Chapter 4, Problem 73P

Chickens with an average mass of 1.7 kg $\text{(k = 0}\text{.45 W/m}\text{.K, and }\alpha \text{ = 0}\text{.13 }\times {\text{ 10}}^{\text{-6}}{\text{ m}}^{\text{2}}\text{/s)}$ and initially at a uniform temperature of 15°C are to be chilled in agitated brine at -7°C. The average heat transfer coefficient between the chicken and the brine is determined experimentally to be 440 W/m² K. Taking the average density of the chicken to be 0.95 g/cm³ and treating the chicken as a spherical lump, determine the center and the surface temperatures of the chicken in 2 h and 45 mm. Also, determine if any part of the chicken will freeze during this process. Solve this problem using the analytical one-term approximation method.