3.4.1.2 Present approach

Heat balance at the liquid-solid interface yields

(3.21)

where is perpendicular to the surface and has to be taken at the solid phase see Appendix . Additionally, note that in many alloys the density change during the solidification is quite substantial which has a significant effect on the moving of the liquid/solid front. We notice that at the die interface and further assume that temperature gradient in the liquid side, , negligible compared to other fluxes. Hence, the speed of the solid/liquid front moves

(3.22)

The main resistance to the heat transfer from the die to the mold (cooling liquid) is in the die mold. Hence, the characteristic heat transfer from the mold is proportional to ¹⁵. The characteristic temperature difference is between the melting temperature and the boiling temperature. The time scale for the front can be estimated by

(3.23)

Note that the solidification time isn't a linear function of the die thickness, , but a function of ¹⁶.