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A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid

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Author(s): Banyal Ajaib Singh

Journal: Journal of Applied Fluid Mechanics
ISSN 1735-3572

Volume: 6;
Issue: 2;
Start page: 191;
Date: 2013;
Original page

Keywords: Thermal convection; Couple-stress fluid; Rayleigh number.

ABSTRACT
The thermal instability of a couple-stress fluid heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper mathematically establishes that the onset of instability at marginal state, cannot manifest itself as stationary convection, if the thermal Rayleigh number R and the couple-stress parameter F, 3 satisfy the inequality   2  2 2  2  1  3 F  3 F  1  3 F  1    , and when the couple-stress parameter F is R  2 2 27 F  1  1  3 F    infinitesimally small, R    27 4 4  2    F  , the result which also clearly mathematically established the stabilizing 1  2     character of the couple-stress.
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