A numerical study of flows driven by a rotating magnetic field in a square container

The magnetically induced fluid flow in a square container is investigated by means of numerical simulations. Low frequency/ low induction conditions are assumed. The effect of the rotating magnetic field gives rise to a time-independent magnetic body force, computed via the electrical potential equation and Ohm's law and a time-dependent part that is neglected due to the low-interaction parameter. The magnetic body force calculation is verified successfully by comparison with the exact solution. The behavior of the fluid flow in the square container reveals similar features to the flow in the cylindrical container, for instance, in the dependence on the intensities of the magnetic field. However, we did find differences in the velocity field distribution. Particularly, in the finite as well as infinite geometry, the velocity field is influenced by the corner of the container and remains non-axisymmetric in a wide range of Taylor numbers.