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Characterization of Rotatory Thermal Convection in Rivlin-Ericksen Viscoelastic Fluid


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1 Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) INDIA 177033, India
     

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A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of uniform vertical rotation. 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 rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical rotation, opposite to gravity and a constant vertical adverse temperature gradient, are necessarily non-oscillatory, in the regime, where the Taylor number and F is is the viscoelasticity parameter. The result is important since it hold for all wave numbers and for horizontal rigid boundaries of infinite extension at the top and bottom of the fluid, and the exact solutions of the problem investigated in closed form, is not obtainable.

Keywords

Thermal Convection, Rivlin-Ericksen Fluid, Rotation, PES, Rayleigh Number, Taylor number. MSC 2000 No.: 76A05, 76E06, 76E15, 76E07.
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  • Characterization of Rotatory Thermal Convection in Rivlin-Ericksen Viscoelastic Fluid

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Authors

Ajaib S. Banyal
Department of Mathematics, Govt. College Nadaun (Hamirpur), (HP) INDIA 177033, India

Abstract


A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of uniform vertical rotation. 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 rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical rotation, opposite to gravity and a constant vertical adverse temperature gradient, are necessarily non-oscillatory, in the regime, where the Taylor number and F is is the viscoelasticity parameter. The result is important since it hold for all wave numbers and for horizontal rigid boundaries of infinite extension at the top and bottom of the fluid, and the exact solutions of the problem investigated in closed form, is not obtainable.

Keywords


Thermal Convection, Rivlin-Ericksen Fluid, Rotation, PES, Rayleigh Number, Taylor number. MSC 2000 No.: 76A05, 76E06, 76E15, 76E07.

References