A phenomenological modelling approach has been developed to solve the free boundary problem of electromagnetic levitation melting in cold crucible with continuous casting. The free boundary problem has been solved to determine the equilibrium shape of the molten metal as a function of electrical operating parameters. The concept of domain derivative formalism has been applied to obtain minimization of the total energy functional of the system in a global framework for determining the free surface of the molten metal under levitated condition. An iterative solution algorithm has been formulated and the magnetic energy is determined by using a boundary integral technique. Distribution of magnetic field has been evaluated on the basis of Biot-Savart's law. The domain derivative approach is found to be a useful mathematical apparatus to achieve faster convergence of the solution of the governing free boundary problem.
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