Volume 3, Issue 4, August 2017, Page: 41-45
Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection
Gangadharaiah, Department of Mathematics, Sir M Visvesvaraya Institute of Technology, Bangalore, India
Received: Apr. 21, 2017;       Accepted: Sep. 15, 2017;       Published: Oct. 23, 2017
DOI: 10.11648/j.ijfmts.20170304.12      View  1860      Downloads  84
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.
Internal Heat Source, Magnetic Field, Marangoni Convection
To cite this article
Gangadharaiah, Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection, International Journal of Fluid Mechanics & Thermal Sciences. Vol. 3, No. 4, 2017, pp. 41-45. doi: 10.11648/j.ijfmts.20170304.12
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This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nield, D. A., “Surface tension and buoyancy effect in cellular motion”, J. Fluid Mech. vol.19, pp. 341-348, 1964.
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.
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.
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.
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.
S. Chandrasekhar., “Hydrodynamic and Hydromagnetic Stability”, oxford at the Clarendon Press, 1961.
Maekava, T., Tanasuwa, I., “Effect of magnetic field on convection”, Int. J. Heat Mass Transfer, vol. 34, pp. 285, 1988.
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.
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.
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.
Carr, M., “Penetrative convection in a superposed porous- medium–fluid layer via internal heating”, J. Fluid Mech. Vol. 509, pp. 305–329, 2004.
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.
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.
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.
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.
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.
Gangadharaiah. Y. H, (2017): Onset of Darcy–Benard Penetrative Convection in Porous Media. Journal of Applied Fluid Mechanics, 10, 661-666,.
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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