(Answered) Spheres of 40-mm diameter heated to a uniform temperature

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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?

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