Solidification of geometrically simple bodies

Pure substances and eutectic mixtures solidify and melt at definite temperatures dE, which differ from substance to substance and are barely dependent on the pressure. The best known example of this is water which at atmospheric pressure, freezes at E = 0 °C. This releases the fusion enthalpy of hE = 333kJ/kg. When a solid body melts the enthalpy of fusion must be supplied to the solid as heat. 

Solidifying processes are important in cryogenics, food and process industries and also in metallurgy. A main point of interest is the speed at which the boundary between the solid and the liquid phase moves. Prom this the time required for solidifying layers of a given thickness can be calculated. The modelling of these processes belongs to the held of transient heat conduction, as the enthalpy of 

A general mathematical solution for this type of thermal conduction problems does not exist. Special explicit solutions have been found by F. Neumann4 in 1865 and J. Stefan in 1891 [2.39], In the first section we will discuss the solution given by J. Stefan. Quasi-steady solutions will be derived in the section following that. These solutions assume that any heat storage in the solidified body can be neglected. In the final section we will look at the improvements for this quasisteady solution in which the heat stored in the body is considered approximately. 

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