Prediction of a 2 D Solidification Front

This study presents an inverse heat transfer method for predicting the two-dimensional time-varying shape of the phase change protective bank on the inside surface of a wall of a high temperature furnace filled with molten material. The objective is to develop a methodology that accurately tracks the moving boundary created during the solidification process, which is crucial for protecting the furnace walls. The proposed method employs the Levenberg-Marquardt least-square minimization technique and relies on nonintrusive temperature measurements. Results demonstrate that the 2-D inverse methodology provides accurate predictions of the moving boundary under typical melting furnace operating conditions. Moreover, for real-time industrial applications, a simpler yet effective quasi-2-D inverse method is introduced, which is nearly 10 times faster than the full 2-D inverse model, while still maintaining accuracy. This efficiency is particularly beneficial in dynamic industrial settings where time is a critical factor.