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Engineering Method of Solving Nonstationary Problem of the Thermal Conductivity of a Deformable Elastomeric Plate

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The article presents an approximate (semianalytical) solution of the one-dimensional nonstationary problem of the thermal conductivity of a uniformly deforming plate (shell) under time-dependent boundary conditions of the third kind, obtained using the proposed piecewise integral heat balance method. It is shown that a change in the thickness of the plate (shell) on deformation affects not only the quantitative, but also the qualitative behavior of temperature and heat flux at different points of the plate. It has been established that with an increase in the frequency of temperature fluctuations on the inner surface of the plate, thermal disturbances penetrate into the plate to a shorter distance.

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References

  1. R. A. Akopyan, Pneumatic Cushioning of Tracks (Issues of Theory and Practice) [in Russian], Vishcha Shkola, Izd. L′vovsk. Univ., L′vov (1979).

  2. A. V. Pozdeev, V. V. Novikov, A. S. D′yakov, A. V. Pokhlebin, I. M. Ryabov, and K. V. Chernyshov, Adjustable Pneumatic and Pneumohydraulic Springs for Vehicle Suspensions [in Russian], Izd. Volgogradsk. GTU, Volgograd (2013).

  3. W. A. Fongue, J. Kieserling, and P. F. Pelz, Air spring damper, on the way to exceptional sliding: Modeling, development and optimization of an air spring damper with regard to ride comfort and handling, in: Proc. 5th Int. Munich Chassis Symposium 2014, Springer Fachmedien Wiesbaden (2014), pp. 219–248.

  4. H. Liu and J. C. Lee, Model development and experimental research on an air spring with auxiliary reservoir, Int. J. Automot. Technol., 12, No. 6, 839–847 (2011).

    Article  Google Scholar 

  5. S. A. Korneev, V. S. Korneev, A. V. Zubarev, and E. V. Kliment′ev, Fundamentals of the Technical Theory of Pneumatic Shock Absorbers [in Russian], Izd. OmGTU, Omsk (2016).

  6. K. F. Chernykh, Nonlinear Theory of Elasticity in Mechanical Engineering Calculations [in Russian], Mashinostroenie, Leningrad (1986).

    Google Scholar 

  7. M. D. Mikhailov, Unsteady-State Temperature Fields in Shells [in Russian], Énergiya, Moscow (1967).

    Google Scholar 

  8. V. S. Zarubin, Temperature Fields in the Design of Flying Vehicles (Calculation Methods) [in Russian], Mashinostroenie, Moscow (1978).

    Google Scholar 

  9. V. S. Zarubin, Engineering Methods for Solving Heat Conduction Problems [in Russian], Énergoatomizdat, Moscow (1983).

    Google Scholar 

  10. A. I. Leontiev (Ed.), Heat and Mass Exchange Theory [in Russian], Vysshaya Shkola, Moscow (1979).

    Google Scholar 

  11. V. S. Zarubin and G. N. Kuvyrkin, Mathematical Models of Thermomechanics [in Russian], FIZMATLIT, Moscow (2002).

    Google Scholar 

  12. C. Truesdell, A First Course in Rational Continuum Mechanics [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  13. V. S. Korneev, S. A. Korneev, and V. V. Shalai, On the question of applicability of the classical heat conduction equation to highly elastic materials undergoing large deformations, Tepl. Prots. Tekh., 11, No. 1, 79–85 (2019).

    Google Scholar 

  14. É. M. Kartashov, Analytical Methods in the Theory of Thermal Conductivity of Solid Bodies [in Russian], Vysshaya Shkola, Moscow (2001).

    Google Scholar 

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

    Google Scholar 

  16. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids [Russian translation], Nauka, Moscow (1964).

    Google Scholar 

  17. N. M. Belyaev and A. A. Ryadno, Methods of the Heat Conduction Theory [in Russian], Vysshaya Shkola, Moscow (1982).

    Google Scholar 

  18. V. S. Korneev, S. A. Korneev, and V. V. Shalai, An approximate analytical solution of the nonstationary problem of thermal conductivity of a deforming plate with time-dependent boundary conditions, Tepl. Prots. Tekh., 11, No. 9, 417–425 (2019).

    Google Scholar 

  19. A. I. Veinik, Approximate Calculation of Heat Conduction Processes [in Russian], GÉI, Moscow–Leningrad (1959).

  20. T. R. Goodman, Heat balance integral and its application to problems involving a change of phase, Trans. ASME J. Heat Transf., 80, No. 2, 335–342 (1958).

    Google Scholar 

  21. T. R. Goodman, Application of integral methods to transient nonlinear heat transfer, Adv. Heat Transf., 1, 51–122 (1964).

    Article  Google Scholar 

  22. A. S. Wood, F. Mosally, and A. Al-Fhaid, On high-order polynomial heat-balance integral implementations, Therm. Sci., 13, No. 2, 11–25 (2009).

    Article  Google Scholar 

  23. E. V. Stefanyuk and V. A. Kudinov, Additional boundary conditions in nonstationary problems of heat conduction, Teplofiz. Vys. Temp., 47, No. 2, 269–282 (2009).

    Google Scholar 

  24. V. A. Kot, The method of boundary characteristics in the problems of heat conduction based on the thermal balance integral, Izv. Nats. Akad. Nauk Belarusi, Ser. Fiz. Tekh. Nauk, No. 2, 54–65 (2016).

  25. I. S. Grigoriev and E. Z. Meilikhov (Eds.), Physical Quantities, Handbook [in Russian], Énergoatomizdat, Moscow (1991).

    Google Scholar 

  26. V. S. Korneyev, S. A. Korneyev, I. A. Pen'kov, and I. N. Kvasov, Experimental study of heat transfer on the rubber-cord cased pneumatic element surfaces under the natural convection, IOP Conf. Ser.: J. Phys., 1050, Article ID 012036-1-012036-8 (2018).

  27. V. A. Galashin, Determination of air spring stiffness with account for heat exchange, Avtomob. Promyshl., No. 11, 21–23 (1965).

  28. P. I. Plastinin, Piston Compressors. 1. Theory and Calculation [in Russian], KolosS, Moscow (2006).

  29. V. E. Shcherba, V. V. Shalai, A. V. Zanin, and A. S. Tegzhanov, Analysis of the process of heating a liquid during compression in the working cavity of the compressor section of a piston hybrid energy machine, Khim. Neftegaz. Mashinostr., No. 7, 25–31 (2019).

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Authors and Affiliations

  1. Omsk State Technical University, 11 Mir Ave., Omsk, 644005, Russia

    V. S. Korneev, S. A. Korneev & V. V. Shalai

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  1. V. S. Korneev
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  2. S. A. Korneev
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  3. V. V. Shalai
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Correspondence to V. S. Korneev.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 96, No. 7, pp. 1728–1738, November–December, 2023.

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Korneev, V.S., Korneev, S.A. & Shalai, V.V. Engineering Method of Solving Nonstationary Problem of the Thermal Conductivity of a Deformable Elastomeric Plate. J Eng Phys Thermophy 96, 1697–1707 (2023). https://doi.org/10.1007/s10891-023-02839-1

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