Assumptions and simplifications
When the liquid is cooling it will have good thermal contact with the mould and hence the interfacial heat transfer coefficient will high. The actual value may vary significantly depending on the actual mould, but for simplicity we will use a constant value of 5000 W m-2 K-1. With such a high value, one must ask whether the assumption of Newtonian cooling will be valid (i.e. whether the temperature throughout the liquid will be uniform). We will assume that there is enough heat transfer through convection for this to be the case.
In reality the values of properties such as the heat capacity and thermal conductivity do vary somewhat with temperature. Values used in the simulation are those in the table which are valid in the temperature range of interest.
A fixed mould-wall temperature of 100 °C has been used. This will be a reasonable estimate for a metallic mould which is actively cooled (e.g. using water), though obviously the temperature of a sand-mould could increase quite significantly during solidification.