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Being extensively used in metallurgy, rotating magnetic fields are also becoming increasingly interesting for application in crystal growth, where they are intended to act by stabilizing the melt flow. For this purpose, it is important to understand the basic interactions of the magnetically induced flow and other flow components like time‐dependent buoyant convection. So a three‐dimensional finite volume method was developed in order to numerically study the effect of a rotating magnetic field on convection in a cylindrical melt volume. The equations of mass, momentum, and heat transport are solved together with the potential equations describing the electromagnetic field. The numerical computation of the Lorenz force distribution is validated by comparison with an analytical solution. The effects of magnetic field parameters on the temperature distributions and the flow patterns in the considered configurations are analysed.

The discretisation scheme presented for an unstructured triangular grid, is able to reflect the physical properties of stationary, nonlinear heat conduction even in the numerical case and leads to a stabilisation of iterative solution techniques for nonlinearities.

The purpose of this paper is to determine how the shape of the container affects the efficiency of a traveling magnetic field (TMF) stirring.

The modeling approach is based on finite element software Comsol which includes harmonic electromagnetic (EM), transient CFD and particle tracing modules. For evaluating efficiency of stirring the particle, homogenization parameter is used.

It has been determined that the use of an elliptical cylinder-shaped vessel allows better heat removal from the side surface and, at the same time, the stirring efficiency does not drop significantly.

The results of the work can be used in the design of EM stirring installations in which exothermic reactions occur.

The transient simulation of particle transport in a TMF-driven melt flow gives the opportunity to estimate the efficiency of stirring process in different vessel shapes.