Casting of a plate is made in a metal mould where heat transfer is controlled at the mould- metal interface. ignore the superheat of the liquid metal and treat the problem as solidification in an infinite plate of a thickness b. derive the mathematical expression for solidification time (t of the casting, given the melting temperature of the cast metal (tm). initial mould temperature (to). heat transfer coefficient (h) at cast-mould interface, density of the cast metal (ps). latent heat of the cast metal (h) are all known.