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Research Journal of Science and Technology
Year : 2017, Volume : 9, Issue : 1
First page : ( 55) Last page : ( 61)
Print ISSN : 0975-4393. Online ISSN : 2349-2988.
Article DOI : 10.5958/2349-2988.2017.00010.9

Instability in Couple-Stress Fluid in the Presence of Magnetic Field

Chaodhary Rajesh Kumar*, Banyal Ajaib S.

Department of Mathematics, Govt. College Nadaun, Dist. Hamirpur, (HP), India-177033

*Corresponding Author E-mail: rajesh90945@gmail.com, ajaibbanyal@rediffmail.com

MSC 2000 No.: 76A05; 76E06; 76E15; 76U05

Online published on 12 January, 2017.

Abstract

The thermal instability of a couple-stress fluid acted upon by uniform vertical magnetic field and heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable for free and perfectly conducting boundaries at the top and bottom of the fluid. It is established that all non decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical magnetic field opposite to gravity and a constant vertical adverse temperature gradient, are necessarily non oscillatory, in the regime
where R is the thermal Rayleigh number, F is the couple-stress parameter and p2 is the magnetic Prandtl number. The result is important since the exact solutions of the problem investigated in closed form, are not obtainable.

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Keywords

Thermal convection, Couple-Stress Fluid, PES, Magnetic Field, Chandrasekhar Number.

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