Journal of Mathematical Sciences

, Volume 192, Issue 6, pp 703–722 | Cite as

Modeling and investigation of heat transfer in plates with thin coatings with regard for the influence of radiation

  • R. F. Terlets’kyi
  • O. P. Turii

We obtain approximate relations based on using generalized boundary conditions (conditions of heat exchange through a coating) for describing heat transfer in irradiated plates with coatings. Their applicability is investigated depending on the radiation properties of the coating and substrate.


Heat Transfer Thermal Radiation Contact Boundary Generalize Boundary Condition Radiative Heat Exchange 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. G. Blokh, Yu. A. Zhuravlev, and L. N. Ryzhkov, Heat Exchange by Radiation. A Handbook [in Russian], Energoatomizdat, Moscow (1991).Google Scholar
  2. 2.
    E. M. Voronkova, B. N. Grechushnikov, G. I. Distler, and I. P. Petrov, Optical Materials for Infrared Engineering [in Russian], Nauka, Moscow (1965).Google Scholar
  3. 3.
    A. P. Gavris’, D. V. Ivashchuk, and P. R. Shevchuk, “Determination of residual stresses in a layered system during two-sided hightemperature spray-coating,” Mat. Met. Fiz.-Mekh. Polya, Issue 29, 8–12 (1989); English translation: J. Sov. Math., 65, No. 4, 1715–1719 (1993).Google Scholar
  4. 4.
    O. R. Hachkevych, R. F. Terlets’kyi, and T. L. Kurnyts’kyi, Mechanothermodiffusion in Semitransparent Bodies, in: Ya. Yo. Burak and R. M. Kushnir (editors), Modeling and Optimization in Thermomechanics of Electroconductive Inhomogeneous Bodies [in Ukrainian], Vol. 2, SPOLOM, Lviv (2007).Google Scholar
  5. 5.
    O. R. Hachkevych, R. F. Terlets’kyi, Yu. R. Sosnovyi, and M. B. Brukhal,’ “Mechanical behavior of cooled bodies with regard for the emission of thermal energy,” Fiz.-Khim. Mekh. Mater., 46, No. 1, 42–50 (2010); English translation: Mater. Sci., 46, No. 1, 47–55 (2010).Google Scholar
  6. 6.
    R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer, McGraw-Hill, New York (1972).Google Scholar
  7. 7.
    A. E. Sheidlin (editor), Radiative Properties of Solid Materials. A Handbook [in Russian], Energiya, Moscow (1974).Google Scholar
  8. 8.
    R. M. Martynyak, Mechanothermodiffusion Interaction of Bodies with Contact Surface Heterogeneities and Defects [in Ukrainian], Author’s Abstract of Doctoral Thesis (Physics and Mathematics), Lviv (2000).Google Scholar
  9. 9.
    S. B. Maslenkov and E. A. Maslenkova, Steels and Alloys for High Temperatures. A Handbook [in Russian], Vol. 1, Metallurgiya, Moscow (1991).Google Scholar
  10. 10.
    Ya. S. Podstrigach and P. R. Shevchuk, “Influence of thin coatings and intermediate layers on diffusion processes and the stressed state in solid bodies,” Zashch. Pokryt. Metal., Issue 5, 180–185 (1971).Google Scholar
  11. 11.
    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: Mater. Sci., 3, No. 5, 420–426 (1968).Google Scholar
  12. 12.
    Ya. S. Podstrigach and P. R. Shevchuk, “The stress-strain state of heated elastic bodies containing inclusions in the form of thin shells,” Prikl. Mekh., 3, No. 6, 8–16 (1967); English translation: Int. Appl. Mech., 3, No. 6, 5–9 (1967).Google Scholar
  13. 13.
    Ya. S. Podstrigach and P. R. Shevchuk, “Temperature fields and stresses in bodies with thin coatings,” Teplov. Napryazh. Elem. Konstruk., Issue 7, 227–233 (1967).Google Scholar
  14. 14.
    N. A. Rubtsov, Radiative Heat Exchange in Continua [in Russian], Nauka, Novosibirsk (1984).Google Scholar
  15. 15.
    V. N. Yurenev and P. D. Lebedev (editors), Thermal Engineering Handbook [in Russian], Vol. 1, Energiya, Moscow (1975).Google Scholar
  16. 16.
    R. F. Terlets’kyi and O. P. Turii, “Thermomechanical behavior of a plate composed of layers with different transparencies under the action of thermal radiation,” Fiz.-Khim. Mekh. Mater., 43, No. 6, 17–26 (2007); English translation: Mater. Sci., 43, No. 6, 769–779 (2007).Google Scholar
  17. 17.
    O. P. Turii, “Nonlinear contact boundary-value problem of thermomechanics for an irradiated bilayer plate joined by an intermediate layer,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 9, 118–132 (2009).Google Scholar
  18. 18.
    Yu. A. Chernukha, “Problem of heat conduction for irradiated multilayer shells,” Mat. Met. Fiz.-Mekh. Polya, Issue 1, 104–109 (1975).Google Scholar
  19. 19.
    W. Espe, Werkstoffkunde der Hochvakuumtechnik, Vol 2: Silikatwerkstoffe, Deutscher Verlag der Wissenschaften, Berlin (1962).Google Scholar
  20. 20.
    A. A. Amosov, “Nonstationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency,” Probl. Mat. Anal., 44, 3–38 (2010); English translation: J. Math. Sci., 165, No. 1, 1–41 (2010).MathSciNetGoogle Scholar
  21. 21.
    R. Coquard, D. Rochais, and D. Baillis, “Experimental investigations of the coupled conductive and radiative heat transfer in metallic/ceramic foams,” Int. J. Heat Mass Transfer, 52, 4907–4918 (2009).MATHCrossRefGoogle Scholar
  22. 22.
    L. H. Liu and P.-F. Hsu, “Analysis of transient radiative transfer in a semitransparent graded index medium,” J. Quant. Spectrosc. RA, 105, No. 3, 357–376 (2007).CrossRefGoogle Scholar
  23. 23.
    M. F. Modest, Radiative Heat Transfer, Academic Press, London–New York (2003).Google Scholar
  24. 24.
    C. Muresan, R. Vaillon, C. Menezo, and R. Morlot, “Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation,” J. Quant. Spectrosc. RA, 84, No. 4, 551–562 (2004).CrossRefGoogle Scholar
  25. 25.
    V. A. Shevchuk, “Modeling and computation of heat transfer in a system “body–multilayer coating,” Heat Transfer Res., 37, No. 5, 412–423 (2006).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • R. F. Terlets’kyi
    • 1
  • O. P. Turii
    • 1
  1. 1.Pidstryhach Institute for Applied Problems of Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

Personalised recommendations