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Research Journal of Engineering and Technology
Year : 2015, Volume : 6, Issue : 1
First page : ( 63) Last page : ( 71)
Print ISSN : 0976-2973. Online ISSN : 2321-581X.
Article DOI : 10.5958/2321-581X.2015.00011.2

Stability of Stratified Rivlin-Ericksen Fluid in the Presence of Horizontal Magnetic Field and Uniform Horizontal Rotation in Porous Medium

Kumar Sanjeev1,*, Sharma Veena2, Kishor Kamal3, Rana G. C.4

1Department of Mathematics, Govt. College Joginder Nagar, Distt. Mandi, (H.P.) India

2Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla

3Department of Mathematics, Govt.Senior Secondary School, Sunder Nagar, India

4Department of Mathematics, Govt. College Naduan Distt. Hamirpur (H.P.) India

*Corresponding Author: sanjeev.gcm@gmail.com

AMS Classification Number:76A10

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, 0, 0) and uniform horizontal rotation (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 (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.

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Keywords

Rivlin-Ericksen fluid, magnetic field, rotation, viscosity, viscoelasticity, porous medium.

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