A Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries
https://doi.org/10.26907/2541-7746.2023.3.236-245
Abstract
A Stefan problem of heat transfer in semi-infinite bodies with an arbitrary number of unsteady moving boundaries during phase transitions was solved. Such problems arise when composite materials are heated at high temperatures, causing the binding agents to decompose (destruct) thermally, which leads to the formation of moving boundaries in the onset and end of phase transitions, mass transfer, etc. An analytical solution of the Stefan problem with an arbitrary number of unsteady moving boundaries was obtained. The heat transfer process with two moving boundaries was analyzed.
Keywords
heat transfer,
Stefan problem,
moving boundary,
composite material,
destruction of binding agents,
analytical solution
Supporting agencies: This study was supported by the Russian Science Foundation (project no. 23-19-00680).
About the Authors
E. L. Kuznetsova
Moscow Aviation Institute (National Research University)
Russian Federation
Russian Federation
Moscow, 125993
S. I. Zhavoronok
Institute of Applied Mechanics, Russian Academy of Sciences
Russian Federation
Russian Federation
Moscow, 125040
References
1. Orekhov A., Rabinskiy L., Fedotenkov G. Analytical model of heating an isotropic half-space by a moving laser source with a Gaussian distribution. Symmetry, 2022, vol. 14, no. 4, art. 650. http://doi.org/10.3390/sym14040650.
2. Fedotenkov G., Rabinskiy L., Lurie S. Conductive heat transfer in materials under intense heat flows. Symmetry, 2022, vol. 14, no. 9, art. 1950. https://doi.org/10.3390/sym14091950.
3. Orekhov A.A., Rabinskiy L.N., Fedotenkov G.V., Hein T.Z. Heating of a half-space by a moving thermal laser pulse source. Lobachevskii J. Math., 2021, vol. 42, no. 8, pp. 1912–1919. http://doi.org/10.1134/s1995080221080229.
4. Sha M., Rabinskiy L.N., Orekhov A.A. Impact of raindrop erosion on structural components. Russ. Eng. Res., 2023, vol. 43, no. 7, pp. 834–837. https://doi.org/10.3103/S1068798X23070195.
5. Formalev V.F., Garibyan B.A., Orekhov A.A. Mathematical modeling of heat transfer in anisotropic half-space based on the generalized parabolic wave heat transfer equation. Lobachevskii J. Math., 2022, vol. 43, no. 7, pp. 1842–1849. https://doi.org/10.1134/S1995080222100110.
6. Sha M., Volkov A.V., Orekhov A.A., Kuznetsova E.L. Micro-dilatation effects in a two-layered porous structure under uniform heating. J. Balk. Tribol. Assoc., 2021, vol. 27, no. 2, pp. 280–294.
7. Formalev V.F., Kolesnik S.A., Mikanev S.V. Simulation of the thermal state of composite materials. High Temp., vol. 41, no. 6, pp. 832–838. https://doi.org/10.1023/B:HITE.0000008341.27025.54.
8. Kuznetsova E.L. Mathematical modeling of heat and mass transfer in composite materials during high-temperature exposure. Cand. Phys.-Math. Sci. Diss. Moscow, MAI, 2006. 138 p. (In Russian)
9. Formalev V.F., Kuznetsova E.L. Multidimensional heat transfer with phase transition in anisotropic composite materials. Mekh. Kompoz. Mater. Konstr., vol. 13, no. 4, pp. 129–141. (In Russian)
10. Carslaw H., Jaeger J. Teploprovodnost’ tverdykh tel [Conduction of Heat in Solids]. Moscow, Nauka, 1964. 487 p. (In Russian)
11. Formalev V.F., Fedotenkov G.V., Kuznetsova E.L. A general approach to simulation of the thermal state of composite materials under high temperature loading. Mekh. Kompoz. Mater. Konstr., 2006, vol. 12, no. 1, pp. 141–156. (In Russian)
Review
For citations:
Kuznetsova E.L., Zhavoronok S.I. A Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2023;165(3):236-245. (In Russ.) https://doi.org/10.26907/2541-7746.2023.3.236-245
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