Chapter 4, Problem 80EP

Oranges of 2.5-in-diameter $\text{(k = 0}\text{.26 Btu/h}\text{.ft}{\text{. }}^{\text{o}}\text{F and }\alpha \text{ = 1}\text{.4 }\times {\text{ 10}}^{\text{-6}}{\text{ ft}}^{\text{2}}\text{/s)}$ and initially at a uniform temperature of 78°F are to be cooled by refrigerated air at 25°F flowing at a velocity of 1 ft/s. The average heat transfer coefficient between the oranges and the air is experimentally determined to be 4.6 Btu/h.ft² °F. Determine how long it will take for the center temperature of the oranges to drop to 40°F. Also, determine if any part of the oranges will freeze during this process. Solve this problem using the analytical one-term approximation method.