Chapter 4, Problem 109EP

A hot dog can be considered to be a cylinder 5 in long and 0.8 in in diameter whose properties $p=61.2{\text{ lbm/ft}}^{\text{3}}\text{, cp = 0}\text{.93 Btu/lbm}{\text{. }}^{\text{o}}\text{F, k = 0}\text{.44 Btu/h}\text{.ft}{\text{. }}^{\text{o}}\text{F and }\alpha \text{ = 0}\text{.0077 }\times {\text{ 10}}^{\text{-6}}{\text{ ft}}^{\text{2}}\text{/h}$. A hot dog initially at 40°F is dropped into boiling water at 212°F. If the heat transfer coeflicient at the surface of the hot dog is estimated to be 120 Btu/h.ft² .°F, determine the center temperature of the hot dog after 5, 10, and 15 mm by treating the hot dog as (a) a finite cylinder and (b) an infinitely long cylinder. Solve this problem using the analytical one-term approximation method.