You are not currently logged in.
Access JSTOR through your library or other institution:
Velocity Effects in Unstable Solidification
SIAM Journal on Applied Mathematics
Vol. 50, No. 1 (Feb., 1990), pp. 1-15
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2102096
Page Count: 15
You can always find the topics here!Topics: Velocity, Solidification, Temperature distribution, Differential equations, Mathematical problems, Boundary conditions, Anisotropy, Heat equation, Liquid phases, Interfacial tension
Were these topics helpful?See something inaccurate? Let us know!
Select the topics that are inaccurate.
Preview not available
The supercooled Stefan problem with surface tension is considered as a model of unstable solidification, with a general anisotropic curvature- and velocity-dependent boundary condition on the moving interface. The problem is reformulated in terms of a history-dependent singular integral equation for the velocity of the boundary. Using this equation, a new linear stability analysis of a flat interface is carried out and the smoothing role of velocity-dependence and the destabilizing effect of anisotropy are demonstrated. The results disagree with previous analyses because transient effects due to the initial temperature field are included, and numerical results are presented that confirm the analysis presented here. It is found that velocity effects cannot increase the range of unstable modes beyond that permitted by surface tension.
SIAM Journal on Applied Mathematics © 1990 Society for Industrial and Applied Mathematics