Journal of Engineering Mathematics
, Volume 35, Issue 4, pp 385404
First online:
The onset of steady BénardMarangoni convection in a twolayer system of conducting fluid in the presence of a uniform magnetic field
 Purna Chandra BiswalAffiliated withDepartment of Mathematics, Italian Institute of Science
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The onset of steady BénardMarangoni convection in two horizontal liquid layers of electrically conducting immiscible fluids subjected to a uniform vertical magnetic field and temperature gradient is analysed by means of a combination of analytical and numerical techniques. The free surface can be either deformable or nondeformable and the interface between the fluids is always assumed to be flat. The effect of the lower layer on the critical values of Rayleigh, Marangoni and wave numbers for the onset of steady convection is investigated. When the free surface is nondeformable, the critical parameters for the onset of pure Marangoni convection are increased, whereas for the onset of pure Bénard convection they are decreased compared to the singlelayer model. The results for a singlelayer and for twolayers are qualitatively similar for BénardMarangoni convection when the free surface is deformable. All disturbances can be stabilized with sufficiently strong magnetic field when the free surface is nondeformable. If the free surface is allowed to deform and gravity waves are excluded, then the layers are always unstable to disturbances with sufficiently small wave number with magnetic field. Inclusion of gravity waves has a stabilizing effect on certain disturbances of small wave number in the presence of weak or moderate magnetic field.
 Title
 The onset of steady BénardMarangoni convection in a twolayer system of conducting fluid in the presence of a uniform magnetic field
 Journal

Journal of Engineering Mathematics
Volume 35, Issue 4 , pp 385404
 Cover Date
 199905
 DOI
 10.1023/A:1004439231890
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 BénardMarangini convection
 conducting fluids
 stability
 twolayer system.
 Industry Sectors
 Authors

 Purna Chandra Biswal ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Italian Institute of Science, Bangalore , 560012, India