A sphere (k = 185 W/m K, = 7.25 x 105 m2/s) of 30-mm diameter

A sphere (k = 185 W/m ∙ K, α = 7.25 x 10–5 m2/s) of 30-mm diameter whose surface is diffuse and gray with an emissivity of 0.8 is placed in a large oven whose walls are of uniform temperature at 600 K. The temperature of the air in the oven is 400 K, and the convection heat transfer coefficient between the sphere and the oven air is 15 W/m2 ∙ K.

(a) Determine the net heat transfer to the sphere when its temperature is 300 K.

(b) What will be the steady-state temperature of the sphere?

(c) How long will it take for the sphere, initially at 300 K. to come within 20 K of the steady-state temperature?

(d) For emissivities of 0.2, 0.4, and 0.8, plot the elapsed time of part (c) as a function of the convection coefficient for 10 < h < 25 W/m2 ∙ K.