THE STABILITY OF SOME PHYSICALLY REALISTIC MODELS USING CHANDRASEKHER'S TECHNIQUES (original) (raw)

STABILITY OF NON-VISCOUS ROTATING FLOW'S

isara solutions, 2014

The paper examines the stability of an in compressible, non-viscous fluid with horizontal magnetic field and vertical rotation confined between two parallel plates, we have obtained some important results about the stability or instability of the system and estimates on the wave velocity of unstable modes.

THE STABILITY OF NON-VISCOUS ROTATING DUSTY FLOW'S WITH THE HELP OF CHANDRASEKHER'S TECHNIQUE

isara solutions, 2015

The paper examines the stability of an incompressible, non-viscous dusty fluid between two parallel plates, in the presence of horizontal magnetic field and vertical rotation. It is shown that the rotation has a stabilizing character and the instability increases with the increase in the number of density of dust particles. Some important results about linearly varying density and magnetic field and exponential varying density and magnetic field with the help of Chandrasekher's technique.

Note on the stability of parallel magnetic fields

Astrophysics and Space Science, 1982

The stability characteristics of parallel magnetic fields when fluid motions are present along the lines of force is studied. The stability criterion for both symmetric (m = 0) and asymmetric (m = 1) modes are discussed and the results obtained by Trehan and Singh (1978) are amended in the present study. The results obtained for the cylindrical geometry are shown to play an important role for ka <4, where k is the wave number, a is the radius of the cylinder, compared to the results obtained by Geronicolas (1977) for the slab geometry.

Hydrodynamic Stability of Plane Poiseuille Flow of Non-Newtonian Fluids in the Presence of a Transverse Magnetic Field

Nihon Reoroji Gakkaishi, 2014

The linear stability of a plane Poiseuille flow of an electrically conducting viscoelastic fluid in the presence of a transverse magnetic field is investigated numerically. The fourth-order modified Orr-Sommerfeld equation governing the stability analysis is solved by a spectral method with expansions in Lagrange polynomials, based on collocation points of Gauss-Lobatto. The combined effects of a magnetic field and fluid's elasticity on the stability picture of the plane Poiseuille flow are investigated in two regards. Firstly, the critical values of a Reynolds number and a wavenumber, indicating the onset of instabilities, are computed for several values of a magnetic Hartman number, M, and at different values of an elasticity number, K. Secondly, the structure of the eigenspectrum of the second-order and second-grade models in the Poiseuille flow is studied. In accordance to previous studies, the magnetic field is predicted to have a stabilizing effect on the Poiseuille flow of viscoelastic fluids. Hence, for second-order (SO) fluids for which the elasticity number K is negative, the critical Reynolds number Re c increases with increasing the Hartman number M, for various values of the elasticity number K. However, for second-grade (SG) fluids (K > 0), the critical Reynolds number Re c increases with increasing the Hartman number only for certain values of the elasticity number K, while decreases for the others.

Stability analysis of magnetic fluids in the presence of an oblique field and mass and heat transfer

MATEC Web of Conferences

In this paper, we investigate an analysis of the stability of a basic flow of streaming magnetic fluids in the presence of an oblique magnetic field is made. We have use the linear analysis of modified Kelvin-Helmholtz instability by the addition of the influence of mass transfer and heat across the interface. Problems equations model is presented where nonlinear terms are neglected in model equations as well as the boundary conditions. In the case of a oblique magnetic field, the dispersion relation is obtained and discussed both analytically and numerically and the stability diagrams are also obtained. It is found that the effect of the field depends strongly on the choice of some physical parameters of the system. Regions of stability and instability are identified. It is found that the mass and heat transfer parameter has a destabilizing influence regardless of the mechanism of the field.

On the Stability of a Compressible Axial Flow with an Axial Magnetic Field

Journal of Fluids, 2013

We consider the stability problem of inviscid compressible axial flows with axial magnetic fields following the work of Dandapat and Gupta (Quarterly of Applied Mathematics, 1975). A numerical study of the stability of some basic flows has been carried out and it is found that an increase in the magnetic field strength has a stabilizing effect on subsonic flows and a destabilizing effect on supersonic flows. An analytical study of the stability problem has also been done in the present paper, but this analytical study is restricted by the approximation ≪ 1 and ≪ 1, where is the Mach number and is the imaginary part of the complex phase velocity. A semicircular region depending on the magnetic field parameter and the Mach number is found for subsonic disturbances and as a consequence it is found that sufficiently strong magnetic field stabilizes all subsonic disturbances. Under a weak magnetic field, it is shown that short subsonic disturbances are stable.

Stability of a compressible fluid cylinder ambient with a bounded conducting medium under general varying magnetic fields

Astrophysics and Space Science, 1990

The stability of a compressible fluid cylinder pervaded by a longitudinal uniform magnetic field-ambient with a bounded conducting medium of negligible inertia penetrated with general varying vacuum magnetic fields has been developed. The stability criterion describing the stability characteristics of that model is derived and discussed analytically in general terms. The axial fields have always stabilizing influences. The azimuthal vacuum field has a destabilizing effect, however, it becomes minimal if the perturbed and the unperturbed vacuum fields are not orthogonal. The magnetodynamic instability of the fluid jet is modified in the presence of the fluid compressibility. The stabilizing influence due to the latter may be realized more clearly on utilizing the numerical methods for investigating the eigenvalue relation.

Hydromagnetic linear instability analysis of Giesekus fluids in plane Poiseuille flow

Communications in Nonlinear Science and Numerical Simulation, 2009

The effects of a fluid's elasticity are investigated on the instability of plane Poiseuille flow on the presence of a transverse magnetic field. To determine the critical Reynolds number as a function of the Weissenberg number, a two-dimensional linear temporal stability analysis will be used assuming that the viscoelastic fluid obeys Giesekus model as its constitutive equation. Neglecting terms nonlinear in the perturbation quantities, an eigenvalue problem is obtained which is solved numerically by using the Chebyshev collocation method. Based on the results obtained in this work, fluid's elasticity is predicted to have a stabilizing or destabilizing effect depending on the Weissenberg number being smaller or larger than one. Similarly, solvent viscosity and also the mobility factor are both found to have a stabilizing or destabilizing effect depending on their magnitude being smaller or larger than a critical value. In contrast, the effect of the magnetic field is predicted to be always stabilizing.

Instability of a compressible annular magnetized fluid

Applied Mathematics and Computation, 2005

The instability of a compressible annular cylindrical fluid jet coaxial with a very dense fluid cylinder of negligible inertia endowed with surface tension and acting upon the electromagnetic force has been developed. A general eigenvalue relation is derived and discussed for all disturbances. The capillary force is destabilizing only for small symmetric perturbations and stabilizing for the rest. The axial fields internal and external to annular jet have stabilizing influences for all wavelengths in all possible perturbation modes. The azimuthal tenuous varying field is purely destabilizing in the symmetric mode but it is stabilizing or destabilizing in the asymmetric modes according to restrictions. The compressibility has a stabilizing tendency for all wavelengths. The capillary instability of the compressible fluid may be completely suppressed above a certain value of the basic magnetic field provided that the tenuous azimuthal field is very low and then the MHD stability arises. Some reported works are deduced as limiting cases.