Direct method of studying heat exchange in multilayered bodies of basic geometric forms with imperfect heat contact

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Authors:


R.M.Tatsiy, orcid.org/0000-0001-7764-2528, Lviv State University of Life Safety, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

O.Yu.Pazen, orcid.org/0000-0003-1655 -3825, Lviv State University of Life Safety, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

S.Ya.Vovk, orcid.org/0000-0001-7007-7263, Lviv State University of Life Safety, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

D.V.Kharyshyn, orcid.org/0000-0002-0927-9998, Lviv State University of Life Safety, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


повний текст / full article



Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2021, (1): 060 - 067

https://doi.org/10.33271/nvngu/2021-1/060



Abstract:



Purpose.
Characteristics of heat transfer processes in multilayer bodies of basic geometric shapes simultaneously under conditions of convective heat transfer on its surfaces and taking into account imperfect thermal contact between the layers.


Methodology.
A direct method was applied to solve a one-parameter family of boundary value problems in the theory of heat conduction. This method is based on the reduction method, the concept of quasiderivatives, a system of differential equations with impulse action, the method of separation of variables, and the modified method of eigenfunctions of Fourier. It is worth noting that the application of the concept of quasiderivatives allows you to circumvent the well-known problem of multiplication of generalized functions, which arises when using the differentiation procedure of the coefficients of a differential equation. Such a procedure, in our opinion, casts doubt on the equivalence of the transition to the differential equation obtained in this way with generalized coefficients.


Findings.
The solution to the problem is obtained in a closed form. The proposed algorithm does not contain a solution to volume conjugation problems. It includes only: a) finding the roots of the corresponding characteristic equations; b) the multiplication of a finite number of known (2 2) matrices; c) the calculation of certain integrals; d) summing the required number of members of the series to obtain the specified accuracy. As an illustration, we consider model examples of heating eight-layer structures in a fire.


Originality.
For the first time, the direct method has been applied to solving the problem of the distribution of an unsteady temperature field over the thickness of multilayer structures of basic geometric shapes simultaneously, in the presence of imperfect thermal contact between the layers.


Practical value.
The implementation of the research results allows us to effectively study the heat transfer processes in multilayer structures, which are found in a number of applied problems.



Keywords:
heat exchange, body shape coefficient, imperfect thermal contact

References.


1. Shatskyi, I., Ropyak, L., & Velychkovych, A. (2020). Model of contact interaction in threaded joint equipped with spring-loaded collet.Engineering Solid Mechanics,8(4), 301-312. https://doi.org/10.5267/j.esm.2020.4.002.

2. Bulbuk, O., Velychkovych, A., Mazurenko, V., Ropyak, L., & Pryhorovska, T. (2019). Analytical estimation of tooth strength, restored by direct or indirect restorations.Engineering Solid Mechanics,7(3), 193-204. https://doi.org/10.5267/j.esm.2019.5.004.

3. Topchevska, K. (2017). Influence of friction power on temperature stresses during single braking. Physicochemical Mechanics of Materials, 53(5), 66-72.

4. Yang, X.J. (2017). A new integral transform operator for solving the heat-diffusion problem.Applied Mathematics Letters, 64, 193-197. https://doi.org/10.1016/j.aml.2016.09.011.

5. Yang, X.J., & Gao, F. (2017). A new technology for solving diffusion and heat equations.Thermal Science,21(1, Part A), 133-140. https://doi.org/10.2298/TSCI160411246Y.

6. Jiang, J., & Zhou, J. (2020). Analytical solutions of Laplaces equation for layered media in a cylindrical domain and its application in seepage analyses.International Journal of Mechanical Sciences, 105781. https://doi.org/10.1016/j.ijmecsci.2020.105781.

7. Vidal, P., Gallimard, L., Ranc, I., & Polit, O. (2017). Thermal and thermo-mechanical solution of laminated composite beam based on a variables separation for arbitrary volume heat source locations.Applied Mathematical Modelling,46, 98-115. https://doi.org/10.1016/j.apm.2017.01.064.

8. Gobiowski, J., & Zarba, M. (2020). Transient Thermal Field Analysis in ACCC Power Lines by the Greens Function Method. Energies, 13(1), 280. https://doi.org/10.3390/en13010280.

9. Norouzi, M., Rahmani, H., Birjandi, A.K., & Joneidi,A.A. (2016). A general exact analytical solution for anisotropic non-axisymmetric heat conduction in composite cylindrical shells.International Journal of Heat and Mass Transfer,93,41-56.https://doi.org/10.1016/j.ijheatmasstransfer.2015.09.072.

10. Eliseev, V.N., & Borovkova, T.V. (2014). The generalized analytical approach to calculating a stationary temperature field in objects of simple geometrical shapes. Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, (1), 46-57.

11. Eliseev, V.N., Tovstonog, V.A., & Borovkova, T.V. (2017). Soluton algorthim of generalized non-stationary heat conduction problem in the bodies of simple geometric shapes. Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, (1), 112-128. https://doi.org/10.18698/0236-3941-2017-1-112-128.

12. Tatsiy, R.M., Pazen, O.Y., Vovk, S.Y., Ropyak, L.Y., & Pryhorovska, T. O. (2019). Numerical study on heat transfer in multilayered structures of main geometric forms made of different materials. Journal of the Serbian Society for Computational Mechanics, 13(2), 36-55. https://doi.org/10.24874/jsscm.2019.13.02.04.

13. Okrepkyi, B., Pyndus, T., & Shelestovskyi, B. (2019). Hot stamp pressure on elastic half-space taking into account imperfect thermal contact through thin intermediate layer. Scientific Journal of TNTU, 96(4), 14-22. https://doi.org/10.33108/visnyk_tntu2019.04.013.

14. Gera, B.V. (2013). Mathematical modelling of nonideal conditions for thermal contact of layers through thing inclusion with heat source. Physical and mathematical modeling and information technology, (18), 61-72.

15. Okrepky, B.S., & Nemish, V.M. (2014). Axes-symmetric temperature problem for a system of two layers in non-ideal termal contact. Interuniversity collection Scientific notes, (47), 131-136.

16. Yang, B., & Liu, S. (2017). Closed-form analytical solutions of transient heat conduction in hollow composite cylinders with any number of layers. International Journal of Heat and Mass Transfer, 108, 907-917. https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.020.

17. Tatsiy, R.M., Pazen, O.Yu., & Stasiuk, M.F. (2019). Calculation of non-stationary temperature field in a multilayered plate under conditions of unique heat contact between layers. Bulletin of the Kokshetau Technical Institute of the KTIKCHSMVD of the Republic of Kazakhstan, 2(34), 40-49.

18. Tatsii, R.M., & Pazen, O.Y. (2018). Direct (classical) method of calculation of the temperature field in a hollow multilayer cylinder. Journal of Engineering Physics and Thermophysics, 91(6), 1373-1384. https://doi.org/10.1007/s10891-018-1871-3.

19. Pazen, O. (2018). Verification Results of the Presentation of the Protection of the Unsteading Temperature Field at the Concrete Construction for the Mind of Thestandard Temperature Refrigeration Fire.Bulletin of Lviv State University of Life Safety, (18), 96-101. https://doi.org/10.32447/20784643.18.2018.10.

20. EN 1991-1-2 (2002). Eurocode 1: Actions on structures Part 1-2: General actions Actions on structures exposed to fire [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]. https://doi.org/10.1002/9783433601570.ch1.

 

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