Question 2:

A 65-kg beef carcass (k = 0.5 W/m·K and α = 0.15 × 10−6 m2 /s) initially at a uniform temperature of 37°C is to be cooled by refrigerated air at −10°C flowing past it. The average heat transfer coefficient between the carcass and the air is 22 W/m2 ·K. Treating the carcass as a cylinder of diameter 24 cm and height 1.4 m and disregarding heat transfer from the base and top surfaces, determine how long it will take for the center temperature of the carcass to drop to 4°C. Also, determine if any part of the carcass will freeze during this process, i.e. if the temperature is below 0°C. Solve this problem using the analytical one-term approximation method. Show that the one term approximation method is valid in this case.

Show your working steps clearly.