International Journal of Technology

Veena Sharma ¹, Anukampa Thakur ¹, Abhishek Sharma ¹

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5, IN

Abstract

In this study, the effect of Hall currents on the onset of stability of saturating porous media an electrically conducting ferromagnetic fluid heated from below using linear stability analysis is investigated. Using the Darcy law to modify the ferromagnetic fluid the momentum equations for a porous medium. The employed model incorporates the effects of polarization force and body couple. The coupled partial differential equations governing the physical problem are reduced to a set of ordinary differential equations using normal mode technique. These equations are solved analytically for stress-free boundaries and numerical results are computed by obtaining approximate solutions using Galerkin method using the software Mathematica for the case of stationary convection. It is found that the magnetic field and magnetization have a stabilizing effect as such their effect is to postpone the onset of thermal instability; whereas Hall currents are found to hasten the same. The medium permeability prepones the onset of convection under certain conditions implying thereby the destabilizing effect.

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Veena Sharma ¹, Radhe Shyam ¹, Sudrshna Sharma ², Abhishek Sharma ³

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla -171 005, IN
2 Department of Mathematics, Government Collage, Ghumarwin, District Bilaspur, IN
3 Bahra University Waknaghat Solan, IN

Abstract

This paper deals with the instability of viscous superposed, fluids saturating porous medium in the presence of horizontal magnetic field and to include the effect of surface tension. Using linear theory and normal mode technique the dispersion relation so obtained is analyzed mathematically for the stable configuration. The effects of medium porosity, surface tension and magnetic field, on the growth rate (imaginary) of the most unstable mode have been investigated numerically. The square of the Alfven velocity accounting for magnetic field and surface tension have stabilizing effect on the system and medium porosity has destabilizing effect on the system. All these numerical results have been depicted graphically. The results show that the magnetic field and surface tension bring about more stability for a certain wave number band on the growth rate of unstable configuration.

Keywords

Kelvin-Helmholtz Instability, Horizontal Magnetic Field, Surface Tension, Porous Medium.

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