On the flow in a channel induction furnace

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Abstract
The channel induction furnace is an electrically efficient device for the heating and stirring of liquid metals. In this paper an axisymmetric model for the channel flow is proposed, in which the fluid is confined to the inside of a torus. An exact solution for the magnetic field is found in terms of toroidal harmonic functions. Finite-difference methods are used to calculate the primary, cross-channel motions under the assumptions of a small skin depth, a constant eddy viscosity and no thermal dependence. Non-axisymmetric perturbations to the channel shape are considered and the perturbed field calculated. The secondary circulation along the channel is discussed.