Solidification Fronts/Viscous Phase Transitions Forwards-Backwards Heat Equations.
Abstract
Directional solidification in the presence of an impurity may be described by a set of impurity concentration and thermal diffusion equations coupled at a free boundary. In the limit of a small distribution coefficient, a long wavelength expansion can be used to obtain a single fourth order parabolic equation describing the deviations of the interface from planarity in the limit in which the deviations are small. Here we present an alternate version of this asymptotic scheme which isolates and preserves the nonlinearities in their original form. While the new asymptotic expansion is of an equivalent level of asymptotic validity, the extrapolated predictions of cusping, blow up and front formation appear to be more accurate.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1987
- Accession Number
- ADA190539
Entities
People
- A. Novick-cohen
- P. Rosenau
Organizations
- Rensselaer Polytechnic Institute