The plumbing system of a house involves a 0.5-m section of a plastic pipe (k=0.16 W/mK) of

Question:

The plumbing system of a house involves a 0.5-m section of a plastic pipe (k = 0.16 W/m⋅K) of inner diameter 2 cm and outer diameter 2.4 cm exposed to the ambient air. During a cold and windy night, the ambient air temperature remains at about − 5°C for 14 h. The combined convection and radiation heat transfer coefficient on the outer surface of the pipe is estimated to be 40 W/m²⋅K, and the heat of fusion of water is 333.7 kJ/kg. Assuming the pipe to contain stationary water initially at 0°C, determine if the water in that section of the pipe will completely freeze that night.