A large number of 3.8 cm OD pipes carrying hot and cold liquids are embedded in concrete in an equilateral staggered arrangement with center line 11.2 cm apart as shown in the sketch. If the pipes in rows A and C are at 16°C while the pipes in rows B and D are at 66°C, determine the rate of heat transfer per foot length from pipe X in row B.
GIVEN
A large number of pipes embedded in concrete as shown below
Outside diameter of pipes (D) = 3.8 cm
The temperature of the pipes in rows A and C = 16°C
The temperature of the pipes in rows B and D = 66°C
FIND
The rate of hat transfer per foot length from pipe X in row B
ASSUMPTIONS
Steady state, two dimensional heat transfer
Uniform thermal conductivity in the concrete
SKETCH
A flux diagram for this problem is shown below
By symmetry, the total heat transfer from the tube X is four times that shown in the flux diagram.
The number of heat flow lanes (M) = 8 ? 4 = 32
The number of curvilinear squares per lane (N) = 7
Therefore, the shape factor is
The heat transfer per unit lengt is
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