Nonlinear Inverse Calibration Heat Conduction Through Property Physics

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Nonlinear Inverse Calibration Heat Conduction Through Property Physics

Frankel, J. I. / Keyhani, M.

This paper proposes a nonlinear calibration approach for inverse heat conduction. A set of observations is put forth based on reformulating the heat equation in terms of thermophysical properties. An emerging pattern suggests a fundamental format for the development of a calibration integral equation that accounts for temperature-dependent thermophysical properties. An arbitrary kernel expansion is proposed in terms of a Taylor series expansion in temperature possessing undetermined coefficients. These undetermined coefficients are estimated using an additional calibration run. This concept preserves the features of the linear calibration methodology previously reported by the authors, while extending the methodology to include temperature-dependent thermophysical properties. This paper articulates an encouraging preliminary study that highlights the initial steps toward developing a nonlinear calibration inverse method. Preliminary numerical results based on simulated data using the proposed generalized temperature function produce highly encouraging results. Finally, a new measure is introduced to facilitate the estimation of the optimal regularization parameter in the context of the local-future-time method.