Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow

Nor Amirah Idris; Norsarahaida Amin; Hamisan Rahmat

doi:doi:10.11648/j.acm.20140306.11

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Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow

Nor Amirah Idris, Norsarahaida Amin, Hamisan Rahmat

Published in Applied and Computational Mathematics (Volume 3, Issue 6)

Received: 4 November 2014 Accepted: 19 November 2014 Published: 24 November 2014

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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.

Published in	Applied and Computational Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.acm.20140306.11
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), 2014. Published by Science Publishing Group

Keywords

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

References

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[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.
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[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.
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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

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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

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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

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@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://article.sciencepublishinggroup.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}
}

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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  -

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Author Information

Nor Amirah Idris

Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, Johor Bahru, Malaysia
Norsarahaida Amin

Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, Johor Bahru, Malaysia
Hamisan Rahmat

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

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Plain Text BibTeX RIS

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

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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

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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://article.sciencepublishinggroup.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