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Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate

Received: 11 August 2015     Accepted: 22 August 2015     Published: 3 September 2015
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Abstract

This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.

Published in American Journal of Applied Mathematics (Volume 3, Issue 5)
DOI 10.11648/j.ajam.20150305.11
Page(s) 206-214
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), 2015. Published by Science Publishing Group

Keywords

Pressure Gradient, Suction and Injection, Magnetohydrodynamic (MHD)

References
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[2] Chinyoka, T., and Makinde, O.D., (2012).Unsteady hydromagnetic flow of a reactive variable viscosity third-grade fluid in a channel with convective cooling. International journal for numerical Methods in Fluids, Vol. 69(2), pp. 353-365
[3] D. Vieru and Siddique I. (2010). Axial Flow of Several Non-Newtonian Fluids through a Circular Cylinder Journal: International Journal of Applied Mechanics. Vol. 02, pp.543
[4] David J Griffiths (1999). Introduction to electrodynamics (Third edition.). Prentice Hall. pp. 559–562.
[5] Govindrajulu T., (1969). Unsteady flow of an incompressible and electrically conducting fluid between two infinite discs rotating in the presence of a uniform axial magnetic field. Journal: ActaMechanica - ACTA MECH, vol. 8, no. 1, pp. 53-62,
[6] Hayat, T., Ahmed, N. and Sajid M. (2008).Analytic Solution for MHD Flow of a Third Order Fluid in a Porous Channel. J. Comput. Appl. Maths., Vol. 214, p. 572-582.
[7] Katagiri, M., (1962). Flow Formation in Couette Motion in Magnetohydrodynamics. Phys. Soc. Jpn., Vol. 17, p. 393-396.
[8] Khan, M., Fetecau, C. and Hayat, T. (2007). “MHD Transient Flows in a Channel of Rectangular Cross-Section with Porous Medium. Physics Letters A, Vol. 369, p. 44.
[9] Khan, M., Maqbool, K. and Hayat, T., (2006). Influence of Hall Current on the Flows of a Generalized Oldroyd-B Fluid in a Porous Space. Acta Mech., Vol. 184, p. 1.
[10] Mishra SP and Muduli JC (1980). Unsteady flow through two porous flat walls in the presence of a magnetic field. Rev. Roum. des Sci Tech. Serie de Mech. Appl., 25, pp. 21-27.
[11] Muhuri, P. K., (1963). Flow Formation in Couette Motion in Magnetohydrodynamics with Suction. J. Phys. Soc. Jpn., Vol. 18, p. 1671-1675.
[12] Seth G. S., Ansari S. and Nandkeolyar R., (2011). Unsteady Hydromagnetic Couette flow within a porous channel. Tamkang journal of Science and Engineering. Vol. 14. No. 1, pp. 7-14
[13] Singh, A. K. and Kumar, N., (1983). Unsteady Magneto- hydrodynamic Couette Flow. Wear, Vol. 89, p. 125-129.
[14] Soundalgekar V.M. (1967). On the flow of an electrically conducting incompressible fluid near an accelerated plate in the presence of a parallel plate, under transverse magnetic field. Proc. Ind. Acad. Sci., 65A, pp. 179-187.
[15] Tao LN (1960). Magnetohydrodynamic effects on the formation of Couette flow. J. Aerospace Sci., 27, pp. 334-338.
[16] M. Sheikholeslami, D. D. Ganji, (2013) Heat transfer of Cu-water nanofluid flow between parallel plates, Powder Technol. 235 pp 873–879.
[17] Guchhait, S., Das, S., Jana, R. N. and Ghosh, S. K. (2011). Combined effects of Hall current and rotation on unsteady Couette flow in porous channel. World J. Mech., Vol. 1. pp. 87-99.
[18] Prasad, B. G. and Kumar, R. (2012). Unsteady hydromagnetic Couette flow through a porous medium in a rotating system, Theo.Appl. Mech. Letters, Vol. 1. DOI: 10.1063/2.1104205.
[19] Seth, G. S., Nandkeolyar, R. and Ansari, Md. S. (2012). Effects of Hall current and rotation on unsteady MHD Couette flow in the presence of an inclined magnetic field, J. Appl. Fluid Mech., Vol. 5, No. 2, pp. 67-74.
[20] Seth, G. S. and Singh, J. K. (2012). Unsteady MHD Couette flow of class-II of a viscous incompressible electrically conducting fluid in a rotating system, Int. J. Appl. Mech. Eng., Vol. 17, No. (2/3). (To appear in 2012).
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Cite This Article
  • APA Style

    Edward Richard Onyango, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. (2015). Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. American Journal of Applied Mathematics, 3(5), 206-214. https://doi.org/10.11648/j.ajam.20150305.11

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    ACS Style

    Edward Richard Onyango; Mathew Ngugi Kinyanjui; Surindar Mohan Uppal. Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. Am. J. Appl. Math. 2015, 3(5), 206-214. doi: 10.11648/j.ajam.20150305.11

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    AMA Style

    Edward Richard Onyango, Mathew Ngugi Kinyanjui, Surindar Mohan Uppal. Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate. Am J Appl Math. 2015;3(5):206-214. doi: 10.11648/j.ajam.20150305.11

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  • @article{10.11648/j.ajam.20150305.11,
      author = {Edward Richard Onyango and Mathew Ngugi Kinyanjui and Surindar Mohan Uppal},
      title = {Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {5},
      pages = {206-214},
      doi = {10.11648/j.ajam.20150305.11},
      url = {https://doi.org/10.11648/j.ajam.20150305.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150305.11},
      abstract = {This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.},
     year = {2015}
    }
    

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    T1  - Unsteady Hydromagnetic Couette Flow with Magnetic Field Lines Fixed Relative to the Moving Upper Plate
    AU  - Edward Richard Onyango
    AU  - Mathew Ngugi Kinyanjui
    AU  - Surindar Mohan Uppal
    Y1  - 2015/09/03
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajam.20150305.11
    DO  - 10.11648/j.ajam.20150305.11
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 206
    EP  - 214
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20150305.11
    AB  - This study concerns a magnetohydrodynamic flow between two parallel porous plates with injection and suction in the presence of a uniform transverse magnetic field with the magnetic field lines fixed relative to the moving plate with a constant pressure gradient. The study is aimed to determine the velocity profiles, the effects of permeability, pressure gradient and induced magnetic field on the flow. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method and implemented in MATLAB. The results obtained are presented in tables and graphs and the observations discussed on the effects of varying various parameters on the velocity profiles. A change is observed to either increase, decrease or to have no effect on the velocity profiles. The effect of magnetic field, time and suction /injection on the flow are discussed. The results provide useful information to the engineers to improve efficiency and performance of machines.
    VL  - 3
    IS  - 5
    ER  - 

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Author Information
  • Dept. Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Dept. Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Dept. Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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