Skip to main content
SpringerLink
Log in

Direct (Classical) Method of Calculation of the Temperature Field in a Hollow Multilayer Cylinder

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

A structural scheme of construction of a solution to a mixed problem for the heat-conduction equation in the case of a hollow multilayer cylinder under the conditions of ideal thermal contact between the layers is proposed and substantiated. The presence of connective heat exchange with the environment is assumed, i.e., boundary conditions of the third kind are observed. Coefficients of the heat-conduction equation are considered to be piecewise-continuous as far as the space coordinate is concerned. The scheme is based on the: reduction method, concept of quasi derivatives, modcern theory of systems of linear differential equations, Fourier method, and modified method of eigenfunctions. A numerical example of calculation of the temperature field in an actual hollow four-layer pipeline under external-fire conditions is given.

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. Yu. M. Kolyano, B. V. Protsyuk, V. M. Sinyuta, S. M. Shebanov, and S. M. Sharov, Transient temperature field in laminated orthotropic cylinder, J. Eng. Phys. Thermophys., 62, No. 2, 245−250 (1992).

    Article  Google Scholar 

  2. B. V. Protsyuk and V. M. Sinyuta, Nonstationary non-axisymmetric temperature fields of multilayer orthotropic cylinders, Mat. Metody Fiz.-Mekh. Polya, 51, No. 4, 221−228 (2008).

    Google Scholar 

  3. B. V. Protsyuk and V. M. Sinyuta, Green′s functions of the nonstationary heat-conduction problems for multilayer plates and cylinders, Abstracts of Papers “Ukrainian Mathematical Congress. Mathematical Physics,” Kiev (2001), p. 26.

  4. R. M. Tatsii and O. Yu. Pazen, General boundary-value problems for the heat conduction equation with piecewise-continuous coefficients, J. Eng. Phys. Thermophys., 89, No. 2, 357−368 (2016).

    Article  Google Scholar 

  5. A. V. Luikov, Heat Conduction Theory [in Russian], Vysshaya Shkola, Moscow (1967).

  6. M. M. Semerak, R. M. Tatsii, and O. Yu. Pazen, Heat-insulating capacity of multilayer engineering structures with allowance for the destruction of an arbitrary layer, Vestn. Kokshet. Tekh. Min. Chrezvych. Sit. Resp. Kazakhstan, 20, No. 4, 8–17 (2015).

    Google Scholar 

  7. R. M. Tatsii and O. Yu. Pazen, Direct method of calculation of a nonstationary temperature field under fire conditions, Pozh Bezopasnost’, No. 26, 135−141 (2015).

    Google Scholar 

  8. R. M. Tatsii, T. I. Ushak, and O. Yu. Pazen, General third boundary-value problem for the heat-conduction equation with piecewise-continuous coeffi cients and internal heat sources, Pozh. Bezopasnost’, No. 27, 120−126 (2015).

    Google Scholar 

  9. V. P. Isachenko, V. A. Osipova, and A. S. Sukomel, Heat Transmission [in Russian], Énergiya, Moscow (1975).

  10. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1976).

  11. R. M. Tatsii, M. F. Stasyuk, V. V. Mazurenko, and O. O. Vlasii, Generalized Quasi-Di fferential Equations [in Russian], Izd. L′vovsk. Gos. Univ. Bezop. Zhiznedeyatel′nosti, L′vov (2017).

  12. V. Ya. Arsenin, Methods of Mathematical Physics [in Russian], Nauka, Moscow 1974.

  13. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).

  14. D. Sheen, Existence theorem for a quasi-differential equation of nth order, Dokl. Ak ad. Nauk SSSR, 18, No. 8, 515−518 (1938).

    Google Scholar 

  15. D. Sheen, On solutions of the self-conjugate differential equation u [n] = lu, Il ≠ 0, belonging to L2[0, ∞), Dokl. Akad. Nauk SSSR, 18, No. 8, 519−522 (1938).

  16. D. Sheen, On quasi-differential operators in a Gilbert space, Dokl. Akad. Nauk SSSR , 18, No. 8, 522−526 (1938).

    Google Scholar 

  17. R. M. Tatsii, M. F. Stasyuk, and V. V. Mazurenko, Simulation of discrete-continuum systems. Foundations of the concept of quasi derivatives, in: Physicomathematical Modeling and Information Technologies, Issue 10, 7−37 (2009).

  18. EN 1991-1-2 (2002) (English): Eurocode 1: Actions on structures — Part 1−2: Genera l actions — Actions on structures exposed to fi re [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC].

Download references

Author information

Authors and Affiliations

  1. L’vov State University of Life Safety, 35 Kleparovskaya Str., L’vov, 79000, Ukraine

    R. M. Tatsii & O. Yu. Pazen

Authors
  1. R. M. Tatsii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Yu. Pazen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 6, pp. 1445–1456, November–December, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tatsii, R.M., Pazen, O.Y. Direct (Classical) Method of Calculation of the Temperature Field in a Hollow Multilayer Cylinder. J Eng Phys Thermophy 91, 1373–1384 (2018). https://doi.org/10.1007/s10891-018-1871-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-018-1871-3

Keywords

Search

Navigation