A numerical model for the recirculating flow of an electromagnetically stirred iron melt in a cylindrical induction furnace crucible is presented. Due to the parameters of the problem, the full set of magnetohydrodynamic flow equations decouples into magnetic and hydrodynamic parts. The diffusion approach of the magnetic vector potential describes the magnetic part of the model. The hydrodynamic part of the model is based on the unsteady ensemble-averaged Navier–Stokes equations in conjunction with a Reynolds stress turbulence model. Such an approach is commonly termed the unsteady Reynolds averaged approach. Here the influence of the electromagnetic field is included by means of a Lorentz force density.

The diffusion equation is solved by a finite-element method. The Lorentz force density in the melt can be deduced from the results. Then the unsteady Reynolds averaged equations are solved by the finite-volume method.

The results of the unsteady Reynolds averaged approach are analysed and compared to the results of the steady Reynolds averaged equations of the flow under consideration and to experimental results obtained from other studies. It is found that the toroidal vortex pair, which is the dominating structure within the flow, interacts by intermittent streamline connections.