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Vorticity generation in creeping flow past a magnetic obstacle Centro de Investigacin en Energa, UNAM, Apartado Postal 34, Temixco, Morelos 62580, Mexico
 

Summary: Vorticity generation in creeping flow past a magnetic obstacle
S. Cuevas*
Centro de Investigación en Energía, UNAM, Apartado Postal 34, Temixco, Morelos 62580, Mexico
S. Smolentsev
and M. Abdou
Mechanical & Aerospace Engineering Department, UCLA, 44-114 Engineering IV, Los Angeles, California 90095-1597, USA
Received 17 February 2006; revised manuscript received 5 September 2006; published 3 November 2006
The generation of vorticity in the two-dimensional creeping flow of an incompressible, electrically conduct-
ing viscous fluid past a localized magnetic field distribution is analyzed under the low magnetic Reynolds
number approximation. It is shown that the Lorentz force produced by the interaction of the induced electric
currents with the nonuniform magnetic field acts as an obstacle for the flow, creating different steady flow
patterns that are reminiscent of those observed in the flow past bluff bodies. First, analytic solutions are
obtained for a creeping flow past a magnetic point dipole, modeled as a Gaussian distribution. Using a
perturbation scheme, the vorticity is expressed as an expansion in the small Reynolds number, and first- and
second-order approximations are calculated. The induced magnetic field, pressure, and stream function are also
determined. Further, full numerical finite difference solutions are obtained for a uniform creeping flow past a
finite size magnetic field distribution produced by a square magnetized plate. Hartmann numbers in the range
1 Ha 100 are explored. Depending on the strength of the magnetic force, stagnation zones or steady vortical
structures are obtained. The analysis contributes to the understanding of flows in nonuniform magnetic fields
and flows produced by localized forces.

  

Source: Abdou, Mohamed - Fusion Science and Technology Center, University of California at Los Angeles

 

Collections: Plasma Physics and Fusion