Conservation theorems for magnetic field and vorticity in two-dimensional conducting fluid flows

1997 ◽  
Vol 8 (1) ◽  
pp. 31-33
Author(s):  
V. B. Gorskii
Keyword(s):  
Magnetic Field ◽  
Fluid Flows ◽  
Conducting Fluid ◽  
Two Dimensional

The effect of a strong magnetic field on two-dimensional flows of a conducting fluid

1963 ◽  
Vol 15 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Magnetic Field ◽  
Perturbation Technique ◽  
The Body ◽  
Conducting Fluid ◽  
Order Effects ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Exterior Region ◽  
Electrically Conducting ◽  
Higher Order Effects

The motion of a viscous, electrically conducting fluid past a finite two-dimensional obstacle is investigated. The magnetic field is assumed to be uniform and parallel to the velocity at infinity. By means of a perturbation technique, approximations valid for large values of the Hartmann number M are derived. It is found that, over any finite region, the flow field is characterized by the presence of shear layers fore and aft of the body. The limit attained over the exterior region represents the two-dimensional counterpart of the axially symmetric solution given by Chester (1961). Attention is focused on a number of nominally ‘higher-order’ effects, including the presence of two distinct boundary layers. The results hold only when M [Gt ] Re; Re = Reynolds number. However, a generalization of the procedure, in which the last assumption is relaxed, is suggested.

Motion of a sphere through a conducting fluid in the presence of a strong magnetic field

1956 ◽  
Vol 52 (2) ◽  
pp. 301-316 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Fluid Velocity ◽  
Steady Motion ◽  
Conducting Fluid ◽  
Two Dimensional ◽  
Conducting Sphere ◽  
Straight Lines ◽  
As If

ABSTRACTThe steady motion of a perfectly conducting sphere in an inviscid conducting fluid in the presence of a strong magnetic field is discussed. It is shown that if the fluid velocity is ultimately steady then it is two-dimensional, and a cylinder of fluid whose generators are parallel to the direction of the field moves with the sphere as if solid. The streamlines outside are straight lines if the sphere moves in the direction of the field but have to execute sharp turns if it moves at right angles to the field. The motion to be expected in practice is discussed using an analogy.

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