Validation of 3D and 2D thermal and electromagnetic models for high-frequency induction heating in crystal growth processes

Induction heating is crucial to various crystal growth techniques, including the Floating Zone (FZ) method, which is used for producing high-quality single silicon crystals. In this work, 3D and 2D axisymmetric numerical models for the high-frequency induction heating in the FZ process are implemented in open-source software tools Elmer and OpenFOAM. The models are compared and validated with in-situ measurements conducted on a model experiment of the FZ process, consisting of a flat inductor that heats a tin rod. The magnetic flux density distribution around the inductor is measured using a 3D induction coil probe, and the rod's surface temperature is measured using an infrared camera. Both numerical models were found to be in good agreement with the experimental data, with deviations mainly due to geometric approximations and simplified thermal modeling. The present measurement setup can be used as a benchmark for other numerical models of high-frequency induction processes.