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Numerical Solution of the Inverse Problem of Heating of a Solid Body by Laser Radiation

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Journal of Engineering Physics and Thermophysics Aims and scope

A study has been made of the process of heating of an inhomogeneous solid body by laser radiation, that is described by a one-dimensional parabolic equation with a volume heat source. The inverse problem of determining the law of variation in the density of laser-radiation power with the depth of the solid body has been posed. The temperature distribution through the body′s depth at a certain fixed instant of time was used as the supplementary condition. A discrete analog of the posed problem has been constructed with finite-difference approximations. To solve the obtained difference problem, a special representation was proposed which allows splitting this problem into two mutually independent difference problems. As a result, an explicit formula has been obtained from which the law of variation in the density of laser-radiation power with the depth of the solid body is restored.

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References

  1. N. N. Rykalin, A. A. Uglov, I. V. Zuev, and A. N. Kokora, Laser and Electron-Beam Treatment of Metals [in Russian], Mashinostroenie, Moscow (1985).

    Google Scholar 

  2. N. B. Delone, Interaction of Laser Radiation with the Substance [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  3. M. N. Libenson, E. B. Yakovlev, and G. D. Shandybina, Interaction of Laser Radiation with the Substance. Part II. Laser Heating and Failure of Materials [in Russian], NIU ITMO, St. Petersburg (2014).

  4. Yu. M. Klimkov, V. S. Maiorov, and M. V. Khoroshev, Interaction of Laser Radiation with the Substance [in Russian], MIIGAiK, Moscow (2014).

    Google Scholar 

  5. V. T. Borukhov and G. M. Zayats, Identification of a time-dependent source term in nonlinear hyperbolic or parabolic heat equation, Int. J. Heat Mass Transf., 91, 1106–1113 (2015).

    Article  Google Scholar 

  6. A. A. Samarskii and P. N. Vabishchevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics, Walter de Gruyter, Berlin (2008).

    MATH  Google Scholar 

  7. P. N. Vabishchevich, Computational identification of the lowest spacewise dependent coefficient of a parabolic equation, Appl. Math. Model, 65, 361–376 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  8. P. N. Vabishchevich, Iterative computational identification of a spacewise dependent source in parabolic equation, Inv. Probl. Sci. Eng., 25, No. 8, 1168–1190 (2017).

    Article  MATH  Google Scholar 

  9. K. Cao and D. Lesnic, Reconstruction of the space dependent perfusion coefficient from final time or time average temperature measurements, J. Comput. Appl. Math., 337, 150–165 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  10. K. Cao and D. Lesnic, Simultaneous reconstruction of the perfusion coefficient and initial temperature from time average temperature measurements, Appl. Math. Model., 68, 523–539 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  11. Kh. M. Gamzaev, S. O. Huseynzade, and G. A. Gasimov, Numerical method to solve identification problem for the lower coefficient and the source in the convection-reaction equation, Cyb. Syst. Anal., 54, No. 6, 971–976 (2018).

    Article  MATH  Google Scholar 

  12. T. Johansson and D. Lesnic, Determination of a spacewise dependent heat source, J. Comput. Appl. Math., 209, 66–80 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  13. K. R. Aida-zade and A. B. Rahimov, An approach to numerical solution of some inverse problems for parabolic equations, Inv. Probl. Sci. Eng., 22, No. 1, 96–111 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  14. A. G. Fatullayev and S. Cula, An iterative procedure for determining an unknown spacewise-dependent coefficient in a parabolic equation, Appl. Math. Lett., 22, 1033–1037 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  15. V. A. Morozov, Methods of Regularization of Unstable Problems [in Russian], Izd. Moskovsk. Univ., Moscow (1987).

    Google Scholar 

  16. O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Problems, Begell House, New York (1995).

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Azerbaijan Oil and Industry University, 20 Azadlyg Ave., AZ 1010, Baku, Azerbaijan

    Kh. M. Gamzaev

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  1. Kh. M. Gamzaev
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Correspondence to Kh. M. Gamzaev.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 96, No. 5, pp. 1135–1141, September–October, 2023.

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Gamzaev, K.M. Numerical Solution of the Inverse Problem of Heating of a Solid Body by Laser Radiation. J Eng Phys Thermophy 96, 1128–1133 (2023). https://doi.org/10.1007/s10891-023-02777-y

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  • DOI: https://doi.org/10.1007/s10891-023-02777-y

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