A new nonlinear surface heat flux calibration method based on Kirchhoff transformation and rescaling principles

作者：Chen Y Y; Frankel J I^*; Keyhani M

来源：Inverse Problems in Science and Engineering, 2014, 22(8): 1394-1421.

DOI：10.1080/17415977.2014.880906

• Kirchhoff transformation
• inverse analysis
• nonlinear calibration
• rescaling
• heat conduction

A novel surface heat flux calibration method is presented applicable to nonlinear inverse heat conduction problems. Quasi-linearization of the nonlinear heat equation is achieved by combining the Kirchhoff transform with time-domain rescaling based on the local temperature measurement. At each time step, the thermophysical properties are held constant throughout the spatial domain though allowed to vary with advancing time. The rescaled forms are then resolved through a calibration framework. The proposed calibration formulation is expressed in terms of Volterra integral equation of the first kind. This functional equation relates the rescaled net unknown surface heat flux to the rescaled net calibration surface heat flux and their corresponding rescaled Kirchhoff transformed variables for the in-depth temperature measurements during the calibration test and unknown runs. Tikhonov regularization is introduced for generating a family of predictions based on the Tikhonov parameter. The L-curve strategy is used for selecting the proper regularization parameter. In this paper, favourable numerical results are demonstrated verifying both accuracy and robustness of the rescaling calibration approach in the presence of significant experiment noise. The methodology works well for a variety of practical isotropic materials. This approach does not require knowledge of the probe position but presently requires knowledge of the host material's thermal diffusivity.

• 出版日期2014