A novel calibration methodology is presented for resolving the front surface heat flux in a one-dimensional nonlinear sample with an unknown time-varying back boundary condition. This method combines the attributes of the recently reported linear two-probe calibration equation and the nonlinear one-probe calibration equation. The proposed calibration formulation is expressed in terms of a Volterra integral equation of the first type. This functional equation relates the rescaled unknown front surface heat flux to two rescaled calibration front surface heat fluxes and corresponding rescaled temperature data at the two in-depth probes when the sample is subjected to the unknown boundary conditions. A localized Tikhonov regularization scheme is introduced for generating the family of predictions based on the Tikhonov parameter spectrum. The L-curve strategy is used to extract the optimal prediction. This paper studies the effectiveness of this new calibration equation for two engineering materials, stainless steel 304 and a carbon composite. Results show that properly regularized predictions are stable and accurate in the presence of significant noise. Moreover, it is demonstrated that a preferred back boundary condition strategy for calibration tests reduces the ill-conditioning effects of the kernel. This new calibration method does not require the specification of the probe locations, although knowledge of the thermophysical properties is necessary.
Journal of Engineering Mathematics – Springer Journals
Published: Jan 23, 2017
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