Conduction time in the liquid metal (solid)

The governing heat equation in the solid phase of the liquid metal is the same as equation () with changing properties to liquid metal solid phase. The characteristic time for conduction is derived similarly as done previously by introducing the dimensional parameters

(3.17)

where is the characteristic time for conduction process and, , denotes the main path of the heat conduction process die cavity. With these definitions, similarly as was done before the characteristic time is given by

(3.18)

Note again that has to be taken for properties of the liquid metal in the solid phase. Also note that the solidified length, , changes during the process and discussing the case where whole die is solidified is not of the interest. Initially the thickness, (or very small). The characteristic time for very thin layers is very small, . As the solidified layer increases the characteristic time increase. However, the temperature profile is almost established (if other processes where to remain in the same conditions). Similar situation can be found in a semi infinite slab undergoes solidification with changes as well as results of increase in the resistance. For the forgoing reasons the characteristic time is very small.