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International Journal of Technology
Year : 2016, Volume : 6, Issue : 2
First page : ( 118) Last page : ( 122)
Print ISSN : 2231-3907. Online ISSN : 2231-3915.
Article DOI : 10.5958/2231-3915.2016.00019.5

Linear Stability Analysis of Multicomponent convection

Prakash Jyoti, Manan Shweta*, Singh Virender

Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-171005, India

*Corresponding Author Email: mananshweta882@gmail.com

Online published on 2 February, 2017.

Abstract

Condition for characterizing nonoscillatory motions, which may be neutral or unstable, for multicomponentis derived. It is analtically proved that the principle of the exchange of stabilities, in multicomponent convection, is valid in the regime where R1, R2…, Rn-1 are the Lewis numbers for the (n-1) concentration components and σ is the Prandtl number and τ1, τ2, …, τn-1 are the Lewis numbers for the (n-1) concentration components respectively. When the complement of this sufficient condition holds good, oscillatory motions of neutral or growing amplitude can exist, and thus it is important to derive upper bounds for the complex growth rate of such motions when atleast one of the bounding surfaces is rigid so that exact solutions of the problem in closed form are not obtainable. Thus as a second problem bounds for the growth rates are also obtained. It is further proved that these results are uniformly valid for all combinations of rigid and dynamically free boundaries.

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Keywords

Multicomponent convection, The principle of the exchange of stabilities, Oscillatory motions, Complex growth rate, Concentration Rayleigh number.

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