This paper aims to develop a new 3D analytical model devoted to the study of nonlinear transient magneto-thermal coupled problems in permanent magnet transverse flux induction heating device (PMTFIHD). Firstly, a 3D analytical solution of magneto-dynamic field problem taking into account the transverse edge effect in the workpiece is derived using variables' separation technique. This transverse edge effect allows determining the exact resulting heating power density, which is the heat source of the transient thermal problem in the work-piece. Secondly, the 3D transient analytical solution of the temperature distribution is obtained by combining variables' separation technique and Green's function method. Then, the previous models are exploited in a transient simulations procedure of the magneto-thermal process allowing the nonlinear physical properties of the part to be taking into account. Finally, the performances of the studied PMTFIHD will be calculated, in order to validate the developed 3D coupled models. The simulation results from the developed models are validated with those obtained by the finite element method and the experimental results.
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