A transient analysis is very important in the casting industry. In Figure 2.13, a simplified casting arrangement is shown (without a runner or raiser). The molten metal is poured into the mould and the metal loses heat to the mould and solidifies. It is often possible to have a small air gap between the metal and the mould. The figure shows an idealized system that has a uniform gap all around the metal. Assume that heat is transferred from the metal to the mould via radiation and conduction. Then heat is conducted through the mould and convected to the atmosphere. Stating all assumptions, derive a system of equations to carry out a transient analysis.
