Affiliation:
1. Department of Mechanical Engineering, The City College of the City University of New York, New York, N. Y.
Abstract
This paper treats the problem of the inward solidification at large Stefan number 1/ε, ε = CP(Ti − Tf)/L, of a finite slab which is initially at an arbitrary temperature Ti above the melting point. The face at which the heat is removed is maintained at a constant temperature below fusion while the opposite face is either (a) insulated or (b) kept at the initial temperature. Perturbation series solutions in ε are obtained for both the short-time scale characterizing the transient diffusion in the liquid phase and the long-time scale characterizing the interface motion. The asymptotic matching of the two series solutions shows that to O(ε1/2) the short-time series solution for interface motion for the insulated Case (a) is uniformly valid for all time. A singular perturbation theory is, however, required for the isothermal Case (b) since the interface motion is affected to this order by the inhomogeneous temperature distribution in the liquid phase.
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
62 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献