3.4.1.1 Miller's approach

Following Eckert's work, Miller and his student [#!poro:millerTrush!#] altered the calculations¹²and based the assumption that the conduction heat transfer characteristic time in die (liquid metal in solid phase) is the same order magnitude as the solidification time. This assumption leads them to conclude that the main resistance to the solidification is in the interface between the die and mold ¹³. Hence they conclude that the solidified front moves according to the following

(3.19)

Where here is the innovative heat transfer coefficient between solid and solid ¹⁴ and is front velocity. Then the filling time is given by the equation

(3.20)

where designates the half die thickness. As a corollary conclusion one can arrived from this construction is that the filling time is linearly proportional to the die thickness since is essentially constant (according to Miller). This interesting conclusion contradicts all the previous research about solidification problem (also known as the Stefan problem). The author not aware of any solidification problem to show similar results. Of course, Miller has all the experimental evidence to back it up.