The Extinction Problem for Three-dimensional Inward Solidification
The Extinction Problem for Three-dimensional Inward Solidification
复制标题
三维向内凝固的消光问题
DOI：
10.1007/s10665-005-3501-2
复制
发表时间：
2005
影响因子：
1.3
通讯作者：
D. Riley
中科院分区：
文献类型：
--
作者：
S. McCue;J. King;D. Riley
研究了初始熔合温度下三维液体向内凝固的单相Stefan问题。特别是，在完全冻结发生之前，有时描述了固-熔界面的形状和速度，以及熄灭点附近的温度场。这是通过使用Baiocchi变换对一般Stefan数实现的。进一步证实了该问题的其他结果，如渐近分析表明界面最终在形状上接近椭球，从而提高了这些结果的准确性。结果是任意的，直到积分常数取决于物理上的Stefan数和液体区域固定边界的形状。一般来说，用分析方法确定这种相关性是不可能的；但是，大Stefan数的极限情况提供了一个例外。对于这个极限，给出了一个相当完备的渐近图，并导出了完全冻结发生所需时间的公式。本文给出的全三维结构域的结果补充并扩展了McCue等人给出的结果。r . Soc。London A 459(2003) 977]，它们仅适用于两个维度，并且发生了明显不同的时间依赖性。
The one-phase Stefan problem for the inward solidification of a three-dimensional body of liquid that is initially at its fusion temperature is considered. In particular, the shape and speed of the solid-melt interface is described at times just before complete freezing takes place, as is the temperature field in the vicinity of the extinction point. This is accomplished for general Stefan numbers by employing the Baiocchi transform. Other previous results for this problem are confirmed, for example the asymptotic analysis reveals the interface ultimately approaches an ellipsoid in shape, and furthermore, the accuracy of these results is improved. The results are arbitrary up to constants of integration that depend physically on both the Stefan number and the shape of the fixed boundary of the liquid region. In general it is not possible to determine this dependence analytically; however, the limiting case of large Stefan number provides an exception. For this limit a rather complete asymptotic picture is presented, and a recipe for the time it takes for complete freezing to occur is derived. The results presented here for fully three-dimensional domains complement and extend those given by McCue et al.[Proc. R. Soc. London A 459 (2003) 977], which are for two dimensions only, and for which a significantly different time dependence occurs.