Classification of melting and solidification

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One-region melting and solidification
(a) Melting (T0 > Tm) (b) Solidification (T0 < Tm)

Figure 1: One-region melting and solidification
Two-region melting and solidification.
(a) Melting (T0 > Tm > Ti) (b) Solidification (T0 < Tm < Ti)

Figure 2: Two-region melting and solidification.
Solidification of a multicomponent PCM
Figure 3: Solidification of a multicomponent PCM

Melting and solidification find application in the geophysical sciences; industrial forming operations such as casting and laser drilling; latent heat energy storage systems; and food and pharmaceutical processing. Any manmade metal products must undergo liquid forms at some point during manufacturing processes and solidify to form intermediate or final products. Melting and solidification processes can be classified as one of three types: one-region, two-region, and multiple-region. The classification depends on the properties of the phase change material (PCM) involved and the initial conditions. For a single-component PCM, melting or solidification occurs at a single temperature. Pure water, for example, melts at a uniform temperature of 0 °C, while pure n-Octadecane (C18H38) melts at 28 °C. For the solid-liquid phase change process of a PCM with a single melting point, the solid-liquid interface appears as a clearly-observable sharp border. Initial conditions for the solid-liquid phase change process of a single-component PCM determine whether the problem will be classified as a one- or two-region problem.

For the melting (or solidification) process, if the initial temperature of the PCM, Ti, equals the melting point, Tm, the temperature in the solid (liquid) phase remains uniformly equal to the melting point throughout the process. In this case, only the temperature distribution in the liquid (solid) phase needs to be determined. Thus, the temperature of only one phase is unknown and the problem is called a one-region problem. Figure 1 shows the temperature distribution of one-dimensional, one-region melting and solidification problems. The surface temperature, T0 , is greater than Tm for melting and is below Tm for solidification.

For the melting process, if the initial temperature of the PCM, Ti, is below the melting point of the PCM, Tm, (or above, for solidification), the temperature distribution of both the liquid and solid phases must be determined; this is called a two-region problem. Figure 2 shows the temperature distribution of one-dimensional two-region melting and solidification problems.

For a multi-component PCM, the solid-liquid phase change process occurs over a range of temperatures (Tm1, Tm2), instead of a single temperature. The PCM is liquid if its temperature is above Tm2 and solid when its temperature is below Tm1. Between the solid and liquid phases there is a mushy zone where the temperature falls within the phase change temperature range (Tm1, Tm2). Successful solution of phase change problems involving these substances requires determination of the temperature distribution in the liquid, solid, and mushy zones; therefore, these are referred to as multiregion problems. The temperature distribution of one-dimensional solidification in a multicomponent PCM is shown in Fig. 3, where it can be seen that the solution requires tracking of two interfaces.

In solid-liquid phase change problems, the location of the solid-liquid interface is unknown before the final solution is obtained and this presents a special difficulty. Since the interface also moves during melting or solidification, such problems are referred to as moving boundary problems and always have time as an independent variable.


Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA
Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

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