Heat flux and thermal contact conductance determination employing inverse heat conduction using model reduction through matrix transform

The inverse heat conduction problem is germane to many applications in metal casting. A new method for solving linear, inverse heat conduction problems using temperature data containing significant noise is presented in this work. The method employs a pulse sensitivity matrix and singular value decomposition to convert the heat transfer problem into the frequency domain. High-frequency fluctuations are eliminated and low-frequency fluctuations are smoothed by properly conditioning the matrices obtained through singular-value decomposition. The technique is demonstrated by considering heat flux measurements obtained from two examples presented in literature. The technique is extended to obtain heat flux and contact conductance jointly from experimentally obtained A356 sand casting temperature data with the corresponding uncertainty. The transient contact conductance measurements contradict previous measurements employing the identical data. Advantages of the new method are reduced matrix size, robust treatment of noisy temperature data, and lack of ad hoc parameters.