Chapter 4, Problem 149P

A watermelon initially at 35°C is to be cooled by dropping it into a lake at 15°C. After 4 h and 40 miii of cooling, the center temperature of the watermelon is titeasured to be 20°C. Treating the watermelon as a 20-cm-diameter sphere and using the properties $\text{k = 0}\text{.618 W/m}\text{.K, }\alpha \text{ = 0}\text{.15 }\times {\text{ 10}}^{\text{-6}}{\text{ m}}^{\text{2}}\text{/s, }p=995{\text{ kg/m}}^{\text{3}}\text{, and }{c}_p\text{ = 4}\text{.18 kJ/kg}\text{.K,}$ determine the average heat transfer coefficient and the surface temperature of the watermelon at the end of the cooling period. Solve this problem using the analytical one-term approximation method.