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Germany; Russia Jena; Omsk
Section Mathematics
Title Boundary conditions and heat resistance at the moving solid-liquid interface
Author(-s) Buchbinder G.L.a, Galenko P.K.b
Affiliations Omsk State Universitya, University of Jenab
Abstract Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases taken at the interface and the quantities characterizing the interfacial surface such as surface temperature and surface heat flux. Introduction of the surface temperature as an independent variable, allows us to describe the scattering energy at the interface. For the steady-state motion of the planar interface the expression for the temperature discontinuity across the phase boundary has been obtained. Effect of Kapitza resistance on interface velocity is considered. It is shown that the thermal resistance leads to non-linearity in solidification kinetics, namely, in “velocity-undercooling” relation. The conditions of the steady-state motion of the planar interface are found.
Keywords crystallization, Kapitza resistance, interface, boundary conditions
UDC 51-72, 531
MSC 74A50
DOI 10.20537/vm160205
Received 23 May 2016
Language Russian
Citation Buchbinder G.L., Galenko P.K. Boundary conditions and heat resistance at the moving solid-liquid interface, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 194-206.
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