The pipe that supplies drinking water to a community in a cold region of the planet is buried a depth of 3m from the ground surface (measured at the centerline of the tube). The outer surface of the pipe can be modeled as an isothermal cylinder of diameter D=0.5m and temperature T=4 C. The temperature of the ground surface is T= 0 C and its thermal conductivity is k = 1 W/m-K. Determine The heat loss from the pipe.

During A harsh winter, the ground surface is frozen to a depth of 1 m. This new position of the freezing front can be modeled as an isothermal plane temperature of T = 0 ° C located at 2m above the centerline of the pipe. Determine the heat transfer loss and how much it increases due to the advancing freezing front.