A 15 cm-OD pipe is buried with its centerline 1.25 m below the surface of the ground [k of soil is 0.35 W/(m K)]. An oil having a density of 800 kg/m3 and a specific heat of 2.1 kJ/(kg K) flows in the pipe at 5.6 L/s. Assuming a ground surface temperature of 5°C and a pipe wall temperature of 95°C, estimate the length of pipe in which the oil temperature decreases by 5.5°C.
GIVEN
FIND
The length of pipe (L) in which the oil temperature decreases by 5.5°C
ASSUMPTIONS
Steady state condition
Two dimensional heat transfer
SKETCH
The rate of heat flow from the pipe can be calculated using the shape factor from for an infinitely
long cylinder
The rate of heat transfer per unit length is given
The total heat loss required to decrease the oil by 5.5°C is
We can estimate the length of pipe in which the oil temperature drops 10°F by assuming the rate of heat loss from the pipe per unit length is constant, then:
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