An Exact Study of the Effects of Parabolic and Inverted Parabolic Temperature Gradients on Surface Tension Driven Magneto Convection in a Composite Layer
R. Sumithra1, Manjunatha.N2
1Dr. R. Sumithra, Department of Mathematics, Government Science College, Bangalore – 560 001, (Karnataka), India.
2Manjunatha.N, Department of Mathematics, Reva Institute of Technology and Management, Yelahanka, Bangalore-560 064, (Karnataka), India.
Manuscript received on 20 November 2014 | Revised Manuscript received on 30 November 2014 | Manuscript published on 30 November 2014 | PP: 36-46 | Volume-3 Issue-5, November 2014 | Retrieval Number: E1271113514/2014©BEIESP
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Abstract: The problem of Surface tension driven Magnetoconvection is investigated in a two layer system comprising an incompressible electrically conducting fluid saturated porous layer over which lies a layer of the same fluid in the presence of a vertical magnetic field. The lower rigid surface of the porous layer is isothermal and the upper free surface is considered to be insulating to temperature perturbations without deformation. At the upper free surface, the surface tension effects depending on temperature are considered. At the interface, the normal and tangential components of velocity, heat and heat flux are assumed to be continuous. The resulting eigenvalue problem is solved exactly for both parabolic and inverted parabolic temperature profiles and analytical expressions of the Thermal Marangoni Number are obtained. Effects of variation of different physical parameters on the Thermal Marangoni Number for both profiles are compared.
Keywords: Eigen value problem, Marangoni number, Surface tension, Temperature profiles.
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