On competition between modes of the onset of Marangoni convection with free-slip bottom under magnetic field
Md. Arifin, Norihan and Rosali, Haliza (2007) On competition between modes of the onset of Marangoni convection with free-slip bottom under magnetic field. In: 12th WSEAS International Conference on Applied Mathematics, 29-31 Dec. 2007, Cairo, Egypt.
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In this paper we use a numerical technique to analyze the onset of Marangoni convection in a horizontal layer of electrically-conducting fluid heated from below and cooled from above in the presence of a uniform vertical magnetic field. The top surface of a fluid is deformably free and the bottom boundary are rigid and free-slip. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the Hartmann , Crispation and Bond numbers. In particular we present an example of a situation in which there is competition between modes at the onset of convection.
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