Article

1998 ◽  
Vol 76 (12) ◽  
pp. 937-947
Author(s):  
M Takashima
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Wave Speed ◽  
Critical Reynolds Number ◽  
Maximum Velocity ◽  
Transverse Magnetic ◽  
Wave Number ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of combined plane Poiseuille and Couette flow of an electricallyconducting fluid under a transverse magnetic field is investigated using linear stability theory.In deriving the equations governing the stability, the so-called magnetic Stokes approximationis made using the fact that the magnetic Prandtl number Prm for most electrically conductingfluids is extremely small. The Chebyshev collocation method is adopted to obtain theeigenvalue equation, which is then solved numerically. The critical Reynolds number Rec,the critical wave number αc, and the critical wave speed cc are obtained for wide ranges ofthe Hartmann number Ha and the parameter k = U0 / (U0 + nu0), where U0 is the maximumvelocity of pure Couette flow and nu0 is the maximum velocity of pure Poiseuille flow. It isfound that a transverse magnetic field has both stabilizing and destabilizing effects on theflow depending on the value of k.PACS Nos. 47.20

Stability of the compressible viscous fluid around the plane Couette flow in the presence of a transverse uniform magnetic field

2018 ◽  
Vol 17 (01) ◽  
pp. 57-84
Author(s):  
Xingwei Zhang ◽  
Guojing Zhang ◽  
Hai-Liang Li
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Transverse Magnetic ◽  
Plane Couette Flow ◽  
Compressible Viscous Fluid ◽  
The Stability

In this paper, we consider the stability of three-dimensional compressible viscous fluid around the plane Couette flow in the presence of a uniform transverse magnetic field and show that the uniform transverse magnetic field has a stabilizing effect on the plane Couette flow. Namely, for a sufficiently large Hartmann number, the compressible viscous plane Couette flow is nonlinear stable for small Mach number and arbitrary Reynolds number so long as the initial perturbation is small enough.

The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field

1955 ◽  
Vol 233 (1192) ◽  
pp. 105-125 ◽  
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Conducting Fluid ◽  
Wave Number ◽  
Neutral Stability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability

The stability under small disturbances is investigated of the two-dimensional laminar motion of an electrically conducting fluid under a transverse magnetic field. It is found that the dominating factor is the change in shape of the undisturbed velocity profile caused by the magnetic field, which depends only on the Hartmann number M . Curves of wave number against Reynolds number for neutral stability are calculated for a range of values of M ; for large values of M the calculations are similar to those which determine the stability of ordinary boundary-layer flow. The critical Reynolds number is found to rise very rapidly with increasing M , so that a transverse magnetic field has a powerful stabilizing influence on this type of flow.

The effect of a radial magnetic field on the stability of Couette flow

1994 ◽  
Vol 72 (5-6) ◽  
pp. 258-265 ◽  
Author(s):  
M. A. Ali
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problem ◽  
Incompressible Fluid ◽  
Couette Flow ◽  
Wave Number ◽  
Rotating Cylinders ◽  
Radial Magnetic Field ◽  
Electrically Conducting ◽  
Angular Velocities ◽  
The Stability

The effect of a radial magnetic field on the stability of an electrically conducting incompressible fluid between two concentric rotating cylinders is considered. The eigenvalue problem for determining the critical Taylor number TC and the corresponding wave number aC is solved numerically for different values of ±μ(= Ω2/Ω1), (where Ω1, and Ω2 are me angular velocities of the inner and outer cylinders, respectively) and for different gap sizes. It is observed that the radial magnetic field stabilizes the flow. This effect is more pronounced for cylinders that are corotating as compared with counter-rotating cylinders or the situation where only the inner one is rotating.

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.

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