A square slab of pure silicon to be used to manufacture microelectronics components is to be cooled in air at 25°C from an initial temperature of 200°C to 30°C. The slab is 0.5 m on a side and 5 mm thick and is hung vertically in calm air, suspended by thin metal wires. Neglect radiant heat transfer.

(a) Determine the time required to cool the slab to an average temperature of 30°C if the external heat transfer resistance is neglected.

(b) Determine the time required to cool the slab to 30°C if natural convection is considered.