Stefan-Neumann problem

Example 5.4 Melting of a Semi-infinite Solid with Constant Thermophysical Properties and a Step Change in Surface Temperature The Stefan-Neumann Problem The previous example investigated the heat conduction problem in a semi-infinite solid with constant and variable thermophysical properties. The present Example analyzes the same conduction problem with a change in phase. 

Interest in such problems was first expressed in 1831 in the early work of G. Lame and B. P. Clapeyron on the freezing of moist soil, and in 1889 by J. Stefan on the thickness of polar ice and similar problems. The exact solution of the phase-transition problem in a semi-infinite medium is due to F. Neumann (who apparently dealt with this kind of problem even before Stefan), and thus, problems of this kind are called Stefan-Neumann problems. The interest in these problems has been growing ever since (7,8). 

The problem discussed here was first solved by J. Stefan [2.39] in 1891. The solution of the more general problem first given by F. Neumann has been discussed... 

In his famous work on the growth and the melting of the ice layer on the polar sea (1, 2, 3) Stefan formulated a widespread engineering problem at Vienna University roughly at the time when Lewis Mills Morton started his first lecture course on chemical engineering at the Massachusetts Institute of Technology. Unconsciously Stefan used the mathematical formulations previously given by Neumann (4) ... 

In the context of this meeting which is devoted to the recollection of the beginnings of engineering education and to the progress of this education, the present introduction cannot be concluded without the remark that also the "changed view" on the Stefan problem can find its precipitate in elementary textbooks on transport phenomena where only the Neumann solution was presented so far, if heat transfer accompanied by a phase change was discussed at all. This will be demonstrated in Section A. 

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