International Journal of Statistics and Applied Mathematics
  • Printed Journal
  • Indexed Journal
  • Refereed Journal
  • Peer Reviewed Journal

International Journal of Statistics and Applied Mathematics

2019, Vol. 4, Issue 5, Part B

Stability of stratified elastico-viscous Rivlin-Ericksen fluid in the presence of variable magnetic field and rotation saturating porous medium


Author(s): Sumit Gupta

Abstract: The influence of viscosity, viscoelasticity, medium permeability and medium porosity on the stability of a stratified elastic-viscous Rivlin –Ericksen fluid is examined for viscoelastic polymeric solutions in the simultaneous presence of a variable horizontal magnetic field and uniform horizontal rotation in porous medium. 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 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 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 and kinematic viscoelasticity 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.

Pages: 85-92 | Views: 177 | Downloads: 16

Download Full Article: Click Here
How to cite this article:
Sumit Gupta. Stability of stratified elastico-viscous Rivlin-Ericksen fluid in the presence of variable magnetic field and rotation saturating porous medium. International Journal of Statistics and Applied Mathematics. 2019; 4(5): 85-92.
Call for book chapter
International Journal of Statistics and Applied Mathematics