The pipe that supplies drinking water to a community in a cold region of the pla

Question

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

Explanation / Answer

heat loss from pipe = [2*3.14*k*L*(Ti - To)]/[ln(Ro/Ri)]

                            = [2*3.14*1*L*(277 - 273)]/[ln(1.5/1.25)]

   heat loss from pipe per unit length = 25.12/0.1823

                                                       = 137.778 W/m

new heat loss from pipe per unit length = [2*3.14*k*(Ti - To)]/[ln(Ro/Ri)]

                                                         = [2*3.14*1*(277 - 273)]/[ln(1/0.75)]

                                                         = 25.12/0.2877

                                                         = 87.319 W/m

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