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

Gangadharaiah

doi:doi:10.11648/j.ijfmts.20170304.12

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

Gangadharaiah

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 4)

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 M_c become larger as the Chandrasekhar number Q increases, internal heat source and the Crispation number C_r 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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[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,.
[18]	Gangadharaiah Y. H., “Double-Diffusive Marangoni convection in a composite system”. International Journal of Innovative Research in Science, Engineering and Technology. 131, 137-144, 2013.

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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
N1  - https://doi.org/10.11648/j.ijfmts.20170304.12
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

Gangadharaiah

Department of Mathematics, Sir M Visvesvaraya Institute of Technology, Bangalore, India

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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}
}

Copy | Download

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
N1  - https://doi.org/10.11648/j.ijfmts.20170304.12
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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