THE SOLUTION OF A CLASS OF TWO-DIMENSIONAL MELTING AND SOLIDIFICATION PROBLEMS.

摘要

Two-dimensional melting and solidification problems are divided into three convenient classes and a general method of solution for one of these is presented. The concept is used of a fictitious body of constant geometry,in which is embedded the real body (whose dimensions are changing due to the change in phase); the fictitious body is acted upon by a fictitious heat flux or (in some problems) a fictitious initial temperature distribution. A set of integro-differential equations is presented to be solved simultaneously,numerically or in series form. The melting of a finite,insulated slab with the melt immediately removed is formulated and an example for a semi-infinite,insulated strip is given. The solidification of a finite insulated slab with zero superheat is formulated and an example for a specific cooling history is given. Two-dimensional effects are introduced by spatial variations of heating or cooling conditions,and short-time series solutions are developed. (Author)