The equations are basically the Navier-Stokes equations augmented by a term representing the effect of the magnetic field. The full term is
and the magnetism depends on the magnetic field and temperature. For a steady magnetic field in the absence of free surfaces the term involving temperature dependence becomes
The dimensionless form of the equations for a steady magnetic field is
where the dimensionless groups are given by:
These equations are solved in FIDAP using a special body force subroutine. Additional equations are used for the case of a rotating magnetic field (work in progress).
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