Nonlinear inverse heat conduction problem of surface temperature estimation by calibration integral equation method

A calibration integral equation method is proposed for estimating the surface temperature in the context of a nonlinear inverse heat conduction problem. The temperature-dependent thermophysical properties and probe positioning are implicitly accounted in the integral equation formulation through cal...

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Bibliographic Details
Published in:Numerical heat transfer. Part B, Fundamentals Vol. 73; no. 5; pp. 263 - 291
Main Authors: Chen, Hongchu, Frankel, Jay I., Keyhani, Majid
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 04.05.2018
Taylor & Francis Ltd
Subjects:
Calibration
Chebyshev approximation
Computer simulation
Conduction heating
Conductive heat transfer
Correlation analysis
Ill posed problems
Integral equations
Parameter estimation
Regularization
Surface temperature
Temperature
Temperature dependence
Thermal expansion
Thermophysical properties
ISSN:1040-7790, 1521-0626
Online Access:Get full text
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Summary:A calibration integral equation method is proposed for estimating the surface temperature in the context of a nonlinear inverse heat conduction problem. The temperature-dependent thermophysical properties and probe positioning are implicitly accounted in the integral equation formulation through calibration tests. A first kind Chebyshev expansion is applied to represent the temperature-dependent property transform function. The undetermined expansion coefficients associated with the Chebyshev expansion are then estimated through two calibration tests. Regularization of the ill-posed problem is achieved by the future-time method. The optimal regularization parameter is estimated using a phase plane and cross-correlation phase plane analyses. Numerical simulation for stainless steel yields highly favorable surface temperature prediction.
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ISSN:1040-7790
1521-0626
DOI:10.1080/10407790.2018.1464316