Changing View on the Classical Stefan Problem

Abstract

In 1891 Stefan calculated the growth of polar ice with the aid of a method proposed by Neumann in 1860, This calculation forms the starting point for activities in the field of moving boundary value problems. Although a phase transition (crystallization) is assumed as the reason for the solidification — notice the accepted role of the latent heat — the concept of “nucleation” has rarely been applied so far. It is only with the increasing importance of relatively slowly crystallizing polymeric materials that supercooling was recognized as a point for the mathematical treatment of molding processes. But this causes a change of view on the subject. So far, basic treatments of transport phenomena have been avoiding molding processes, despite their technological importance. Apparently, these processes seem too difficult for beginners. In the present paper, however, it will be shown that one can give a useful classification of crystallization phenomena without relying on too complicated calculation methods.