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Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection

Received: 21 April 2017     Accepted: 15 September 2017     Published: 23 October 2017
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Abstract

Marangoni convection in a horizontal layer with a uniform internal heat source and vertical magnetic field is analyzed. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The upper surface of a fluid layer is deformably free. The eigen value equations of the perturbed state obtained from the normal mode analysis are solved by using regular perturbation method with as wave number. The results show that the critical Marangoni number Mc become larger as the Chandrasekhar number Q increases, internal heat source and the Crispation number Cr decreases.

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 4)
DOI 10.11648/j.ijfmts.20170304.12
Page(s) 41-45
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), 2017. Published by Science Publishing Group

Keywords

Internal Heat Source, Magnetic Field, Marangoni Convection

References
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[2] S. H. Davis, and G. M. Homsy., “Energy stability theory for free surface problems: buoyancy-thermocapillary layers”, J. Fluid Mech, vol. 98, pp. 527-553, 1980.
[3] Takashima, M., “Surface tension driven instability in a horizontal liquid layer with a deformable free surface. I. Stationary convection”, Journal of the Physical Society of Japan. Vol. 50, pp. 2745–2750, 1981.
[4] Char, M. I., Chen, C. C., “Effect of non-uniform basic temperature gradients on the onset of oscillatory Marangoni convection in a magnetic field”, Acta Mech. Vol.161, pp. 17–30, 2003.
[5] Hashim, I., Wilson, S. K., “The onset of Benard -Marangoni convection in a horizontal layer of fluid”, Int. J. Engg, Sci, vol.37, pp. 643, 1999.
[6] S. Chandrasekhar., “Hydrodynamic and Hydromagnetic Stability”, oxford at the Clarendon Press, 1961.
[7] Maekava, T., Tanasuwa, I., “Effect of magnetic field on convection”, Int. J. Heat Mass Transfer, vol. 34, pp. 285, 1988.
[8] Wilson, S. K., “The effect of uniform internal heat generation on the onset of steady Marangoni convection in a horizontal layer of fluid”, Acta Mech. Vol. 124, pp. 63-69, 1997.
[9] Bachok, N., Arifin, N. M., “Feedback control of the Marangoni-Benard convection in a horizontal fluid layer with internal heat generation”, Microgravity Sci. Technol. vol. 22, pp.97–105.2010.
[10] M. I. Char, K. T. Chiang., “Stability analysis of Benard–Marangoni convection in fluids with internal heat generation”, J. Phys. D, vol. 27, pp. 748–755. 1964.
[11] Carr, M., “Penetrative convection in a superposed porous- medium–fluid layer via internal heating”, J. Fluid Mech. Vol. 509, pp. 305–329, 2004.
[12] Chang, M. H., “Stability of convection induced by selective absorption of radiation in a fluid overlying a porous layer”, Phys. Fluids. Vol. 16, pp. 3690–3698, 2004.
[13] Chang, M. H., “Thermal convection in superposed fluid and porous layers subjected to a horizontal plane couette flow”, Phys. Fluids. Vol. 17, pp. 1–7. 2005.
[14] Chang, M. H., “Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow”, Phys. Fluids. Vol. 18, pp. 3-10, 2006.
[15] Gangadharaiah. Y. H., “Bernard-Marangoni Convection in a Fluid layer Overlying a Layer of an Anisotropic Porous Layer with Deformable Free surface”, Journal of Applied Fluid Mechanics, vol. 9, pp. 221-229, 2016.
[16] Gangadharaiah. Y. H., “Onset of Benard–Marangoni Convection in a Composite Layers with Anisotropic Porous Material”, Journal of Applied Fluid Mechanics, vol. 10, pp. 661-66, 2017.
[17] Gangadharaiah. Y. H, (2017): Onset of Darcy–Benard Penetrative Convection in Porous Media. Journal of Applied Fluid Mechanics, 10, 661-666,.
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    Gangadharaiah. (2017). Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection. International Journal of Fluid Mechanics & Thermal Sciences, 3(4), 41-45. https://doi.org/10.11648/j.ijfmts.20170304.12

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    ACS Style

    Gangadharaiah. Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection. Int. J. Fluid Mech. Therm. Sci. 2017, 3(4), 41-45. doi: 10.11648/j.ijfmts.20170304.12

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    AMA Style

    Gangadharaiah. Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection. Int J Fluid Mech Therm Sci. 2017;3(4):41-45. doi: 10.11648/j.ijfmts.20170304.12

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  • @article{10.11648/j.ijfmts.20170304.12,
      author = {Gangadharaiah},
      title = {Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection},
      journal = {International Journal of Fluid Mechanics & Thermal Sciences},
      volume = {3},
      number = {4},
      pages = {41-45},
      doi = {10.11648/j.ijfmts.20170304.12},
      url = {https://doi.org/10.11648/j.ijfmts.20170304.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20170304.12},
      abstract = {Marangoni convection in a horizontal layer with a uniform internal heat source and vertical magnetic field is analyzed. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The upper surface of a fluid layer is deformably free. The eigen value equations of the perturbed state obtained from the normal mode analysis are solved by using regular perturbation method with   as wave number. The results show that the critical Marangoni number Mc become larger as the Chandrasekhar number Q increases, internal heat source and the Crispation number Cr decreases.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection
    AU  - Gangadharaiah
    Y1  - 2017/10/23
    PY  - 2017
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    DO  - 10.11648/j.ijfmts.20170304.12
    T2  - International Journal of Fluid Mechanics & Thermal Sciences
    JF  - International Journal of Fluid Mechanics & Thermal Sciences
    JO  - International Journal of Fluid Mechanics & Thermal Sciences
    SP  - 41
    EP  - 45
    PB  - Science Publishing Group
    SN  - 2469-8113
    UR  - https://doi.org/10.11648/j.ijfmts.20170304.12
    AB  - Marangoni convection in a horizontal layer with a uniform internal heat source and vertical magnetic field is analyzed. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The upper surface of a fluid layer is deformably free. The eigen value equations of the perturbed state obtained from the normal mode analysis are solved by using regular perturbation method with   as wave number. The results show that the critical Marangoni number Mc become larger as the Chandrasekhar number Q increases, internal heat source and the Crispation number Cr decreases.
    VL  - 3
    IS  - 4
    ER  - 

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Author Information
  • Department of Mathematics, Sir M Visvesvaraya Institute of Technology, Bangalore, India

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