Optimal control of induction heating for semi-solid aluminum alloy forming

The thixoforming technique requires reheating the feedstock to a semi-solid state with a uniform temperature distribution, a uniform globular microstructure and an optimum liquid fraction. The presence of the skin effect during induction heating results in an exponential heat source distribution within the material as well as an uneven temperature profile from surface-to-core. In this study, the conjugate gradient method with adjoint equations is used to find an optimal heating/cooling strategy to achieve uniform temperature distribution along the radius of a cylinder in a relatively short time. It is found that a modified conjugate gradient method may be a more suitable algorithm to solve this optimization problem. The physical and mathematical models take into account the temperature-dependent thermo-physical properties. Radiative and convective heat losses are also considered.