An exact solution in the stability of m. h. d. Couette flow

1972 ◽  
Vol 327 (1569) ◽  
pp. 269-278 ◽  
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Couette Flow ◽  
Stability Problem ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Mhd Stability ◽  
Arbitrary Magnetic Field ◽  
The Stability ◽  
Conducting Cylinders

The MHD stability problem for dissipative Couette flow in a narrow gap between corotating, conducting cylinders with an axial magnetic field is solved exactly. Results are presented for an arbitrary magnetic field; in particular, previous results on the zero and infinite magnetic field limits are verified.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

scholarly journals Stability of narrow-gap MHD Taylor-Couette flow with radial heating and constant heat flux at the outer cylinder

2005 ◽  
Vol 32 (4) ◽  
pp. 359-384 ◽  
Author(s):  
R.K. Deka
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Outer Cylinder ◽  
Constant Heat Flux ◽  
Wave Number ◽  
Narrow Gap ◽  
Critical Wave Number ◽  
Constant Heat

A linear stability analysis has been presented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field and constant heat flux at the outer cylinder. The narrow-gap equations with respect to axisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of boundary conditions, conducting and non-conducting walls are considered. A parametric study covering on the basis of ?, the ratio of the angular velocity of the outer cylinder to that of inner cylinder, Q, the Hartmann number which represents the strength of the axial magnetic field, and N, the ratio of the Rayleigh number and Taylor number representing the supply of heat to the outer cylinder at constant rate is presented. The three cases of ? < 0 (counter rotating), ? > 0 (co-rotating) and ? = 0 (stationary outer cylinder) are considered wherein the magnetic Prandtl number is assumed to be small. Results show that the stability characteristics depend mainly on the conductivity on the cylinders and not on the heat supplied to the outer cylinder. As a departure from earlier results corresponding to isothermal as well as hydromagnetic flow, it is found that the critical wave number is strictly a monotonic decreasing function of Q for conducting walls. Also, the presence of constant heat flux leads to a fall in the critical wave number for counter rotating cylinders, which states that for large values of -?, there occur transition from axisymmetric to non-axisymmetric disturbance whether the flow is hydrodynamic or hydromagnetic and this transition from axisymmetric to non-axisymmetric disturbance occur earlier as the strength of the magnetic field increases.

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.

The stability of Couette flow in the presence of an axial magnetic field

1963 ◽  
Vol 17 (1) ◽  
pp. 52-60 ◽  
Author(s):  
Ulrich H. Kurzweg
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Taylor Number ◽  
Asymptotic Formulas ◽  
Magnetic Prandtl Number ◽  
The Mean ◽  
The Stability ◽  
Gap Spacing

The stability of Couette flow between concentric, co-rotating cylinders in an axial magnetic field is examined for fluids of arbitrary magnetic Prandtl number Pm = ν/η, where ν is the kinematic and η the magnetic viscosity of the fluid. It is assumed that the gap spacing d between the cylinders is small compared to the mean radius and that no magnetic disturbances penetrate into the cylinder walls. The critical Taylor number at which non-oscillatory disturbances are marginally stable is determined as a function of the magnetic Prandtl number and the dimensionless parameter S = (Vad/v)2, where Va is the Alfvén velocity. Asymptotic formulas relating the critical Taylor number to the magnitude of the magnetic field are derived for the limiting conditions of very small and very large magnetic Prandtl number.

scholarly journals HYDROMAGNETIC STABILITY OF STREAMING COMPRESSIBLE CYLINDER PERVADED BY MAGNETIC FIELD

2014 ◽  
Vol 12 (4) ◽  
pp. 3421-3427
Author(s):  
Shimaa L. Azwz
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Axial Magnetic Field ◽  
Wave Length ◽  
Magnetic Intensity ◽  
Axisymmetric Mode ◽  
Small Wave ◽  
Mhd Stability ◽  
The Stability ◽  
Compressible Cylinder

The Stability of MHD compressible streaming fluid cylinder of radius endowed with surface tension and pervaded by axial magnetic field has been developed. The stability criterion is established in general form. The model is capillary unstable only in the axisymmetric mode m=0, the electromagnetic forces acting interior and exterior the fluid cylinder are stabilizing and the MHD stability is destabilizing for small wave length. In the latter case the instability shrinks with increasing the magnetic intensity. However the compressibility has a stabilizing tendency.

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