A large cast iron container (k=52W/mK and =1.70 10 5 m 2 /s) with 4-cm-thick walls is

Question:

A large cast iron container (k = 52 W/m⋅K and α = 1.70 ×  10⁻⁵ m²/s) with 4-cm-thick walls is initially at a uniform temperature of 0°C and is filled with ice at 0°C. Now the outer surfaces of the container are exposed to hot water at 55°C with a very large heat transfer coefficient. Determine how long it will be before the ice inside the container starts melting. Also, taking the heat transfer coefficient on the inner surface of the container to be 250 W/m²⋅K, determine the rate of heat transfer to the ice through a 1.2-m-wide and 2-m-high section of the wall when steady operating conditions are reached. Assume the ice starts melting when its inner surface temperature rises to 0.1°C.