Discuss the following:
Q: A 30-cm-OD pipe with a surface temperature of 90°C carries steam over a distance of 100 m. The pipe is buried with its center line at a depth of 1 m, the ground surface is - 6°C, and the mean thermal conductivity of the soil is 0.7 W/(m K). Calculate the heat loss per day, and the cost, if steam heat is worth $3.00 per 106 kJ. Also, estimate the thickness of 85% magnesia insulation necessary to achieve the same insulation as provided by the soil with a total heat transfer coefficient of 23 W/(m2 K) on the outside of the pipe.
GIVEN
A buried steam pipe
Outside diameter of the pipe (D) = 30 cm = 0.3 m
Surface temperature (Ts) = 90°C
Length of pipe (L) = 100 m
Depth of its center line (Z) = 1 m
The ground surface temperature (Tg) = -6°C
The mean thermal conductivity of the soil (k) = 0.7 W/(m K)
Steam heat is worth $3.00 per 106 kJ
The heat transfer coefficient (hc) = 23 W/(m2 K) for the insulated pipe
ASSUMPTIONS
Steady state conditions
Uniform thermal conductivity
Two dimensional heat transfer from thepipe
