Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W 1m:!. . K on the sphere surfaces, the thermo physical properties of the sphere material are p = 3000 kg/m3, c = 850 J/kg ∙ K, and k = 15 W/m ∙ K.

(a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed?

(b) The spheres are then placed in a packing carton that prevents further heat transfer to the environment. What uniform temperature will the spheres eventually reach?