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The Impact of the Weak Magnetic Field on Hydromagnetic Nanofluid Flow Via Divergent and Convergent Channels

Received: 10 February 2024     Accepted: 27 February 2024     Published: 7 March 2024
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Abstract

This paper has studied the effect of a low-intensity of magnetism acting on hydromagnetics of nanoparticles (Silver-water) via divergent-convergent channels. The study aimed at determining the effect of Hartmann and Reynolds numbers, the distribution of energy in the system, and the volume fraction of nanofluid particles on the movement of nanofluid particles, the distribution of temperature, and the distribution of concentration of nanofluid particles. The governing equations were transformed to a linear system of the differential equations and numerical solutions were found using the collocation technique and MATLAB was used to generate the results. It is discovered, varying the Reynolds values decreases the distribution of temperature for divergent medium. Variation in Reynolds values augments the distribution of temperature for the shrinking walls. The observation shows that increasing Hartmann values reduces the velocity profile in both channels which are diverging –converging channels. This is because Lorentz intensity is generated by the magnetism that alters the movement of nanofluid flow hence reduction in the velocity distribution. The concentration of nanofluid reduces in both channels when the distribution of energy in the system is augmented. The distribution of temperature increases in both channels when the energy in the system is augmented. Variation in the distribution of energy facilitates the transferring of heat to nanoparticles hence the temperature profile of nanofluid is increased. The distribution of the velocity is constant when varying the energy intensity. The heat generation resulted in a variation of temperature and had minimum impact on the movement of the nanoparticles for both channels. The concentration of nanofluid is increased in the divergent channel when Reynolds values are increased. The reduction occurs in the concentration of nanofluid when Reynolds values are increased. As the distance between molecules becomes wider due to augmenting the energy, this results in a reduction of concentration distribution of the nanofluid in both channels. These research findings are applied in medical sciences, engineering, geophysics, and astrophysics.

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 10, Issue 1)
DOI 10.11648/j.ijfmts.20241001.12
Page(s) 15-24
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Weak Magnetic Field, Reynolds Number, MHD Nanofluid, Divergent, and Convergent Channels

