Influence of Vertical Magnetic Field on the Onset of Rayleigh-Benard-Marangoni Convection in Superposed fluid and Porous Layers with Deformable Free Surface

Ananda ¹ , K ² , Gangadharaiah ³ , Y.H. ⁴

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.5 , pp.1-18, Oct-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.118

Online published on Oct 31, 2018

Copyright © Ananda, K, Gangadharaiah, Y.H. . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
When a thin horizontal fluid layer overlying a porous layer is heated from below, convection starts after that the temperature difference between the lower and upper surfaces has reached a critical value. Two effects are responsible for this motion: buoyancy and variation of the surface tension with temperature; the first effect is usually referred to as Rayleigh-Benard instability, the second as Marangoni instability. In the present work, we examine the role of the application of a vertical magnetic field on a thin horizontal electrically conducting fluid layer overlying a porous layer. An analytical solution is obtained for constant-flux thermal boundary conditions, for which the onset of supercritical cellular convection occurs at a vanishingly small wave number and can thus be predicted by the present theory. The critical Rayleigh number, , and critical Marangoni number, , are found to depend on the Chandrasekhar number, ,the depth ratio, , the Darcy number, , the Bond number, , and the Crispation number, Results are presented for a wide range of each of the governing parameters. The results are compared with limiting cases of the problem and are found to be in agreement.

Key-Words / Index Term :
Bernard-Marangoni convection; Magnetic field; Two-layer System

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