Analytical and numerical aspects of the electromagnetic stirring induced by alternating magnetic fields

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Abstract
The dynamic effects of an alternating magnetic field on containers of conducting fluid are investigated in two special cases: (i) an infinitely long circular cylinder in a uniform magnetic field normal to the generators; (ii) a truncated circular cylinder in a uniform magnetic field parallel to the axis. Neglecting the motion effects in Maxwell's equations, the problem is conveniently decoupled into electromagnetic and dynamic parts. Using either analytical or numerical solutions of the electromagnetic equations, the electromagnetic forces are calculated and introduced in the motion equations. In the first case, asymptotic solutions of the Navier–Stokes equations valid for high frequencies are calculated and compared with numerical solutions obtained for the same geometry. The second case has been studied numerically, and the solutions are presented and interpreted.

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