Three-dimensional magneto-thermal analytical model for planar induction heater of nonmagnetic conducting materials considering transverse finite length effects

Purpose This paper aims to present a three-dimensional nonlinear magneto-thermal analytical model for a planar permanent-magnet induction heater, enabling the evaluation of the spatiotemporal temperature distribution in a non-magnetic conducting plate. The coupled 3D magneto-thermal problem is formulated using the sub-domain method, image theory and the equivalent thermal network. Design/methodology/approach The 3D magneto-thermal problem is solved through a nonlinear coupling between an electromagnetic analytical model and a transient thermal analysis. The electromagnetic model is derived by solving the three-dimensional Maxwell equations in Cartesian coordinates. First, the analytical expression for the heating power is determined for an infinitely wide conducting plate using a hybrid formulation. Then, the method of images is applied to account for finite-width extremity effects. The thermal model is obtained using the equivalent thermal network method. To analyze the accuracy of the magneto-thermal model, the analytical results are compared with those obtained from the 3D finite element (FE) multiphysics simulation. Findings The obtained results show the accuracy of the proposed magneto-thermal model, even for geometries with a very strong 3D edge effects. The analytical model directly takes into account the magnetic edge effects, the transverse finite width of the conducting plate, the reaction field and the temperature-dependent nonlinearity of the physical properties, without using correction factors. The use of a direct formulation of induced currents in the conducting part allowed us to determine a new analytical expression for the heating power. The magneto-thermal analytical model shows a good compromise between accuracy and computation time. Practical implications The proposed magneto-thermal model significantly reduces computation time compared to 3D FE simulations, making it a robust tool for the quick and accurate optimization and design of planar permanent-magnet induction heater systems. Originality/value A new 3D magneto-thermal analytical model for determining the spatiotemporal temperature distribution on a planar heater has been developed. This model accounts for magnetic edge effects, the finite width of the workpiece and the reaction field, while improving computation time thanks to the new analytical expression for the heating power derived from a hybrid formulation.