2005/02/23 by D. Temkin, D. E. Temkin, Temkin, D.
Computer Science · Materials Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Solidification and crystal growth phenomena #cond-mat.mtrl-sci
paper · pdf · doi:10.48550/arxiv.cond-mat/0502551
submitted to Acta Materialia
arxiv created 2005/02/23 · openalex publication_date 2005/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We demonstrate that for a migration of a liquid layer between the melting and the solidification front an exact steady-state solution with two parabolic fronts can be found. A necessary condition hereby is that the temperature of the solidification front exceeds the temperature of the melting front (both temperatures are supposed to be constant). It is shown that in pure materials and alloys there exist two types of solutions with two convex and with two concave parabolas respectively. While a steady-state process with two planar interfaces is only possible for a single point, the processes with two parabolas are possible inside a region of control parameters. The relations between the Peclet numbers and the control parameters are obtained.