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International Journal of Technology
Year : 2016, Volume : 6, Issue : 2
First page : ( 81) Last page : ( 86)
Print ISSN : 2231-3907. Online ISSN : 2231-3915.
Article DOI : 10.5958/2231-3915.2016.00012.2

A Characterization Theorem in Magnetohydrodynamic Triply DiffusiveConvection with Viscosity Variations

Prakash Jyoti, Kumar Rajeev*

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

*Corresponding Author Email: rajeevkumar2012math@gmail.com

Online published on 2 February, 2017.

Abstract

The paper mathematically establishes that magnetohydrodynamic triply diffusive convection, with variable viscosity and with one of the components as heat with diffusivity κ, cannot manifest itself as oscillatory motions of growing amplitude in an initially bottom heavy configuration if the two concentration Rayleigh numbers R1 and R2, the Lewis numbers τ1 and τ2 for the two concentrations with diffusivities κ1 and κ2 respectively (with no loss of generality κ > κ1> κ2), μmin (the minimum value of viscosity μ in the closed interval [0, 1]) and the Prandtl number σ satisfy the inequality provided D2μ is positive everywhere. It is further proved that this result is uniformly valid for any combination of rigid and/or free perfectly conductingboundaries.

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Keywords

Triply diffusive convection, variable viscosity, concentration Rayleigh number, oscillatorymotion, initially bottom heavy configuration and Chandrasekhar number.

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