Analytical study of the processes of thermal conductivity at high intensity heating

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.79990

Keywords:

thermal conductivity, parabolic type, hyperbolic type, velocity of heat propagation, microwave heating

Abstract

The analytical study of the processes of thermal conductivity at high intensity heating of dense bodies, similar to clay and plastic materials, was conducted. The conditions of applicability for the hyperbolic and parabolic equation of thermal conductivity for the composition of mathematical models of high intensity heating were explored. It was found that for the small Fourier numbers, the solution of hyperbolic equation of thermal conductivity makes it possible to determine thickness of the thermal layer and its change over time. Based on the example of manufacturing technical ceramics, it was demonstrated that the possible heating rates are considerably below the boundary rate, within which the velocity of heat propagation may be accepted as infinitely high. The conclusion was drawn that in the course of construction of mathematical models for the processes of thermal treatment in the technologies for the production of technical ceramics and the products similar to them in the intensity of heating, it is rational to take the thermal conductivity equation of parabolic type as the basis. The analytical solution, which makes it possible to calculate temperature field of the semi­restricted array under conditions of microwave heating, was obtained on the basis of the equation of thermal conductivity with internal heat sources, taking into consideration heat exchange with the environment. Results of computational experiment testify to the correctness of the proposed dependency.

Author Biographies

Natalia Kolesnychenko, Odesa National Academy of Refrigeration Dvoryanska str., 1/3, Odesa, Ukraine, 65082

Postgraduate student

Department of Heat-and-Power Engineering and Fuel Pipeline Transportation

Educational & Scintific Institute of Cold, Cryotechnologies and Environmental Energy 

Natalya Volgusheva, Odesa National Academy of Refrigeration Dvoryanska str., 1/3, Odesa, Ukraine, 65082

PhD, Associate Professor

Department of Heat-and-Power Engineering and Fuel Pipeline Transportation

Educational & Scientific Institute of Cold, Cryotechnologies and Environmental Energy

Iryna Boshkova, Odesa National Academy of Refrigeration Dvoryanska str., 1/3, Odesa, Ukraine, 65082

Doctor of Technical Sciences, Associate professor

Department of Heat-and-Power Engineering and Fuel Pipeline Transportation

Educational & Scintific Institute of Cold, Cryotechnologies and Environmental Energy 

