Geodesic
A mathematical model of synthesis of a three-layer (copper--titanium silicide--steel) compound in a combustion mode
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 86 (2023), pp. 94-103

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This work presents a two-dimensional mathematical model of self-propagating high-temperature synthesis (SHS) of a specimen consisting of three layers (copper foil – 5Ti + 3Si compacted mixture – steel substrate). A numerical study of the mathematical model is carried out using the finite-difference method. The limiting frontal SHS modes of a three-layer specimen of rectangular cross-section are determined, taking into account the copper layer melting and the thermocapillary wetting of Ti$_5$Si$_3$ synthesis products by the melt with the formation of a composite material during thermal interaction with the steel substrate. The critical minimum thickness of the main internal synthesis layer allowing one to obtain titanium silicides in the frontal combustion mode is calculated. The maximum temperature in the combustion front near the critical conditions is 1652 K. The depth of capillary wetting of the synthesis products with copper melt is in the range of 2-4 mm.
Keywords: self-propagating high-temperature synthesis, melting, thermocapillary flow, metal composite material. 
@article{VTGU_2023_86_a6,
     author = {V. G. Prokof'ev},
     title = {A mathematical model of synthesis of a three-layer (copper--titanium silicide--steel) compound in a combustion mode},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {94--103},
     publisher = {mathdoc},
     number = {86},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_86_a6/}
}
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V. G. Prokof'ev. A mathematical model of synthesis of a three-layer (copper--titanium silicide--steel) compound in a combustion mode. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 86 (2023), pp. 94-103. http://geodesic.mathdoc.fr/item/VTGU_2023_86_a6/