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Equivalence of Normalized Thermal-Wave Fields Between Curved and Flat Surfaces and Its Application in the Characterization of Curved Samples

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Abstract

Equivalence of the normalized thermal-wave fields between curved and flat surfaces under certain conditions is investigated based on theoretical models of cylindrical, spherical, and flat solids with multilayer structures. The principle and the physical mechanism of the elimination of the surface curvature effect from the overall photothermal signal of the curvilinear solid are suggested. The effects of the relative values of radii of curvature of the curvilinear solid, the thickness of the inhomogeneous surface layer, and the measurement azimuthal angle on the validity of the equivalence principle are discussed. Consistent experimental reconstructions of thermophysical depth profiles of hardened cylindrical steel rods of various diameters are performed and obtained based on both the curvilinear theory and the equivalent flat surface theory.

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Acknowledgments

This study has been sponsored by the National Natural Science Foundation of China (Grant No. 60877063), Scientific Research Foundation for the Returned Overseas Chinese Scholars, Education Ministry of China, and the project of the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions. One of us (AM) is grateful to the Canada Foundation for Innovation (CFI) and the Ontario Research Fund (ORF) for instrumentation support.

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Authors and Affiliations

  1. Institute of Modern Optical Technologies, Soochow University, Suzhou, 215006, Jiangsu, China

    Chinhua Wang, Jie Zhang & Liwang Liu

  2. Center for Advanced Diffusion-Wave Technologies (CADIFT), Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canada

    Andreas Mandelis

Authors
  1. Chinhua Wang
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  2. Jie Zhang
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  3. Liwang Liu
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  4. Andreas Mandelis
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Correspondence to Chinhua Wang.

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Wang, C., Zhang, J., Liu, L. et al. Equivalence of Normalized Thermal-Wave Fields Between Curved and Flat Surfaces and Its Application in the Characterization of Curved Samples. Int J Thermophys 34, 1429–1434 (2013). https://doi.org/10.1007/s10765-013-1441-z

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  • DOI: https://doi.org/10.1007/s10765-013-1441-z

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