Calculate the rate of heat transfer between a 15-cm-OD pipe at 120°C and a 10-cm-OD pipe at 40°C. The two pipes are 330-m-long and are buried in sand [k = 0.33 W/(m K)] 12 m below the surface (Ts = 25°C). The pipes are parallel and are separated by 23 cm (center to center) distance.
GIVEN
Two parallel pipes buried in sand
Pipe 1
Outside diameter (D1) = 15 cm = 0.15 m
Temperature (T1) = 120°C
Pipe 2
Outside diameter (D2) = 10 cm = 0.1 m
Temperature (T2) = 40°C
Length of pipes (L) = 330 m
Thermal conductivity of the sand (k) = 0.33 W/(m K)
Depth below surface (d) = 1.2 m
Surface temperature (Ts) = 25°C
Center to center distance between pipes (s) = 23 cm = 0.23 m
FIND
The rate of heat transfer between the pipes (q)
ASSUMPTIONS
The thermal conductivity of the sand is uniform
Two dimensional, steady state heat transfer
For the pipe-to-pipe heat transfer, the surface is not important since Z >> D. The shape factor for this
geometry,
The rate of heat transfer per unit length is
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