Research Journal of Engineering and Technology

G. C. Rana ¹, Rakesh Kumar ², Ramesh Chand ³

Affiliations
1 Department of Mathematics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
2 Department of Physics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
3 Department of Mathematics, Govt. College Dharampur, District Mandi, Himachal Pradesh, IN

Abstract

In this paper we investigate the effect of AC electric field on the onset of instability of an elastico-viscous Rivlin-Ericksen dielectric fluid layer stimulated by the dielectrophoretic force due to the variation of dielectric constant with temperature. By applying linear stability theory and normal mode analysis method, we derive the dispersion relation describing the influence of viscelasticity and AC electric field. For the case of stationary convection, it is observed that Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid whereas AC electric field hastens the stationary convection. The present results are in good agreement with the earlier published results.

Keywords

Walter’ (Model B') Fluid, AC Electric Field, Electrohydrodynamic, Viscosity, Viscoelasticity.

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Ramesh Chand ¹, S. K. Kango ², Vikram Singh ³

Affiliations
1 Department of Mathematics, Government College, Nurpur, HP, IN
2 Department of Mathematics, Government College Haripur (Manali), HP, IN
3 Department of Mathematics, Jawalaji Degree College Jawalamukhi, HP, IN

Abstract

Double Diffusive convection in a horizontal layer of Maxwell visco-elastic fluid in a porous medium in the presence of constant vertical magnetic field and Soret coefficient is investigated. Flow in porous medium is characterized by Darcy model. The normal mode method is used to find linear stability analysis for the fluid layer confined between two free-free boundary surfaces. The stability criterions for stationary and oscillatory convection have been derived. Effects of various parameters on the stationary have been obtained analytically and graphically.

Keywords

Maxwell Visco-Elastic Fluid, Chandrasekhar Number, Soret Parameter, Rayleigh-Darcy Number, Magnetic Prandtl Number.

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G. C. Rana ¹, Ramesh Chand ²

Affiliations
1 Department of Mathematics, NSCBM Govt. P. G. College, Hamirpur-177 005, Himachal Pradesh, IN
2 Department of Mathematics, Govt. P. G. College, Dhaliara-177 103, Himachal Pradesh, IN

Abstract

The effect of rotation on the onset of convection in compressible Rivlin-Ericksen elastico-viscous fluid heated from below saturating a porous medium is considered. For the porous medium, the Brinkman model is employed. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, compressibility, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation has stabilizing effect whereas Darcy number and medium permeability have destabilizing/stabilizing effect on the system under certain conditions. The effects of rotation, Darcy number and medium permeability have also been shown graphically.

Keywords

Rivlin-Ericksen Fluid, Thermal Convection, Viscoelasticity, Rotation, Brinkman-Porous Medium.

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Ramesh Chand ¹

Affiliations
1 Department of Mathematics, Government P. G. College, Dhaliara-177103, Himachal Pradesh,, IN

Abstract

The effect of rotation on the thermal instability of Oldroydian visco-elastic fluid in porous medium is studied. The Brinkman-Darcy model has been used for porous medium. A linear stability analysis based upon normal mode analysis is used to find solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically and graphs have been plotted to study the effects of the Taylor number and Brinkman-Darcy number on the stationary convection.

Keywords

Thermal Instability, Oldroydian Visco-Elastic Fluid, Brinkman-Darcy Number, Prandtl-Darcy Number, Rotation.

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