A transient analysis is very important in the casting industry. In Figure 2.11, a simplified casting arrangement is shown (without a runner or raiser). The molten metal is poured into the mold and the metal loses heat to the mold and solidifies. It is often possible to have a small air gap between the metal and mold. The figure shows an idealized system which has a uniform gap all around the metal. Assume that heat is transferred from the metal to the mold via radiation and conduction. Then heat is conducted through the mold and convected to the atmosphere. Stating all assumptions, derive a system of equations to carry out a transient analysis.

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Mold Metal Air gap