "MIXED CONVECTION BOUNDARY LAYER FLOW ON A SOLID SPHERE IN A VISCOELASTIC MICROPOLAR FLUID," in Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017) pp. 111-117. doi:https://doi.org/10.1007/978-981-13-7279-7_14.

A. C. Eringen, "THEORY OF MICROPOLAR FLUIDS," Journal of mathematics and Mechanics, pp. 1-18, 1966. https://doi.org/10.1512/iumj.1967.16.16001

T. Chen and A. Mucoglu, "ANALYSIS OF MIXED FORCED AND FREE CONVECTION ABOUT A SPHERE," International Journal of Heat and Mass Transfer, vol. 20, no. 8, pp. 867-875, 1977. doi: https://doi.org/10.1016/0017-9310(77)90116-8

R. Nazar and N. Amin, "FREE CONVECTION BOUNDARY LAYER ON AN ISOTHERMAL SPHERE IN A MICROPOLAR FLUID," International Communications in Heat and Mass Transfer, vol. 29, no. 3, pp. 377-386, 2002, doi: https://doi.org/10.1016/S0735-1933(02)00327-5.

R. Nazar, N. Amin, and I. Pop, "MIXED CONVECTION BOUNDARY LAYER FLOW ABOUT AN ISOTHERMAL SPHERE IN A MICROPOLAR FLUID," International Journal of Thermal Sciences, vol. 42, no. 3, pp. 283-293, 2003, doi: https://doi.org/10.1016/S1290-0729(02)00027-3.

L. A. Aziz, A. R. M. Kasim, M. Z. Salleh, N. S. Yusoff, and S. Shafie, "MAGNETOHYDRODYNAMICS EFFECT ON CONVECTIVE BOUNDARY LAYER FLOW AND HEAT TRANSFER OF VISCOELASTIC MICROPOLAR FLUID PAST A SPHERE," in Journal of Physics: Conference Series, p. 012003.doi:https://doi.org/10.1088/1742-6596/890/1/012003.

N. S. Khashi’ie, N. Arifin, E. H. Hafidzuddin, and N. Wahi, "MHD MIXED CONVECTIVE STAGNATION POINT FLOW WITH HEAT GENERATION PAST A SHRINKING SHEET," ASM Sci. J, pp. 71-81, 2019.

H. A. Nabwey, A. M. Rashad, A. M. EL-Hakiem, and S. I. Alshber, "EFFECTIVENESS OF NEWTONIAN HEATING ON MAGNETO-FREE CONVECTIVE FLOW OF POLAR NANOFLUID ACROSS A SOLID SPHERE," Fractal and Fractional, vol. 6, no. 2, p. 57, 2022, doi: https://doi.org/10.3390/fractalfract6020057.

M. K. A. Mohamed, N. M. Sarif, N. Noar, M. Z. Salleh, and A. Ishak, "VISCOUS DISSIPATION EFFECT ON THE MIXED CONVECTION BOUNDARY LAYER FLOW TOWARDS SOLID SPHERE," Trans. Sci. Technol, vol. 3, no. 1-2, pp. 59-67, 2016.

S. H. M. Yasin, M. K. A. Mohamed, Z. Ismail, B. Widodo, and M. Z. Salleh, "NUMERICAL INVESTIGATION OF FERROFLUID FLOW AT LOWER STAGNATION POINT OVER A SOLID SPHERE USING KELLER-BOX METHOD," Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, vol. 94, no. 2, pp. 200-214, 2022, doi: https://doi.org/10.37934/arfmts.94.2.200214.

Published
2026-08-24
How to Cite
[1]
L. A. Aziz, A. R. M. Kasim, M. Z. Salleh, and S. M. Zokri, “COMPARATIVE STUDY ON FREE VERSUS MIXED CONVECTION IN MHD BOUNDARY LAYER FLOW OF VISCOELASTIC MICROPOLAR FLUID OVER A SPHERE”, BAREKENG: J. Math. & App., vol. 20, no. 4, pp. 2997-3010, Aug. 2026.
Issue
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2026 Laila Amera Aziz, Abdul Rahman Mohd Kasim, Mohd Zuki Salleh, Syazwani Mohd Zokri

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Authors who publish with this Journal agree to the following terms:

  1. Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
  2. Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
  3. Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.