# FINITE ELEMENT ANALYSIS OF STIRRING INDUCED BY AN ALTERNATING MAGNETIC FIELD

M. BERELOWITZ (Computational Mechanics Laboratory, Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel)
P. BAR‐YOSEPH (Computational Mechanics Laboratory, Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel)

ISSN: 0961-5539

Article publication date: 1 February 1992

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## Abstract

The numerical investigation into the stirring induced by an alternating magnetic field, applied in the axial direction of a closed axisymmetric container of conducting fluid, is presented. The interaction between the azimuthal current and magnetic field results in Lorentz forces in the meridional plane which induce the fluid flow. The magnetic Reynolds number is assumed to be smaller than the frequency magnetic Reynolds number. The electromagnetic equations are thus decoupled from the fluid flow equations. The electromagnetic field is first solved, and the body forces determined from this are introduced into the Navier‐Stokes equations. With the flow field known, the quality of mixing is determined by solving the tracer dispersion equation. The finite element method based on a Galerkin formulation is used for the solution of the equations. Three cases are examined: a finite length cylinder, a finite length cylinder with rounded corners and a sphere. In general, two vortices are formed, the equatorial vortex closest to the equator and the end vortex at the closed end. Results show that the introduction of the rounded corner increases the size and strength of the end vortex with the opposite effect on the equatorial vortex. Of the three frequency magnetic Reynolds numbers considered (Rw=30, 100 and 800), Rw=100 results in the best mixing for all cases. Rounding the corner of the cylinder only results in a definite improvement of mixing at Rw=800. The sphere results in even better mixing than this at Rw=800, but is worse than the first two geometries for Rw=30 and 100 when the interaction parameter is large.

## Citation

BERELOWITZ, M. and BAR‐YOSEPH, P. (1992), "FINITE ELEMENT ANALYSIS OF STIRRING INDUCED BY AN ALTERNATING MAGNETIC FIELD", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 2 No. 2, pp. 155-169. https://doi.org/10.1108/eb017487

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