Plastic spheres, 0.02 m in diameter and initially at 120°C, are cooled by allowing them to drop into a large pool of water at 20°C. The spheres have a density of 1050 kg/m³, a heat capacity of 900 J/kg K, and a thermal conductivity of 2.8 W/m K.

(a) Estimate as accurately as possible the convective heat transfer coefficient.

(b) Predict the distance that the spheres would have to fall to reach a temperature of 40°C if the external resistance is assumed to be dominant.

(c) Predict the distance that the spheres would have to fall to reach a center temperature of 40°C if the external resistance is neglected.

(d) Predict the distance that the spheres would have to fall to reach a center temperature of 40°C if both resistances are considered. (e)
For the conditions of part (d), determine the surface temperature of the spheres when the center temperature reaches 40°C.