A slab of pure aluminum is 2 cm thick, 1 m wide, and 1 m tall. It is initially at a temperature of 500oC. What is the temperature of the slab after 3 minutes for the following cases?
a. If the slab is exposed to air at 20oC flowing on both sides with h = 150 W/m2·K. (Neglect radiation).
b. If the slab is exposed to air at 20oC flowing on both sides with h = 150 W/m2·K, but one side(1 m x 1 m) is covered by a sheet of plastic that is 1 cm thick with kplas = 0.5 W/m·K. I. e. air flows on one surface of the metal and one surface of the plastic. (Neglect radiation).
c. If the slab (only metal) is in a vacuum chamber with walls that are held at a temperature of 100oC. Consider the slab to have a thin coating of oxidation that results in an emissivity of 0.8.
d. If the slab (only metal) is exposed to air at 20oC flowing on both sides with h = 150 W/m2·K but there is an electric current of 300 A flowing through the plate, with a voltage of 150 V across the plate. (Neglect radiation)
Also, determine the Biot number for the slab in each case and explain any complexity in calculating it.