Applied and Computational Mathematics

| Peer-Reviewed |

Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow

Received: 04 November 2014    Accepted: 19 November 2014    Published: 24 November 2014
Views:       Downloads:

Share This Article

Abstract

This paper investigates the effect of gravitational acceleration on unsteady biomagnetic fluid flow in a channel under the influence of a spatially varying magnetic field. The study on biomagnetic fluid under the action of an applied magnetic field is important in the development of Biomagnetic Fluid Dynamics (BFD). Most existing studies analyze flows in steady state conditions and the effect of gravitational acceleration has not been addressed. For the mathematical model, the Navier-Stokes equations, energy equation and an additional term that describes the magnetic force and gravitational effect which is consistent with the principles of ferrohydrodynamics (FHD) are employed. The nonlinear governing differential equations are non-dimensionalized and then discretized based on a finite difference technique on a staggered grid system. The solution of these problems is obtained numerically using pressure correction method with SIMPLE algorithm. For a range of governing parameters such as the magnetic number MnF and Richardson number Ri, the numerical results show that the gravitational acceleration has a profound effect on both velocity and temperature profiles. The streamlines plotted also show that vortices appear near the lower plate where the magnetic source is located.

DOI 10.11648/j.acm.20140306.11
Published in Applied and Computational Mathematics (Volume 3, Issue 6, December 2014)
Page(s) 285-294
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

Gravitational Acceleration, Biomagnetic Fluid Flow, Unsteady, FHD, SIMPLE Algorithm

References
[1] Anderson, Computational Fluid Dynamics: The Basic with Applications, McGraw-Hill, Inc., 1995.
[2] Andersson, H. I. and Valnes, O. A., “Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole”, Acta Mech., 128(39), 1998.
[3] Bashtovoy, V. G., Berkovsky, B. M. and Vislovich, A. N., “Introductionto Thermomechanics of Magnetic Fluids”, Hemisphere, Springer-Verlag, Berlin, 1988.
[4] Erwan Hafizi Kasiman, “Mixed formulation for Navier-Stokes equations with magnetic effect in rectangular channel”, Masters Thesis. Department of Mathematical Sciences, Universiti Teknologi Malaysia, Johor Bahru, 2012.
[5] Fertman, V. E., Magnetic Fluids Guidebook: Properties and Applications, Hemisphere, New York, 1990.
[6] Higashi, T., Yamagishi, A., Takeuchi, T., Kawaguchi, N., Sagawa, S., Onishi, S and Date, M., “Orientation of erythrocytes in a strong static magnetic field”, J. Blood, 82(1328), 1993.
[7] Haik, Y., Chen, J. C. and Pai, V. M., Development of bio-magnetic fluid dynamics, Proceedings of the IX International Symposium on Transport Properties in Thermal Fluids Engineering, Singapore, Pacific Center of Thermal Fluid Engineering, S. H. Winoto, Y. T. Chew, N. E. Wijeysundera, eds, Hawaii, U.S.A., June 25-28, 1996, pp 121-126.
[8] Loukopoulos, L. C. and Tzirtzilakis, E. E., “Biomagnetic channel flow in spatially varying magnetic field”, Int. J. Eng. Sci., 42, 2004, pp 571 – 590.
[9] Muthucumaraswamy, R., Raj, M. S. and Subramanian, V. S. A., “Heat transfer effects on accelerated vertical plate with variable temperature and mass flux”, ACTA TECHNICA CORVINIENSIS, 2010.
[10] Nursalasawati Rusli, “The computational modeling and simulation of two and three dimensional models of biomagnetic fluid flow in an artery”, Ph.D Thesis, Department of Mathematical Sciences, Universiti Teknologi Malaysia, Johor Bahru, 2012.
[11] Papadopoulos, P. K and Tzirtzilakis, E. E., “Biomagnetic flow in a curved square duct under the influence of an applied magnetic field”, Phys. Fluids, 16(8), 2004, pp 2952 - 2962.
[12] Stemme, O., “Magnetic wound treatment”, in Magnetism in Medicine, edited by W. Andra and H. Nowak, Wiley, Berlin, 1998, pp 489-494.
[13] Saha, S., Saha, G., Ali, M. and Islam, M. Q., “Combined free and forced convection inside a two-dimensional multiple ventilated rectangular enclosure”, ARPN Journal of Engineering and App. Sciences, 1(3), 2006.
[14] Tzirtzilakis, E. E, “A simple numerical methodology for BFD problems using stream function vorticity formulation”, Communications in Numer. Methods in Engineering, 2000, pp 1 - 6.
[15] Tzirtzilakis, E. E., Kafoussias, N. G. and Hatzikonstantinou, P. M., “Biomagnetic fluid flow in a rectangular duct”, 4th GRACM Congress on Computational Mechanics, Patras-Greece, 27-29 June, 2002.
[16] Tzirtzilakis, E. E. and Kafoussias, N. G., “Biomagnetic fluid flow over a stretching sheet with nonlinear temperature dependent magnetization”, Z. angew. Math. Phys., 54, 2003, pp 551 – 565.
[17] Tzirtzilakis, E. E. and Tanoudis, G. B., “Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer”, Int. J. Numer. Methods Heat Fluid Flow, 13(830), 2003.
[18] Tzirtzilakis, E. E., Sakalis, V. D., Kafoussias, N. G. and Hatzikonstantinou, P. M., “Biomagnetic fluid flow in a 3D rectangular duct”, Int. J. Numer. Meth. Fluids, 44, 2004, pp 1279–1298.
[19] Tzirtzilakis, E. E., “A mathematical model for blood flow in magnetic field”, Phys. Fluids, 17(7), 2005.
[20] Tzirtzilakis, E. E. and Loukopoulos, V. C., “Biofluid flow in a channel under the action of a uniform localized magnetic field”, Comput. Mech., 36(5), 2005, pp 360 – 374.
[21] Tzirtzilakis, E. E., Xenos, M., Loukopoulos, V. C. and Kafoussias, N. G., “Turbulent biomagnetic fluid flow in a rectangular channel under the action of a localized magnetic field”, Int. Journal of Engineering Science, 44, 2006, pp 1205 - 1224.
[22] Tzirtzilakis, E. E., “Biomagnetic fluid flow in a channel with stenosis”, Physica D., 237(1), 2007, pp 66 - 81.
[23] Tzirtzilakis, E. E. and Xenos, M. A., “Biomagnetic fluid flow in a driven cavity”, Meccanica, 48, 2013, pp 187 - 200.
Author Information
  • Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, Johor Bahru, Malaysia

  • Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, Johor Bahru, Malaysia

  • Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, Johor Bahru, Malaysia

Cite This Article
  • APA Style

    Nor Amirah Idris, Norsarahaida Amin, Hamisan Rahmat. (2014). Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow. Applied and Computational Mathematics, 3(6), 285-294. https://doi.org/10.11648/j.acm.20140306.11

    Copy | Download

    ACS Style

    Nor Amirah Idris; Norsarahaida Amin; Hamisan Rahmat. Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow. Appl. Comput. Math. 2014, 3(6), 285-294. doi: 10.11648/j.acm.20140306.11

    Copy | Download

    AMA Style

    Nor Amirah Idris, Norsarahaida Amin, Hamisan Rahmat. Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow. Appl Comput Math. 2014;3(6):285-294. doi: 10.11648/j.acm.20140306.11

    Copy | Download

  • @article{10.11648/j.acm.20140306.11,
      author = {Nor Amirah Idris and Norsarahaida Amin and Hamisan Rahmat},
      title = {Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {6},
      pages = {285-294},
      doi = {10.11648/j.acm.20140306.11},
      url = {https://doi.org/10.11648/j.acm.20140306.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20140306.11},
      abstract = {This paper investigates the effect of gravitational acceleration on unsteady biomagnetic fluid flow in a channel under the influence of a spatially varying magnetic field. The study on biomagnetic fluid under the action of an applied magnetic field is important in the development of Biomagnetic Fluid Dynamics (BFD). Most existing studies analyze flows in steady state conditions and the effect of gravitational acceleration has not been addressed. For the mathematical model, the Navier-Stokes equations, energy equation and an additional term that describes the magnetic force and gravitational effect which is consistent with the principles of ferrohydrodynamics (FHD) are employed. The nonlinear governing differential equations are non-dimensionalized and then discretized based on a finite difference technique on a staggered grid system. The solution of these problems is obtained numerically using pressure correction method with SIMPLE algorithm. For a range of governing parameters such as the magnetic number MnF and Richardson number Ri, the numerical results show that the gravitational acceleration has a profound effect on both velocity and temperature profiles. The streamlines plotted also show that vortices appear near the lower plate where the magnetic source is located.},
     year = {2014}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow
    AU  - Nor Amirah Idris
    AU  - Norsarahaida Amin
    AU  - Hamisan Rahmat
    Y1  - 2014/11/24
    PY  - 2014
    N1  - https://doi.org/10.11648/j.acm.20140306.11
    DO  - 10.11648/j.acm.20140306.11
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 285
    EP  - 294
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20140306.11
    AB  - This paper investigates the effect of gravitational acceleration on unsteady biomagnetic fluid flow in a channel under the influence of a spatially varying magnetic field. The study on biomagnetic fluid under the action of an applied magnetic field is important in the development of Biomagnetic Fluid Dynamics (BFD). Most existing studies analyze flows in steady state conditions and the effect of gravitational acceleration has not been addressed. For the mathematical model, the Navier-Stokes equations, energy equation and an additional term that describes the magnetic force and gravitational effect which is consistent with the principles of ferrohydrodynamics (FHD) are employed. The nonlinear governing differential equations are non-dimensionalized and then discretized based on a finite difference technique on a staggered grid system. The solution of these problems is obtained numerically using pressure correction method with SIMPLE algorithm. For a range of governing parameters such as the magnetic number MnF and Richardson number Ri, the numerical results show that the gravitational acceleration has a profound effect on both velocity and temperature profiles. The streamlines plotted also show that vortices appear near the lower plate where the magnetic source is located.
    VL  - 3
    IS  - 6
    ER  - 

    Copy | Download

  • Sections