The Existence and Stability of Regions with Superheating in the Classical Two-phase One-dimensional Stefan Problem with Heat Sources
- 1 March 1983
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 30 (2) , 215-230
- https://doi.org/10.1093/imamat/30.2.215
Abstract
It is proved that in the one-dimensional two-phase Stefan problem regions with superheating (supercooling) appear when sufficiently strong volume heat sources (sinks) are present. The stability of the problem with superheating is considered. It is proved that when the heat flux, on the free boundary, from the solid is greater than that from the liquid then the free boundary is linearly unstable against three-dimensional perturbations. From these results it follows that the classical model for the melting of a metal under Joule heating has a linearly unstable free boundary. Such models are applicable to the electrical welding of metals.Keywords
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