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The most suitable model for the casting situation was a Rankine-Hastings equation, in which a single unit with heat balance involves the formation of two materials: one is the melt, and the other is the solid. The Rankine-Hastings equation is the most common formulation for descriptions of the processes involved in phase change. The volatile-free component of a Rankine-Hastings equation defines the melting point of a system, meaning that the liquidus temperature is fixed by the equation. It is the liquidus temperature that determines the observed change in state, from solid to liquid, and not the liquidus temperature itself.[100]

This indicates that the heat released in the solidification process is not constant, even if all thermal inertia and heat transfer effects are excluded for simplification. Another point the modeler is interested in is the trend seen in the temperature dependent on the heat flux during solidification. For this specific problem, a local sense of rate of solidification was developed.

The initial model consisted of one phase and several levels representing layers of material. The first layer represented the bulk material, the second the layer that was solidified first, the third the second layer solidified, etc. The last layer represented the remainder of the material solidified just prior to the filling cycle. Each layer was discretized into subdivisions that represent material quantities such as the amount of melt, the reservoir volume, and the solid content. By adding more levels, the model could show multiple nucleation events.

The melt is discretized into several subdivisions, representing the initial amount of melt, and is considered a liquid phase. The solid contained in the separate layers is considered a solid phase. d2c66b5586

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