Skip to main content
SpringerLink
Log in

Nonstationary Temperature Problem for a Cylindrical Shell with Multilayer Thin Coatings

  • Published:
Materials Science Aims and scope

We construct a mathematical model for the determination of nonstationary temperature fields in cylindrical shells with unilateral thin multilayer coatings placed in media with different temperatures. The obtained analytic solution is compared with the numerical and experimental results by analyzing an example of finding the nonstationary temperature field in a cylindrical reactor vessel whose wall is protected against corrosion by a two-layer coating. The relative difference between the results of theoretical calculations and experimental data does not exceed 5%.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

References

  1. R. K. Melekhov and V. I. Pokhmurs’kyi, Structural Materials of Power-Generating Plant [in Ukrainian], Naukova Dumka, Kyiv (2003).

  2. L. B. Getsov and A. I. Rybnikov, “Mechanisms of deformation and fracture of multilayer coatings during thermal cycling,” Fiz.-Khim. Mekh. Mater., 29, No. 6, 48–55 (1993); English translation: Mater. Sci., 29, No. 6, 604–611 (1993).

  3. B. P. Rusyn, N. P. Anufrieva, N. R. Hrabovska, and V. H. Ivanyuk, “Nondestructive testing of the state of surfaces damaged by corrosion pitting,” Fiz.-Khim. Mekh. Mater., 49, No. 4, 90–96 (2013); English translation: Mater. Sci., 49, No. 4, 516–524 (2014).

  4. Ya. S. Podstrigach and P. R. Shevchuk, “Effect of surface layers on diffusion processes and the resulting stress state in solids,” Fiz.-Khim. Mekh. Mater., 3, No. 5, 575–583 (1967); English translation: Soviet Mater. Sci., 3, No. 5, 420–426 (1968).

  5. Ya. S. Podstrigach and P. R. Shevchuk, “Temperature fields and stresses in bodies with thin coatings,” Therm. Stresses Struct. Elem., Issue 7, 227–233 (1967).

  6. V. F. Chekurin and B. V. Procjuk, “Identification of the parameters of multilayer coatings according to the thermoelastic displacements of the surface of heating,” Fiz.-Khim. Mekh. Mater., 40, No. 1, 7–15 (2004); English translation: Mater. Sci., 40, No. 1, 1–13 (2004).

  7. V. A. Shevchuk, “Nonstationary one-dimensional problem of heat conduction for a cylinder with a thin multilayer coating,” Mat. Metody Fiz.-Mekh. Polya, 54, No. 2, 179–185 (2011); English translation: J. Math. Sci., 184, No. 2, 215–223 (2012).

  8. L. P. Shvets’ and O. I. Yatskiv, “On the construction of solution of boundary-value diffusion problem with nonclassical boundary conditions,” Visn. Derzh. Univ. “L’vivs’ka Politekhnika,” Ser. Prykl. Mat., No. 346, 165–168 (1998).

  9. R. M. Shvets’ and O. I. Yatskiv, “Interconnected problem of mechanical thermal diffusion for layered bodies of canonical shape with thin interlayers,” Dopov. Akad. Nauk Ukrainy, No. 11, 65–69 (1993).

  10. R. M. Shvets’ and O. I. Yatskiv, “Extension of the method of eigenfunctions to the boundary-value problems of mechanical diffusion for multilayer bodies with interlayers,” Mat. Metody Fiz.-Mekh. Polya, 41, No. 4, 155–161 (1998); English translation: J. Mater. Sci., 107, No. 1, 3691–3696 (2001).

  11. R. M. Shvets’, O. I. Yatskiv, and B. Ya. Bobyk, “Some approaches to the solution of problem of the heating of a solid elastic cylinder under nonstationary boundary condition,” Prykl. Probl. Mekh. Mat., Issue 5, 186–194 (2007).

  12. R. M. Shvets’, O. I. Yatskiv, and B. Ya. Bobyk, “Identification of the boundary thermophysical parameters of a cylinder under nonstationary conditions of heat exchange with environment,” Fiz.-Mat. Model. Inform. Technol., Issue 12, 198–207 (2010).

