In this talk, we investigate a mathematical model of induction heating consisting of eddy current equations coupled with a nonlinear heat equation. The magnetic induction B is assumed a nonlinear function of the magnetic field and the electric conductivityσis temperature-dependent. The source term in the heat equation is handled approximately by the truncated quadratic Joule heating term. For the electromagnetic part, we present the potential-field T-ψformulation based on decomposition of the magnetic field. Using the theory of monotone operator and Rothe's method, we prove the existence of a weak solution to this coupled nonlinear system. Finally, we solve it by means of the T-ψnodal finite element method and show some numerical simulations.