References

  1. Wetherhold, R. C., Seelman, S., Wang, J. (1996). The use of functionally graded materials to eliminate or control thermal deformation. Composites Science and Technology, 56 (9), 1099–1104. doi: 10.1016/0266-3538(96)00075-9
  2. Lukasiewicz, S. A., Babaei, R., Qian, R. E. (2003). Detection of material properties in a layered body by means of thermal effects. Journal of Thermal Stresses, 26 (1), 13–23. doi: 10.1080/713855763
  3. Ayzikovich, S. M., Aleksandrov, V. M., Vasilev, A. S., Krenev, L. I., Trubchik, I. S. (2011). Analiticheskie resheniya smeshannyih osesimmetrichnyih za-dach dlya funktsionalno-gradientnyih sred. Moscow: Fizmatlit, 192.
  4. Sheppard, L. M. (1988). Manufacturing ceramics with microwave: the potential for economical production. Am. Ceram. Soc. Bull, 67, 3041–3086.
  5. Bykov, Y. V., Egorov, S. V., Eremeev, A. G., Plotnikov, I. V., Rybakov, K. I., Semenov, V. E. et. al. (2012). Fabrication of metal-ceramic functionally graded materials by microwave sintering. Inorganic Materials: Applied Research, 3 (3), 261–269. doi: 10.1134/s2075113312030057
  6. Luo, Z., Jin, S., Chen, J. (2016). A reduced-order extrapolation central difference scheme based on POD for two-dimensional fourth-order hyperbolic equations. Applied Mathematics and Computation, 289, 396–408. doi: 10.1016/j.amc.2016.05.032
  7. Shen, W., Little, L., Hu, L. (2010). Anti-diffusive methods for hyperbolic heat transfer. Computer Methods in Applied Mechanics and Engineering, 199 (17-20), 1231–1239. doi: 10.1016/j.cma.2009.12.013
  8. Ordóñez-Miranda, J., Alvarado-Gil, J. J. (2012). Determination of thermal properties for hyperbolic heat transport using a frequency-modulated excitation source. International Journal of Engineering Science, 50 (1), 101–112. doi: 10.1016/j.ijengsci.2011.08.012
  9. Shashkov, A. G., Bubnov, V. A., Yanovskiy, S. Yu. (2010). Volnovyie yavleniya teploprovodnosti. Moscow: Editorial USSR, 296.
  10. Lyikov, A. V. (1967). Teoriya teploprovodnosti. Moscow, 600.
  11. Maurer, M. J., Thompson, H. A. (1973). Non-Fourier Effects at High Heat Flux. Journal of Heat Transfer, 95 (2), 284. doi: 10.1115/1.3450051
  12. Isaev, K. B. (2004). K voprosu ob uchete konechnoy skorosti rasprostraneniya tepla v tverdom tele. Tr. V Minskogo mezhd. foruma MMF-2004, 1–6.
  13. Kudinov, V. A., Kudinov, I. V. (2010). Ob odnom metode polucheniya tochnogo analiticheskogo resheniya giperbolicheskogo uravneniya teploprovodnosti na osnove ispolzovaniya ortogonalnyih metodov. Vestnik Samarskogo Tehnicheskogo universiteta. Seriya Fiziko-matematicheskie nauki, 5 (21), 159–169.
  14. Antimonov, M. S. (2008). Chislenno-analiticheskie metodyi resheniya zadach teploprovodnosti na osnove ortogonalnyih metodov vzveshennyih nevyazok. Ulyanovskiy gosudarstevenyi tehnicheskiy universitet, 24.
  15. Isayev, K. (2003). Application of solutions of inverse heat conduction problems for research of materials thermal conductivity in wide range of its values and temperatures. Proceed. 4-th Baltic Heat Transfer Conference. “Advances in Heat Transfer Engineering”, 201–208.
  16. Chester, M. (1963). Second Sound in Solids. Physical Review, 131 (5), 2013–2015. doi: 10.1103/physrev.131.2013
  17. Samarskiy, A. A., Nikolaev, E. S. (1978). Metodyi resheniya setochnyih uravneniy. Moscow: Nauka, 592.
  18. Lukas, R. (2005). Mikrowelleunterstütze Wärmt- und Stoffübertragung beim Trocknen und Entbindern Technischer Keramik. Dissertation zur Erlagung des akademischen Grades Doktor-Ingenieur. Freibur, 125.
  19. Willert-Porada, M. A., Borchert, R. (1997). Microwave sintering of metal-ceramic FGM. Functionally Graded Materials, 349–354. doi: 10.1016/b978-044482548-3/50058-5
  20. Chatterjee, A., Basak, T., Ayappa, K. G. (1998). Analysis of microwave sintering of ceramics. AIChE Journal, 44 (10), 2302–2311. doi: 10.1002/aic.690441019
  21. Averin, B. V. (2009). Obschaya shema resheniya kraevoy zadachi nestatsionarnoy teploprovodnosti s vnutrennimi istochnikami teplotyi dlya mnogosloynyih konstruktsiy. Vestnik Samarskogo Tehnicheskogo universiteta. Seriya Fiziko-matematicheskie nauki, 2 (19), 274–277.
  22. Shumskayte, M. Y., Glinskih, V. N. (2015). Analiz vliyaniya ob'emnogo soderzhaniya i tipa glinistyih mineralov na relaksatsionnyie harakteristiki peschano-alevritovyih obraztsov kerna. Geologiya, geofizika i razrabotka neftyanyih mestorozhdeniy. Vsesoyuzn. NII organizatsii, upravleniya i ekonomiki neftegazovoy promyishlennosti, 7, 35–38.

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Published

2016-10-30

How to Cite

Kolesnychenko, N., Volgusheva, N., & Boshkova, I. (2016). Analytical study of the processes of thermal conductivity at high intensity heating. Eastern-European Journal of Enterprise Technologies, 5(8 (83), 26–31. https://doi.org/10.15587/1729-4061.2016.79990

Issue

Vol. 5 No. 8 (83) (2016): Energy-saving technologies and equipment

Section

Energy-saving technologies and equipment

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Copyright (c) 2016 Natalia Kolesnychenko, Natalya Volgusheva, Iryna Boshkova

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