Geodesic
A Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 3, pp. 236-245 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{UZKU_2023_165_3_a4,
     author = {E. L. Kuznetsova and S. I. Zhavoronok},
     title = {A {Stefan} problem for composite materials with an arbitrary number of moving phase-transition boundaries},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {236--245},
     year = {2023},
     volume = {165},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a4/}
}
TY  - JOUR
AU  - E. L. Kuznetsova
AU  - S. I. Zhavoronok
TI  - A Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2023
SP  - 236
EP  - 245
VL  - 165
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a4/
LA  - ru
ID  - UZKU_2023_165_3_a4
ER  - 
%0 Journal Article
%A E. L. Kuznetsova
%A S. I. Zhavoronok
%T A Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2023
%P 236-245
%V 165
%N 3
%U http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a4/
%G ru
%F UZKU_2023_165_3_a4
E. L. Kuznetsova; S. I. Zhavoronok. A Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 3, pp. 236-245. http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a4/

[1] A. Orekhov, L. Rabinskiy, G. Fedotenkov, “Analytical model of heating an isotropic half space by a moving laser source with a Gaussian distribution”, Symmetry, 14:4 (2022), 650 | DOI

[2] G. Fedotenkov, L. Rabinskiy, S. Lurie, “Conductive heat transfer in materials under intense heat flows”, Symmetry, 14:9 (2022) | DOI

[3] A. A. Orekhov, L. N. Rabinskiy, G. V. Fedotenkov, T. Z. Hein, “Heating of a half-space by a moving thermal laser pulse source”, Lobachevskii J. Math., 42:8 (2021), 1912–1919 | DOI | MR | Zbl

[4] M. Sha, L. N. Rabinskiy, A. A. Orekhov, “Impact of raindrop erosion on structural components”, Russ. Eng. Res, 43:7 (2023), 834–837 | DOI

[5] V. F. Formalev, B. A. Garibyan, A. A. Orekhov, “Mathematical modeling of heat transfer in anisotropic half-space based on the generalized parabolic wave heat transfer equation”, Lobachevskii J. Math, 43:7 (2022), 1842–1849 | DOI | MR | Zbl

[6] M. Sha, A. V. Volkov, A. A. Orekhov, E. L. Kuznetsova, “Micro-dilatation effects in a two layered porous structure under uniform heating”, J. Balk. Tribol. Assoc., 27:2 (2021), 280–294

[7] V. F. Formalev, S. A. Kolesnik, S. V. Mikanev, “Modelirovanie teplovogo sostoyaniya kompozitsionnykh materialov”, TVT, 41:6 (2003), 935–941

[8] Ek. L. Kuznetsova, Matematicheskoe modelirovanie teplomassoperenosa v kompozitsionnykh materialakh pri vysokointensivnom nagreve, Dis. ... kand. fiz. mat. nauk, MAI, M., 2006, 138 pp.

[9] V. F. Formalev, Ek. L. Kuznetsova, “Mnogomernyi teploperenos pri nalichii fazo vykh perekhodov v anizotropnykh kompozitsionnykh materialakh”, Mekh. komp. i konstr. mater., 13:4 (2007), 129–141

[10] G. Karslou, D. Eger, Teploprovodnost tverdykh tel, Nauka, M., 1964, 487 pp.

[11] V. F. Formalev, G. V. Fedotenkov, Ek. L. Kuznetsova, “Obschii podkhod k modelirovaniyu teplovogo sostoyaniya kompozitsionnykh materialov pri vysokotemperaturnom nagruzhenii”, Mekh. komp. i konstr. mater., 12:1 (2006), 141–156