A spherical work piece of pure copper with a diameter of 15 mm and an emissivity of 0.5 is suspended in a large furnace with walls at a uniform temperature of 600°C. Air flows over the work piece at a temperature of 900°C and a velocity of 7.5 m/s.

(a) Determine the steady-state temperature of the work piece.

(b) Estimate the time required for the work piece to come within 5°C of the steady-state temperature if it is at an initial, uniform temperature of 25°C.

(c) In order to decrease the time to heat the work piece, the air velocity is doubled, with all other conditions remaining the same. Determine the steady-state temperature of the work piece and the time required for it to come within 5°C of this value. Plot on the same graph the work piece temperature histories for the two velocities.