References
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[2] Ritchie (19320. Experimental researches in Voltaic Electricity and Electromagnetism, Phil. Trans. Roy Soc. London Vol. 122.279.
[3] Hartmann. J., Lazarus. F. (1937). Hg, Dynamics, PartII, Kgl. Danske Videnskab Selskab, mat, mat, mat. Fys. Medd, Vol. 15 no 7.
[4] Mishra Ashish, Alok K. Pandey, Ali J. Chamkha Manoj Kumar (2020). Role of Nanoparticles and Heat Generation/Absorption on MHD Flow of Silver-Water Nanofluid through Porous Stretching/Shrinking Converging/Diverging Channels. Journal of the Egyptian Mathematical Society. Volume 28. Article Number: 17.
[5] Tesfaye Kebede, Eshetu Haile, Awgichew, Walelign. (2020). Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluid. Journal of Applied Mathematics. Volume 2020, Article ID1890972, 13 pages.
[6] Jafari, A., Zamankhan, P., Mousavi, S. M., Kolari. P. (2009). Numerical Investigation of the Blood Flow. Part II: In Capillaries. Communication in Nonlinear Science and Numerical Simulation, 14(4), 1396-1402.
[7] Shira. Hey Zaki M, Liu H, Himeno R, Sun Z (2006). Numerical Coupling Model to Analyze the Blood Flow, Temperature and Oxygen Transport in Human Breast Tumor under Laser irradiation. Com Biol Medi 36: 130-135.
[8] Felicien Habiyaremye, Agnes Mburu, Mary Wainaina. (2018). Magnetohydrodynamic Flow of Viscous Electrically Conducting Incompressible Fluid through Vertical Plates Subjected to Inclined Magnetic Field. International Journal of Scientific and Technical Research in Engineering (IJSTRE). www.ijstre.com Volume 3 Issue 6 ǁ August 2018.
[9] Jeffery, G. B. "L. The two-dimensional steady motion of a viscous fluid." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 29, no. 172 (1915): 455-465.
[10] Makinde. O. D. (1997). Steady Flow in a Linearly Diverging Asymmetrical Channel. CAMES 4, PP. 157-165.
[11] Makinde. O. D. (1999). Extending the Utility of Perturbation Series in Problems of Laminar Flow in Porous Pipe and a Divergent Channel. Journal of Austral Mathematics. Soc. Ser. B41, pp. 118-128.
[12] Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. (2022). The Effect of Strong Magnetic Field on Unsteady MHD Nanofluid Flow through Convergent-Divergent Channel with Heat and Mass Transfer. International Journal of Fluid Mechanics & Thermal Sciences, 8(3), 41-52. https://doi.org/10.11648/j.ijfmts.20220803.11
[13] Makinde. O. D. (2008). Effect of Arbitrary Magnetic Reynolds Number on MHD Flows in Convergent-Divergent Channels. International Journal of Numerical Methods for Heat and Fluid Flow. Vol. 18 ISS: 6pp697-700.
[14] Eduard Onyango. R., Mathew N. Kinyanjui, Mark Kimathi, Surindar M. Uppal. (2020). Unsteady Jeffery-Hamel Flow in the Presence of Oblique Magnetic Field with Suction and Injection. Applied and Computational Mathematics; 9(1): 1-13.
[15] Virginia M. Kitetu, Thomas T. M. Onyango, Jackson K. Kwanza. (2019). Control Volume Approach for Determining Effect of Hartmann Number, Nanoparticle Volume Fraction and Suction parameter on MHD Nanofluid Flow over Stretched Surface. Analysis of MHD Nanofluid Flow as a Result of Stretching Surface and Suction. International Journal of Research and Innovation in Applied Science. Vol. 4, ISS4 ISS 2454-6194.
[16] Felicien Habiyaremye, Mary Wainaina, Mark Kimathi. The Effect of Heat and Mass Transfer on Unsteady MHD Nanofluid Flow through Convergent-Divergent Channel. International Journal of Fluid Mechanics & Thermal Sciences. Vol. 8, No. 1, 2022, pp. 10-22. https://doi.org/ 10.11648/j.ijfmts.20220801.12.
[17] Haroun, N. A., Sibanda, P., Modal, S., Motsa, SS. (2015). On Unsteady MHD mixed Convection in a Nanofluid due to Stretching /Shrinking Surface with Suction/Injection using the Spectral Relaxation Method. Boundary Value Problem, (1), 24.
[18] Maxwell, J. C. (1881). A Treatise on Electricity and Magnetism, Second Ed. Clarendo Press, Oxford, UK.
[19] Einstein. (1956). Investigation on the Theory of Brownian Motion, Dover, New York.
[20] Brinkman, H. C. (1952). The Viscosity of Concentration Suspensions and Solutions. The Journal of Chemical Physics, 20(4) 571-581.
[21] Park, B. C., Choi, Y. I. (1998). Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particles, Experimental Heat. 11 pp. 151-170.
[22] Xuan, Y. Roetzel, W. (2000). Conceptions for Heat Transfer Correlation of Nanofluid. International Journal of Heat and Mass Transfer, 43, 3701-3707.
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  • APA Style

    Habiyaremye, F., Wainaina, M. (2024). The Impact of the Weak Magnetic Field on Hydromagnetic Nanofluid Flow Via Divergent and Convergent Channels. International Journal of Fluid Mechanics & Thermal Sciences, 10(1), 15-24. https://doi.org/10.11648/j.ijfmts.20241001.12

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    ACS Style

    Habiyaremye, F.; Wainaina, M. The Impact of the Weak Magnetic Field on Hydromagnetic Nanofluid Flow Via Divergent and Convergent Channels. Int. J. Fluid Mech. Therm. Sci. 2024, 10(1), 15-24. doi: 10.11648/j.ijfmts.20241001.12

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    AMA Style

    Habiyaremye F, Wainaina M. The Impact of the Weak Magnetic Field on Hydromagnetic Nanofluid Flow Via Divergent and Convergent Channels. Int J Fluid Mech Therm Sci. 2024;10(1):15-24. doi: 10.11648/j.ijfmts.20241001.12

