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Numerical method for the inverse heat transfer problem in composite materials with Stefan-Boltzmann conditions

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Abstract

In this paper, one specific kind of heat transfer problem with nonlinear Stefan-Boltzmann conditions are considered in a three dimensional multi-layer domain. Theoretical results for forward and inverse problems are presented. Numerical simulations of specific models from applications are provided to demonstrate the heat transfer process in the composite materials of forward problem. One reconstruction method is proposed to find the corrosion part, and the numerical examples show that the reconstruction algorithm is effective.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Xiaoyi Hu, Xiang Xu & Wenbin Chen

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  1. Xiaoyi Hu
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  2. Xiang Xu
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  3. Wenbin Chen
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Corresponding author

Correspondence to Wenbin Chen.

Additional information

Communicated by the guest editors Benny Hon, Jin Cheng and Masahiro Yamamoto.

X. Hu was partially supported by Natural Science Foundation of China(10771138), X. Xu was partially supported by Natural Science Foundation of China(10871050) and W. Chen was supported by NSFC Tianyuan Fund for Mathematics(10826105), the National Basic Research Program(2005CB321701) and 111 project grant(B08018).

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Hu, X., Xu, X. & Chen, W. Numerical method for the inverse heat transfer problem in composite materials with Stefan-Boltzmann conditions. Adv Comput Math 33, 471–489 (2010). https://doi.org/10.1007/s10444-009-9131-x

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  • DOI: https://doi.org/10.1007/s10444-009-9131-x

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