A melting model with a different thermal conductivity is created to represent the thermal properties of the metals and the different phases. The model can then be imported into the simulation environment and the temperature evolution is computed. We used the average value of  for aluminum and magnesium alloys (Figure 2) and ,  for titanium (Figure 3).
By measuring the temperatures of the solid particles in the furnace, it is possible to identify all the phases that had formed. Therefore, the thermal conductivities can be estimated and, where needed, increased. All thermal conductivities reported in the literature assume water as a moisture control agent. However, this parameter is not required for magmas to be generated, and thus thermal conductivities for magmas have yet to be reported. However, a thermal conductivity of 0.0038 W/(m K) for oxide coatings has been reported in several literature sources, such as  and .
Solidification is the last phase in the casting process. The boundary conditions change during solidification and creep (due to constant weight of the ingot) during its growth. After solidification, the ingot is usually drilled or machined, thin surface regions (towards completion of casting) are discarded, and heat expansion has to be prevented at the end of the ingot run, by tapering off the ingot heating. At the beginning of the tapering operation, the ingot supports the weight of the newly formed material and does not contribute to the bulge of the die. The ingot narrows during tapering until a 1.5 cm diameter annulus is reached, below which the ingot is anchored to the die. This control of the melt cooling rate via narrow shaping is the difference between DC and HPDC. The required shape is determined by the geometry of interior cooling rods (for the top of the casting) and by heat conservation considerations for the exterior (bottom of the casting).
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