The effect of compressibility, rotation and magnetic field on thermal instability of Walters’ fluid permeated with suspended particles in porous medium

Abstract

The purpose of this paper is to study the effects of compressibility, rotation, magnetic field, and suspended particles on thermal stability of a layer of visco-elastic Walters' (model B') fluid in porous medium. Using linearized theory and normal mode analysis, dispersion relation has been obtained. In case of stationary convection, it is found that the rotation has stabilizing effect on the system. The magnetic field may have destabilizing effect on the system in the presence of rotation while in the absence of rotation it always has stabilizing effect. The medium permeability has destabilizing effect on the system in the absence of rotation while in the presence of rotation it may have stabilizing effect. The suspended particles and compressibility always have destabilizing effect. Due to vanishing of viscoelastic parameter, the compressible visco-elastic fluid behaves like Newtonian fluid. Graphs have also been plotted to depict the stability characteristics. The viscoelasticity, magnetic field and rotation are found to introduce oscillatory modes into the system which were non-existent in their absence.

Triple Diffusive Convection of a Non-Newtonian Fluid Under the Combined Effect of Compressibility and Variable Gravity

“…The convection problem when the fluid layer is heated and soluted from below is studied by Veronis [2] and Nield [3]. The instability of non-Newtonian fluids has been studied by several authors [4][5][6][7][8][9][10][11][12][13][14][15] and [16,17,18,19,20,21]. There are so many problems in engineering, oceanography and limnology which can be studied by double diffusive convection.…”

“…The variation of R with k (2, 4, 6...) for P 1 =0 5,. H 2 =20, H 3 =30, S 1 =20, S 2 =30, G=5, 2and suspended particle parameter H 1(=20, 40, 60, 80).…”

A compressibility corrections of the pressure strain linear part models

“…In the recent years, the research in the field of compressible turbulence has received considerable attention. These years marked by an increase of numerical [1][2][3][4][5][6], experimental [7,8] and modeling works allowed a better understanding of the compressibility phenomena. The reason behind motivation is that the advance in the compressible turbulence area is found to be essential for the development in designing a new generation of the supersonic aircraft and the high speed combustion.…”

“…The DNS results [4,5] and the experiences [7,8] reached similar conclusions concerning the role of the pressure in the developed compressible plane mixing layers. As a consequence, in several studies [2,3,10,11], the pressure strain modeling has been considered as an important attractive research in the second order closure for the compressible turbulence flows.…”

On triply diffusive convection in completely confined fluids

“…This phenomenon is called double-diffusive convection. To determine the conditions under which these convective motions will occur, the linear stability of two superposed concentration (or one of them may be temperature gradient) gradients has been studied by Stern [1], Veronis [2], Nield [3], Baines and Gill [4], Turner [5], Akrour et al [6], El-Maghlany et al [7], Periyanagounder et al [8], Aggarwal and Makhija [9] and Aggarwal and Verma [10].…”