Numerical /Analytical Investigations of Stability of Stratified Rotatory Elastico –Viscous Walter’s (Model ) Fluid in the Presence of Variable Magnetic Field, Suspended Particles Saturating Porous Media

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Sumit Gupta
Virender Sharma

Abstract

The influence of viscosity, viscoelasticity, medium permeability, medium porosity and suspended particles on the stability of a stratified elastic-viscous fluid is examined for viscoelastic polymeric solutions in the simultaneous presence of a variable horizontal magnetic field  and uniform horizontal rotation in porous medium. These solutions are known as Walters’ (model ) fluid and their rheology is approximated by the Walters’ (model ) fluid constitutive relations, proposed by Walters’. The effects of coriolis force on the stability are chosen along the direction of the magnetic field and transverse to that of the gravitational field . Assuming the exponential stratifications in density, viscosity and viscoelasticity, the appropriate solution for the case of free boundaries is obtained using a linearized stability theory and normal mode analysis method. The dispersion relation is obtained and the behaviour of growth rates with respect to kinematic viscosity, kinematic viscoelasticity, medium permeability, dust particles and medium porosity is examined numerically using Newton-Raphson method through the software Fortran-90 and Mathcad. In contrast to the Newtonian fluids, the system is found to be unstable, for stable stratifications, for small wavelength perturbations. It is found that the magnetic field stabilizes the certain wave number band, for unstable stratification in the presence of rotation, suspended particles and this wave number range increases with the increase in magnetic field and decreases with the increase in kinematic viscoelasticity implying thereby the stabilizing effect of magnetic field,kinematic viscoelasticity , suspended particles and the kinematic viscosity has a stabilizing effect on the system for the low wave number range.  The medium permeability has enhancing effect on the growth rates with its increase for a fixed wave number. These results are shown graphically.

Keywords:
Walters’ (model ) fluid, magnetic field, rotation, viscosity, viscoelasticity, medium permeability, medium porosity, suspended particles.

Article Details

How to Cite
Gupta, S., & Sharma, V. (2020). Numerical /Analytical Investigations of Stability of Stratified Rotatory Elastico –Viscous Walter’s (Model ) Fluid in the Presence of Variable Magnetic Field, Suspended Particles Saturating Porous Media. Asian Journal of Pure and Applied Mathematics, 2(3), 9-20. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/884
Section
Original Research Article

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