Effect of Suspended Particles and Magnetic Field on the Stability of Jeffrey Fluid in Porous Medium

Effect of Suspended Particles and Magnetic Field on the Stability of Jeffrey Fluid in Porous Medium

Pushap Lata Sharma*, Mohini Kapalta^*2

Department of Mathematics & Statistics, Himachal Pradesh University, Summer Hill, Shimla, India

ABSTRACT:

The effect of suspended particles on the onset of convection in a horizontal Jeffrey fluid layer saturated a porous medium in the presence of magnetic field is investigated. The physical system is heated from below such that uniform temperature gradient is maintained. Linear stability theory based upon the normal mode technique is employed for stability analysis. The magnetic field has a stabilizing effect and suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has a destabilizing effect on the system. The graphs have been plotted to study the effects of suspended particles, Jeffrey fluid, medium permeability on stationary convection.

1 Introduction

Natural convection in porous medium is considered due to its various applications in several fields such as heat-exchanger, oil recovery, construction materials, soil mechanics, minimising pollutant generation and material industry. Nield and Bejan[8] [8] have written a book on convection in porous medium. Chandrasekhar [4] has discussed the thermal instability of fluid layers heated from below. Lapwood [7], Wooding [21] and [9] have researched on convection of fluid in porous medium.

Bhatia and Steiner [1] and Sharma [16] have examined the instability in viscoelastic fluid in hydromagnetics and found that magnetic field has stabilizing effect on the stationary convection. Sharma [15] studied the convection in compressible fluids when there is both magnetic field and rotation. Sharma and Aggarwal [17] found that suspended particles have destabilizing effect and magnetic field has stabilizing effect on stationary convection. [18,19] worked upon the effect of magnetic field on the onset of thermal instability.

Scanlon and Segel [13] examined the impact of suspended particles on the onset of Bénard convection and found that whereas small particles increased the exponential growth of unstable disturbances, coarse particles slowed it down. Chand et al. [3] has studied the effects of suspended particles under more realistic boundary conditions. Rana and Kumar [11] and Rana and Thakur [12] investigated the effects of rotation and suspended particles in a porous medium by heating fluid from below. Numerous other scholars have also looked on convection with suspended particles, such as [2,14,20].

There are several applications for non-Newtonian fluid in the geophysical, chemical, and biological sciences. The variety of commercial and technical applications of non-Newtonian fluids has raised interest in their study. The non-Newtonian Jeffrey fluid, which has a time derivative rather than a convective derivative, is one of the most basic non-Newtonian fluid models. Rana and Gautam [10][10] studied the effect of Jeffrey nanofluid on the onset of thermal instability in porous medium. Hayat et al. [6] investigated heat transfer analysis in convective flow of Jeffrey fluid with nanoparticles. Choi and Jeffrey [5] studied the thermal conductivity of fluids with nanoparticles.

Given the importance of the several applications mentioned above, we are particularly interested in studying how magnetic field and suspended particles affect the stability of Jeffrey fluid heated from below in porous media in the current work.

2 MATHEMATICAL MODEL:

Consider a Jeffrey fluid confined between two parallel horizontal planes  and  saturated by layer of porous medium subjected to uniform magnetic field and gravity  force acting vertically. The physical system is heated from below such that uniform temperature  gradient is maintained.