Unconstrained optimization of coupled magneto-thermal problems

The shape optimization of coupled systems by a gradients-based method is presented. The design specifications are in one system, while the critical parameters are in both systems. The method is demonstrated using an induction heating system. The magnetic and thermal models coexist in the same geometry. The eddy currents calculated from the electromagnetic solution is used as the thermal sources for the thermal finite element analysis. The objective is to achieve a required steady state temperature profile by modifying the geometry of the magneto-thermal domain. The objective function, defined as a function of the state variable temperature is no longer linked directly to the design parameters of the magneto-thermal system through the classic design sensitivity analysis but through the 'coupled' one. The proposed algorithm allows the calculation of the gradient of the object function with respect to the design parameters.