  13. V. A. Shevchuk, “Modeling and computation of heat transfer in a system “body-multilayer coating,” Heat Transfer Res., 37, No. 5, 412–423 (2006).

  14. Ya. S. Podstrigach and R. N. Shvets, Thermoelasticity of Thin Shells [in Russian], Naukova Dumka, Kiev (1978).

  15. O. E. Andreikiv and O. V. Hembara, Fracture Mechanics and Durability of Metal Materials in Hydrogen-Containing Environments [in Ukrainian], Naukova Dumka, Kyiv (2008).

  16. O. Ye. Andreykiv, V. R. Skalsky, and O. V. Hembara, “The method of evaluation of high-temperature hydrogen fracture of bimetal elements of a structure,” Fiz.-Khim. Mekh. Mater., 36, No. 4, 15–22 (2000); English translation: Mater. Sci., 36, No. 4, 489–498 (2000).

  17. O. V. Gembara, “Finite-element simulation of mass transfer in structurally inhomogeneous materials,” Fiz.-Khim. Mekh. Mater., 39, No. 5, 89–95 (2003); English translation: Mater. Sci., 39, No. 5, 712–720 (2003).

  18. O. E. Andreykiv and O. V. Gembara, “Evaluation of the residual service life of structural elements in hydrogen-containing media,” Probl. Prochn., No. 3, 34–42 (2006); English translation: Strength Mater., No. 3, 241–247 (2006).

  19. Ya. L. Ivanitskii, O. V. Gembara, T. I. Titova, N. A. Shul’gan, N. M. Gvozdyuk, S. A. Bocharov, and A. V. Voronov, “Investigation of peeling resistance in a bimetallic joint of petrochemical reactors in hydrogen environment,” Fiz.-Khim. Mekh. Mater., 45, No. 6, 50–56 (2009); English translation: Mater. Sci., 45, No. 6, 810–816 (2009).

  20. V. Panasyuk, Ya. Ivanytskyi, and O. Hembara, “Assessment of hydrogen effect on fracture resistance under complex-mode loading,” Eng. Fract. Mech., 83, 54–61 (2012).

  21. V. V. Panasyuk, Ya. L. Ivanyts’kyi, О. V. Hembara, and V. M. Boiko, “Influence of the stress-strain state on the distribution of hydrogen concentration in the process zone,” Fiz.-Khim. Mekh. Mater., 50, No. 3, 7–14 (2014); English translation: Mater. Sci., 50, No. 3, 315–323 (2014).

  22. O. Andreykiv, O. Gembara, and V. Skalsky, “Fracture of bimetallic structural elements under hydrogen – temperature interaction,” in: 14th European Conf. Fracture ECF-14 “Mechanics beyond 2000” (Krakow, Sept. 8–13, 2002), Vol. 1, Krakow (2002), pp. 73–80.

  23. O. V. Kronshtal’ and V. S Kharin, “Effect of heterogeneity of materials and heat cycles on diffusion of hydrogen as a factor of the risk of development of hydrogen degradation of metals,” Fiz.-Khim. Mekh. Mater., 28, No. 6, 7–20 (1992); English translation: Soviet Mater. Sci., 28, No. 6, 475–486 (1992).

Download references

Acknowledgment

The present work was supported by the Doctoral Scientific Research Fund from the Hubei University of Technology (No. BSQD2017048).

Author information

Authors and Affiliations

  1. School of Computer Science, Hubei University of Technology, Wuhan, China

    J.-L. Chen

  2. Ukrainian Academy of Printing, Lviv, Ukraine

    N. О. Hembara

  3. Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine

    M. М. Hvozdyuk

Authors
  1. J.-L. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. О. Hembara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. М. Hvozdyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. М. Hvozdyuk.

Additional information

Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 54, No. 3, pp. 49–57, May–June, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, JL., Hembara, N.О. & Hvozdyuk, M.М. Nonstationary Temperature Problem for a Cylindrical Shell with Multilayer Thin Coatings. Mater Sci 54, 339–348 (2018). https://doi.org/10.1007/s11003-018-0190-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11003-018-0190-3

Keywords

Search

Navigation