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  • @article{10.11648/j.ijfmts.20241001.12,
      author = {Felicien Habiyaremye and Mary Wainaina},
      title = {The Impact of the Weak Magnetic Field on Hydromagnetic Nanofluid Flow Via Divergent and Convergent Channels},
      journal = {International Journal of Fluid Mechanics & Thermal Sciences},
      volume = {10},
      number = {1},
      pages = {15-24},
      doi = {10.11648/j.ijfmts.20241001.12},
      url = {https://doi.org/10.11648/j.ijfmts.20241001.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20241001.12},
      abstract = {This paper has studied the effect of a low-intensity of magnetism acting on hydromagnetics of nanoparticles (Silver-water) via divergent-convergent channels. The study aimed at determining the effect of Hartmann and Reynolds numbers, the distribution of energy in the system, and the volume fraction of nanofluid particles on the movement of nanofluid particles, the distribution of temperature, and the distribution of concentration of nanofluid particles. The governing equations were transformed to a linear system of the differential equations and numerical solutions were found using the collocation technique and MATLAB was used to generate the results. It is discovered, varying the Reynolds values decreases the distribution of temperature for divergent medium. Variation in Reynolds values augments the distribution of temperature for the shrinking walls. The observation shows that increasing Hartmann values reduces the velocity profile in both channels which are diverging –converging channels. This is because Lorentz intensity is generated by the magnetism that alters the movement of nanofluid flow hence reduction in the velocity distribution. The concentration of nanofluid reduces in both channels when the distribution of energy in the system is augmented. The distribution of temperature increases in both channels when the energy in the system is augmented. Variation in the distribution of energy facilitates the transferring of heat to nanoparticles hence the temperature profile of nanofluid is increased. The distribution of the velocity is constant when varying the energy intensity. The heat generation resulted in a variation of temperature and had minimum impact on the movement of the nanoparticles for both channels. The concentration of nanofluid is increased in the divergent channel when Reynolds values are increased. The reduction occurs in the concentration of nanofluid when Reynolds values are increased. As the distance between molecules becomes wider due to augmenting the energy, this results in a reduction of concentration distribution of the nanofluid in both channels. These research findings are applied in medical sciences, engineering, geophysics, and astrophysics. 
    },
     year = {2024}
    }
    

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  • TY  - JOUR
    T1  - The Impact of the Weak Magnetic Field on Hydromagnetic Nanofluid Flow Via Divergent and Convergent Channels
    AU  - Felicien Habiyaremye
    AU  - Mary Wainaina
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    DO  - 10.11648/j.ijfmts.20241001.12
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    JF  - International Journal of Fluid Mechanics & Thermal Sciences
    JO  - International Journal of Fluid Mechanics & Thermal Sciences
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    EP  - 24
    PB  - Science Publishing Group
    SN  - 2469-8113
    UR  - https://doi.org/10.11648/j.ijfmts.20241001.12
    AB  - This paper has studied the effect of a low-intensity of magnetism acting on hydromagnetics of nanoparticles (Silver-water) via divergent-convergent channels. The study aimed at determining the effect of Hartmann and Reynolds numbers, the distribution of energy in the system, and the volume fraction of nanofluid particles on the movement of nanofluid particles, the distribution of temperature, and the distribution of concentration of nanofluid particles. The governing equations were transformed to a linear system of the differential equations and numerical solutions were found using the collocation technique and MATLAB was used to generate the results. It is discovered, varying the Reynolds values decreases the distribution of temperature for divergent medium. Variation in Reynolds values augments the distribution of temperature for the shrinking walls. The observation shows that increasing Hartmann values reduces the velocity profile in both channels which are diverging –converging channels. This is because Lorentz intensity is generated by the magnetism that alters the movement of nanofluid flow hence reduction in the velocity distribution. The concentration of nanofluid reduces in both channels when the distribution of energy in the system is augmented. The distribution of temperature increases in both channels when the energy in the system is augmented. Variation in the distribution of energy facilitates the transferring of heat to nanoparticles hence the temperature profile of nanofluid is increased. The distribution of the velocity is constant when varying the energy intensity. The heat generation resulted in a variation of temperature and had minimum impact on the movement of the nanoparticles for both channels. The concentration of nanofluid is increased in the divergent channel when Reynolds values are increased. The reduction occurs in the concentration of nanofluid when Reynolds values are increased. As the distance between molecules becomes wider due to augmenting the energy, this results in a reduction of concentration distribution of the nanofluid in both channels. These research findings are applied in medical sciences, engineering, geophysics, and astrophysics. 
    
    VL  - 10
    IS  - 1
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Author Information
  • Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya

  • Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya

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