An analytical solution of the basic Couette flow affected by a three-dimensional magnetic field

1990 ◽  
Vol 327 (1) ◽  
pp. 13-24 ◽  
Author(s):  
M. Weinstein
Keyword(s):  
Magnetic Field ◽  
Analytical Solution ◽  
Couette Flow ◽  
Three Dimensional

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.

MHD Couette Flow in Cylindrical Porous Annulus with Perfectly Conducting Walls

2013 ◽  
Vol 284-287 ◽  
pp. 829-833
Author(s):  
Sian Wun Guo ◽  
Jik Chang Leong
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Analytical Solution ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Variable Order ◽  
Radial Magnetic Field ◽  
Mhd Couette Flow ◽  
The Magnetic Field ◽  
Direction Opposite

This work obtained an analytical solution for a steady cylindrical MHD Couette flow in a porous medium between two perfectly conducting rotating cylinders under the influence of a non-uniform radial magnetic field. Since part of the analytical solution is expressed in terms of the integral of the Modified Bessel function of the first and second kinds of variable order, numerical integration was performed. Current results indicate that the flow may become more uniform when the strength of the external magnetic field is increased. The magnetic fluid tends to slow down if the permeability of the porous medium decreases. If the porous annulus is thick, the momentum of the flow is more difficult to propagate from the outer cylinder into the inner part of the annulus. If both the inner and outer cylinders rotate, the shear effect the inner cylinder imposes is only relatively influential in the region close to it. A decrease in Da no less than 10-2 may increase the amount of magnetic field induced. The transfer of momentum across the annular space is easier in a thin porous annulus than a thick one and hence induces a stronger magnetic field. If the inner cylinder rotates in the direction opposite of the outer one, the magnetic field in the clockwise direction will be induced in some region.

Hydromagnetic Taylor–Couette flow: numerical formulation and comparison with experiment

2002 ◽  
Vol 463 ◽  
pp. 361-375 ◽  
Author(s):  
A. P. WILLIS ◽  
C. F. BARENGHI
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Liquid Metals ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Hydrodynamic Calculations ◽  
Numerical Formulation ◽  
Taylor Couette ◽  
Prandtl Numbers ◽  
Taylor Couette Flow

Taylor–Couette flow in the presence of a magnetic field is a problem belonging to classical hydromagnetics and deserves to be more widely studied than it has been to date. In the nonlinear regime the literature is scarce. We develop a formulation suitable for solution of the full three-dimensional nonlinear hydromagnetic equations in cylindrical geometry, which is motived by the formulation for the magnetic field. It is suitable for study at finite Prandtl numbers and in the small Prandtl number limit, relevant to laboratory liquid metals. The method is used to determine the onset of axisymmetric Taylor vortices, and finite-amplitude solutions. Our results compare well with existing linear and nonlinear hydrodynamic calculations and with hydromagnetic experiments.

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