The Use of Inverse Heat Conduction Models for Estimation of Transient Surface Heat Flux in Electroslag Remelting

Abstract

Three inverse heat conduction models were evaluated for their ability to predict the transient heat flux at the interior surface of the copper mold in the electroslag remelting (ESR) process for use in validating numerical ESR simulations and real-time control systems. The models were evaluated numerically using a simple one-dimensional (1D) test case and a 2D pseudo-ESR test case as a function of the thermocouple locations and sample frequency. The sensitivity of the models to measurement errors was then tested by applying random error to the numerically calculated temperature fields prior to the application of the inverse models. This error caused large fluctuations in the results of the inverse models, but these could be mitigated by implementing a simple Savitzky–Golay filter for data smoothing. Finally, the three inverse methods were applied to a fully transient ESR simulation to demonstrate their applicability to the industrial process. Based on these results, the authors recommend that the 2D control volume method described here be applied to industrial ESR trials.