The Solid-Liquid Phase Interface Dynamics in an Undercooled Melt with a Solid Wall

被引：0

作者：

Titova, Ekaterina A. ^{[1
]}

Alexandrov, Dmitri V. ^{[1
]}

机构：

[1] Ural Fed Univ, Dept Theoret & Math Phys, Lab Multiscale Math Modeling, Lenin Ave 51, Ekaterinburg 620000, Russia

来源：

MATHEMATICS | 2024年 / 12卷 / 02期

关键词：

boundary integral equation; Green's function technique; phase transitions; propagation of curved solid-liquid interfaces; undercooled melts; dendrites; DENDRITIC GROWTH; PURE METAL; SOLIDIFICATION; ALLOY; FLOW; PREDICTIONS; STABILITY; SELECTION; MODEL;

D O I：

10.3390/math12020327

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A new boundary integral equation for the interface function of a curved solid/liquid phase interface propagating into an undercooled one-component melt is derived in the presence of a solid wall in liquid. Green's function technique is used to transform a purely thermal boundary value problem to a single integro-differential equation for the interface function in two- and three-dimensional cases. It is shown that a solid wall represents an additional source of heat and melt undercooling can be negative in the vicinity of the wall. The new boundary integral equation has a limiting transition to previously developed theory in the absence of a solid wall.

引用

页数：11