scholarly journals Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

2016 ◽  
Vol 8 (2) ◽  
pp. 69 ◽  
Author(s):  
Ahmad R. AlHamdan ◽  
Sameh A. Alkharashi
Keyword(s):  
Magnetic Field ◽  
Porous Media ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Immiscible Fluids ◽  
Horizontal Magnetic Field ◽  
Uniform Velocity ◽  
Stability Diagrams ◽  
The Stability ◽  
Complex Coefficients

The current study concerns, the effect of a horizontal magnetic field on the stability of three horizontal finite layers of immiscible fluids in porous media. The problem examines few representatives of porous media, in which the porous media are assumed to be uniform, homogeneous and isotropic. The dispersion relations are derived using suitable boundary and surface conditions in the form of two simultaneous Mathieu equations of damping terms having complex coefficients. The stability conditions of the perturbed system of linear evolution equations  are investigated  both analytically and numerically and stability diagrams are obtained. The stability diagrams are discussed in detail in terms of various parameters governing the flow on the stability behavior of the system such as the streaming velocity, permeability of the porous medium and the magnetic properties. In the special case of uniform velocity, the fluid motion has been displayed in terms of streamlines concept, in which the streamlines contours are plotted. In the  uniform velocity motion, a fourth order polynomial equation with complex coefficients is obtained. According to the complexity of the mathematical treatments, when the periodicity of the velocity is taken into account, the method of multiple scales is applied to obtain stability solution for the considered system.<br />It is found that a stability effect is found for increasing, the magnetic permeability ratio, the magnetic field, and  the permeability parameter  while the opposite influence is observed for increasing the upper layer velocity.

Nonlinear hydrodynamic Rayleigh—Taylor instability of viscous magnetic fluids: effect of a tangential magnetic field

1994 ◽  
Vol 51 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Yusry O. El-Dib
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Magnetic Fluids ◽  
Taylor Instability ◽  
Stable Region ◽  
Solvability Conditions ◽  
System A ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Complex Coefficients

The nonlinear Rayleigh—Taylor instability of viscous magnetic fluids is considered under the influence of gravity and surface tension in the presence of a constant tangential magnetic field. The method of multiple-scales expansion is employed. A nonlinear Schrödinger equation with complex coefficients is imposed from the solvability conditions and used to analyse the stability of the system. A quadratic dispersion relation with complex coefficients is obtained. The Hurwitz criterion for a quadratic polynomial with complex coefficients is used to control the stability of the system. It is found that an increase in the viscosity increases the extent of the stable region in the presence of a magnetic field. Finally it is shown that the magnetic permeability of the fluid affects the stability conditions.

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

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

2020 ◽  
Vol 330 ◽  
pp. 01035
Author(s):  
Rabah Djeghiour ◽  
Bachir Meziani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Magnetic Fluids ◽  
Physical Parameters ◽  
Stability Diagrams ◽  
Stability And Instability ◽  
Mass And Heat Transfer ◽  
Model Equations ◽  
The Stability ◽  
Oblique Magnetic Field

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.

Hydromagnetic Stability of Two Rivlin-Ericksen Elastico-Viscous Superposed Conducting Fluids

1997 ◽  
Vol 52 (6-7) ◽  
pp. 528-532
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Unstable Configuration ◽  
The Stability ◽  
Superposed Fluids ◽  
The Magnetic Field ◽  
Conducting Fluids

Abstract The stability of the plane interface separating two Rivlin-Ericksen elastico-viscous superposed fluids of uniform densities when the whole system is immersed in a uniform horizontal magnetic field has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities and equal kinematic viscoelasticities. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave-number range of the unstable configuration. The behaviour of growth rates with respect to kinematic viscosity and kinematic viscoelasticity parameters are examined numerically.

Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids

2001 ◽  
Vol 56 (6-7) ◽  
pp. 416-439
Author(s):  
Mohamed Fahmy El
Keyword(s):  
Magnetic Field ◽  
Stable Configuration ◽  
Retardation Time ◽  
Horizontal Magnetic Field ◽  
Fluid Velocities ◽  
Unstable Configuration ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids ◽  
Alfven Velocity

Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range of the unstable configuration even in the presence of the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a.

scholarly journals Larmor Radius and Collisional Effects on the Dynamic Stability of a Composite Medium

1972 ◽  
Vol 25 (3) ◽  
pp. 259 ◽  
Author(s):  
PK Bhatia ◽  
JM Steiner
Keyword(s):  
Magnetic Field ◽  
Dynamic Stability ◽  
Variable Density ◽  
Composite Medium ◽  
Larmor Radius ◽  
Combined Effects ◽  
Composite Media ◽  
Horizontal Magnetic Field ◽  
The Stability ◽  
Streaming Motion

The combined effects of a finite ion Larmor radius and collisions with neutral atoms on the dynamic stability of a composite medium are investigated. The stability analysis has been carried out for a semi-infinite composite medium of variable density in the presence and absence of a uniform streaming motion. Wave propagations transverse to the direction of the uniform horizontal magnetic field have been considered. It is found that the effects of the collisions as well as the finite ion Larmor radius are stabilizing on both streaming and non-streaming composite media.

Rayleigh-Taylor Instability of a Stratified Magnetized Medium in the Presence of Suspended Particles

1984 ◽  
Vol 39 (10) ◽  
pp. 939-944 ◽  
Author(s):  
R. K. Chhajlani ◽  
R. K. Sanghvi ◽  
P. Purohit
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Suspended Particles ◽  
Frequency Parameter ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Horizontal Magnetic Field ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
The Magnetic Field

Abstract The hydromagnetric Rayleigh-Taylor instability of a composite medium has been studied in the presence of suspended particles for an exponentially varying density distribution. The prevalent horizontal magnetic field and viscosity of the medium are assumed to be variable. The dispersion relation is derived for such a medium. It is found that the stability criterion is independent of both viscosity and suspended particles. The system can be stabilized for an appropriate value of the magnetic field. It is found that the suspended particles can suppress as well as enhance the growth rate of the instability in certain regions. The growth rates are obtained for a viscid medium with the inclusion of suspended particles and without it. It has been shown analytically that the growth rate is modified by the inclusion of the relaxation frequency parameter of the suspended particles.

Hydromagnetic stability of a thin electrically conducting fluid film flowing down the outside surface of a long vertically aligned column

2009 ◽  
Vol 223 (2) ◽  
pp. 415-426 ◽  
Author(s):  
P-J Cheng
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Conducting Fluid ◽  
Fluid Film ◽  
Electrically Conducting ◽  
Free Film ◽  
Electrically Conducting Fluid ◽  
Non Linear ◽  
The Stability

This article considers the stability of a thin electrically conducting fluid film flowing down the outer surface of a long vertical cylinder in the presence of an applied magnetic field. Using the long-wave perturbation method to solve the generalized non-linear kinematic equations with free film interface, the normal mode approach is first used to compute the linear stability solution. The method of multiple scales is then used to obtain the weak non-linear dynamics. The results indicate that both subcritical instability and supercritical stability conditions are possible. The degree of instability in the film flow is intensified by the lateral curvature of the cylinder. The results also show that increasing the strength of the magnetic field tends to enhance the stability.

Nonlinear electrohydrodynamic Rayleigh–Taylor instability with mass and heat transfer: effect of a normal field

1994 ◽  
Vol 72 (9-10) ◽  
pp. 537-549 ◽  
Author(s):  
Abou El Magd A. Mohamed ◽  
Abdel Raouf F. Elhefnawy ◽  
Y. D. Mahmoud
Keyword(s):  
Heat Transfer ◽  
Multiple Scales ◽  
Landau Equation ◽  
Finite Thickness ◽  
Surface Charges ◽  
Stability Diagrams ◽  
Dielectric Fluids ◽  
Mass And Heat Transfer ◽  
The Stability ◽  
Cubic Nonlinear Schrödinger Equation

The nonlinear electrohydrodynamic stability of two superposed dielectric fluids with interfacial transfer of mass and heat is presented for layers of finite thickness. The fluids are subjected to a normal electric field in the absence of surface charges. Using a technique based on the method of multiple scales it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. When the mass and heat transfer are neglected, the cubic nonlinear Schrödinger equation is obtained. Further, it is shown that, near the marginal state, a nonlinear diffusion equation is obtained in the presence of mass and heat transfer. The various stability criteria are discussed both analytically and numerically and the stability diagrams are obtained.

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