scholarly journals Convective Instability in a Hele Shaw Cell with the Effect of Through Flow and Magnetic Field

2018 ◽  
Author(s):  
Dhananjay Yadav
Keyword(s):  
Magnetic Field ◽  
Convective Instability ◽  
Fluid Layer ◽  
Analytical Investigation ◽  
Linear Stability Theory ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Through Flow ◽  
The Stability ◽  
Hele Shaw Cell

In this paper, an analytical investigation of the combined effect of through flow and magnetic field on the convective instability in an electrically conducting fluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory. The Galarkin method is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability of the system is examined analytically as well as graphically. It is observed that the through flow and magnetic field have both stabilizing effects, while the Hele-Shaw number has destabilizing effect on the stability of system. It is also found that the oscillatory mode of convection possible only when the magnetic Prandtl number takes the values less than unity.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

THE STAEILITY OF COUETTE FLOW IN AN AXIAL MAGNETIC FIELD

1958 ◽  
Vol 36 (11) ◽  
pp. 1509-1525 ◽  
Author(s):  
E. R. Niblett
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Theoretical Prediction ◽  
Viscous Flow ◽  
Rotation Speed ◽  
Axial Magnetic Field ◽  
Radioactive Isotopes ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability

Chandrasekhar's theory of the stability of viscous flow of an electrically conducting fluid between coaxial rotating cylinders with perfectly conducting walls is extended to include the case of non-conducting walls, and it is found that their effect is to reduce the critical Taylor numbers and increase the wavelength of the instability patterns by considerable amounts. An experiment designed to measure the values of magnetic field and rotation speed at the onset of instability in mercury between perspex cylinders is described. The radioactive isotopes Hg197 and Hg203 were used to trace the flow. The results support the theoretical prediction that the boundary conditions can have a large effect on the motion.

scholarly journals Effects of Magnetic Field and Non-Uniform Basic Temperature Gradient

2002 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
S. Pranesh
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Conducting Fluid ◽  
Wave Number ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

The effects of a non-uniform temperature gradient and magnetic field on the onset of convection in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free/adiabatic boundary and a lower rigid/isothermal boundary have been considered. A linear stability analysis is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the Eigen values. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid without Suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

The effect of pulsating throughflow on the onset of magneto convection in a layer of nanofluid confined within a Hele-Shaw cell

2019 ◽  
Vol 233 (5) ◽  
pp. 1074-1085 ◽  
Author(s):  
Dhananjay Yadav
Keyword(s):  
Magnetic Field ◽  
Convective Motion ◽  
Lewis Number ◽  
Joint Effect ◽  
Linear Stability Theory ◽  
Number Formula ◽  
The Stability ◽  
The Impact ◽  
Profile Approach ◽  
Hele Shaw Cell

In this article, the joint effect of pulsating throughflow and magnetic field on the onset of convective instability in a nanofluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory and frozen profile approach. The model utilized for nanofluid combines the impacts of Brownian motion and thermophoresis, while for Hele-Shaw cell, Hele-Shaw model is considered. The Galerkin technique is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability framework is examined analytically. It is observed that the pulsating throughflow and magnetic field have both stabilizing effects. The impact of increasing the Hele-Shaw number [Formula: see text], the modified diffusive ratio [Formula: see text] and the nanoparticle Rayleigh number [Formula: see text] is to quicken the convective motion, while the Lewis number [Formula: see text] has dual impact on the stability framework in the existence of pulsating throughflow. It is also established that the oscillatory mode of convective motion is possible only when the value of the magnetic Prandtl number [Formula: see text] is not greater than unity.

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.

Evolution of wave packets in magnetohydrodynamics

1995 ◽  
Vol 53 (2) ◽  
pp. 145-167 ◽  
Author(s):  
Anju Pusri ◽  
S. K. Malik
Keyword(s):  
Magnetic Field ◽  
Wave Packets ◽  
Stability Diagram ◽  
Envelope Soliton ◽  
Electrically Conducting ◽  
Self Focusing ◽  
Electrically Conducting Fluid ◽  
Regions Of Stability ◽  
Taylor Problem ◽  
The Stability

The propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field is investigated in (2 + 1) dimensions. The evolution of wave envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of different regions of instability. The effect of the applied magnetic field is not only significant but also different for different regions of stability. ‘Envelope soliton’ and ‘waveguide’ solutions of the amplitude equation are also discussed. The self-focusing phenomenon that arises when the amplitude of the wave becomes infinite in finite time is also examined. It is found that in a certain region of the stability diagram it may be easier to observe this phenomenon in the presence of a magnetic field. The Rayleigh-Taylor problem is also studied and various criteria for the existence of instability are obtained.

The stability of hydromagnetic Couette flow

1964 ◽  
Vol 60 (3) ◽  
pp. 635-651 ◽  
Author(s):  
P. H. Roberts
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Conducting Fluid ◽  
Theoretical Studies ◽  
Numerical Computations ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability ◽  
Gap Width

AbstractThe theoretical studies of Chandrasekhar on the stability of Couette flow in a viscous, electrically conducting, fluid in the presence of a uniform axial magnetic field are extended to include cases of finite gap width between the cylinders, and cases in which the conductivity of the walls of the containing cylinders is finite. In addition, the non-axisymmetric modes of instability are discussed, and the results of numerical computations are presented.

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