Research Journal of Engineering and Technology

Sanjeev Kumar ¹, Veena Sharma ², Kamal Kishor ³, G. C. Rana ⁴

Affiliations
1 Department of Mathematics, Govt. College, Joginder Nagar, Distt. Mandi, (H.P.), IN
2 Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla, IN
3 Department of Mathematics, Govt. Senior Secondary School, Sunder Nagar, IN
4 Department of Mathematics, Govt. College, Naduan, Distt. Hamirpur (H.P.), IN

Abstract

The influence of viscosity, viscoelasticity and medium permeability on the stability of stratified Rivlin-Ericksen viscoelastic fluid is examined for viscoelastic polymeric solutions in the simultaneous presence of a uniform horizontal magnetic field ⃗H (H, 0, 0) and uniform horizontal rotation Ω(Ω, 0, 0). These solutions are known as Rivlin-Ericksen fluids and their rheology is approximated by the Rivlin-Ericksen constitutive relations, proposed by Rivlin and Ericksen [13]. The effects of Coriolis forces on the stability is chosen along the direction of the magnetic field and transverse to that of the gravitational field g (o,o,-g). The system is found to be stable for all wave numbers for stable stratifications and unstable for unstable stratifications for the stratifications in density, viscosity, viscoelasticity, medium permeability and medium porosity. The system can be completely stabilized by large enough magnetic field, which was unstable in the absence of magnetic field; provided the initial configuration is top-heavy density wise. The kinematic viscosity and kinematic viscoelasticity have damping effects on the growth rates with the increase in kinematic viscosity and kinematic viscoelasticity, respectively, for a fixed wave number. The medium permeability has enhancing effects on the growth rates with its increase for a fixed wave number. The above results have also been shown graphically.

Keywords

Rivlin-Ericksen Fluid, Magnetic Field, Rotation, Viscosity, Viscoelasticity, Porous Medium, AMS Classification Number:76A10.

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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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G. C. Rana ¹, H. S. Jamwal ², Kalpna Chadha ³

Affiliations
1 Department of Mathematics, Sidharth Govt. College, Nadaun-177 005, Himachal Pradesh, IN
2 Department of Mathematics, Apex Professional University, Pasighat, Arunachal Pradesh, IN
3 Department of Mathematics, NSCBM Govt. P. G. College Hamirpur, Himachal Pradesh, IN

Abstract

In this paper, the combined effect of uniform rotation and AC electric field on the onset of instability in a horizontal layer of an elastico-viscous dielectric fluid layer is examined both analytically and graphically. Rivlin-Ericksen fluid model is used to describe rheological behaviour of an elastico-viscous fluid. The stability criteria for stationary and oscillatory convection are derived for the case of free-free boundaries. It is observed that Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid in the case of stationary convection and rotation has stabilizing effect whereas AC electric field has destabilizing influence on the stability of the system. The necessary condition for the existence of oscillatory convection is also obtained. The effect of rotation and AC electric field has also been shown graphically. The present results are in agreement with the earlier published results.

Keywords

Rivlin-Ericksen Fluid, Rotation, AC Electric Field, Electrohydrodynamic, Viscosity, Viscoelasticity.

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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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