Skip to main content
SpringerLink
Log in

Method of Measuring Thermal Relaxation in the Solid State

  • Heat and Mass Transfer and Physical Gasdynamics
  • Published:
High Temperature Aims and scope

Abstract

The differential equations of heat conduction of a solid body, which are a consequence of the Fourier, Cattaneo–Vernotte, and Lykov’s equations, are considered. A mathematical model of the transient, three-period process in a circular plate is constructed in the form of a solution to the hyperbolic boundary value problem of heat conduction with boundary conditions of the third kind. The method to determine the Bio numbers in each period of the transition process and the time of thermal relaxation is described by the results of experimental and theoretical studies of transient thermal processes in the center of round plates of different thicknesses made of polymethylmethacrylate upon their sudden immersion in hot water.

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

Similar content being viewed by others

References

  1. Maxwell, J.C., On the dynamical theory of gases, Philos. Trans. R. Soc. London, 1867, vol. 157, p. 49.

    Article  ADS  Google Scholar 

  2. Lykov, A.V., Teploprovodnost’ i diffuziya (Thermal Conductivity and Diffusion), Moscow: Gizlegprom, 1941.

    Google Scholar 

  3. Lykov, A.V., Teoriya teploprovodnosti (Theory of Heat Conduction), Moscow: Vysshaya Shkola, 1967.

    Google Scholar 

  4. Shashkov, A.G., Bubnov, V.A., and Yanovskii, S.Yu., Volnovye yavleniya teploprovodnosti: Sistemno-strukturnyi podkhod (Wave Phenomena of Thermal Conductivity: System-Structural Approach), Moscow: Editorial URSS, 2004.

    Google Scholar 

  5. Herwig, H. and Beckert, K., Heat Mass Transfer, 2000, vol. 36, p. 387.

    Article  ADS  Google Scholar 

  6. Kirsanov, Yu.A. and Kirsanov, A.Yu., Izv. Ross. Akad. Nauk, Energ., 2015, no. 1, p. 113.

    Google Scholar 

  7. Kirsanov, Yu.A., Kirsanov, A.Yu., Gil’fanov, K.Kh., and Yudakhin, A.E., Russ. Aeronaut. (Iz VUZ), 2015, vol. 58, no. 3, p. 251.

    Article  Google Scholar 

  8. Kirsanov, Yu.A., Kirsanov, A.Yu., and Yudakhin, A.E., High Temp., 2017, vol. 55, no. 1, p. 114.

    Article  Google Scholar 

  9. Cattaneo, C., Atti Semin. Mat. Fis. Univ. Modena, 1948, vol. 3, p. 83.

    Google Scholar 

  10. Cattaneo, C., C. R. Seances Acad. Sci., Vie Acad., 1958, vol. 247, no. 4, p. 431.

    Google Scholar 

  11. Vernotte, P., C. R. Seances Acad. Sci., Vie Acad., 1958, vol. 246, no. 22, p. 3154.

    Google Scholar 

  12. Luikov, A.V., J. Eng. Phys. Therophys., 1965, vol. 9, no. 3, p. 189.

    Article  Google Scholar 

  13. Brovkin, L.A., Izv. Vyssh. Uchebn. Zaved., Energ., 1984, no. 8, p. 111.

    Google Scholar 

  14. Kartashov, E.M., Izv. Vyssh. Uchebn. Zaved., Energ., 2015, no. 4, p. 38.

    Google Scholar 

  15. Kartashov, E.M., J. Eng. Phys. Therophys., 2016, vol. 89, no. 2, p. 346.

    Article  Google Scholar 

  16. Tzou, D.Y., J. Heat Transfer, 1995, vol. 117, p. 8.

    Article  Google Scholar 

  17. Liu, K.C. and Chang, P.C., Appl. Math. Modell., 2007, vol. 31, p. 369.

    Article  Google Scholar 

  18. Kudinov, V.A. and Kudinov, I.V., High Temp., 2013, vol. 51, no. 2, p. 268.

    Article  Google Scholar 

  19. Fizicheskii entsiklopedicheskii slovar’ (Physical Encyclopedic Dictionary), Moscow: Sovetskaya Entsiklopediya, 1960, vol. 1, p. 664.

  20. Kirsanov, Yu.A., Kirsanov, A.Yu., Zaripov, Z.I., and Yudakhin, A.E., Tr. Akademenergo, 2016, no. 2, p. 7.

    Google Scholar 

  21. Andrianov, A.V., Falyakhov, I.V., Suslikov, E.V., Evdokimov, Yu.K., and Kirsanov, A.Yu., Vestn. Kazansk. Tekhnol. Univ., 2011, vol. 14, no. 16, p. 240.

    Google Scholar 

  22. Kartashov, E.M., Izv. Ross. Akad. Nauk, Energ., 2015, no. 2, p. 138.

    Google Scholar 

  23. Kirsanov, Yu.A., Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., 1995, no. 4, p. 88.

    Google Scholar 

  24. Kartashov, E.M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel (Analytical Methods in the Theory of the Thermal Conductivity of Solids), Moscow: Vysshaya Shkola, 1985.

    Google Scholar 

  25. Kamke, E., Differentialgleichungen. Lösungmethoden und Lösungen. I. Gewöhnliche Differentialgleichungen (Differential Equations: Solution Methods and Solutions. I. Ordinary Differential Equations), Leipzig: Academische, 1959.

    Google Scholar 

  26. Kirsanov, Yu.A., Tsiklicheskie teplovye protsessy i teoriya teploprovodnosti v regenerativnykh vozdukhopodogrevatelyakh (Cyclic Thermal Processes and the Theory of Thermal Conductivity in Regenerative Air Heaters), Moscow: Fizmatlit, 2007.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan Research Center, Russian Academy of Sciences, Tatarstan, Russia

    Yu. A. Kirsanov & A. E. Yudakhin

  2. Kazan National Research Technical University (KNITU-KAI), Tatarstan, Russia

    A. Yu. Kirsanov

  3. Kazan State Power Engineering University (KSPU), Tatarstan, Russia

    A. E. Yudakhin

Authors
  1. Yu. A. Kirsanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Yu. Kirsanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. E. Yudakhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. A. Kirsanov.

Additional information

Original Russian Text © Yu.A. Kirsanov, A.Yu. Kirsanov, A.E. Yudakhin, 2018, published in Teplofizika Vysokikh Temperatur, 2018, Vol. 56, No. 3, pp. 446–454.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kirsanov, Y.A., Kirsanov, A.Y. & Yudakhin, A.E. Method of Measuring Thermal Relaxation in the Solid State. High Temp 56, 425–432 (2018). https://doi.org/10.1134/S0018151X18030112

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0018151X18030112

Search

Navigation