Determine the rate of heat transfer per unit length from a 5-cm-OD pipe at 150°C placed eccentrically within a larger cylinder of 85% Magnesia wool as shown in the sketch. The outside diameter of the larger cylinder is 15 cm and the surface temperature is 50°C.
GIVEN
A pipe placed eccentrically within a larger cylinder of 85% Magnesia wool as shown in the sketch
Outside diameter of the pipe (Dp) = 5 cm = 0.05 m
Temperature of the pipe (Ts) = 150°C
Outside diameter of the larger cylinder (Do) = 15 cm = 0.15 m
Temperature of outer pipe (To) = 50°C
FIND
The rate of heat transfer per meter length (q)
ASSUMPTIONS
Two dimensional heat flow (no end effects)
The system is in steady state
Uniform thermal conductivity
SKETCH
The rate of heat transfer can be estimated from a flux plot
The number of flow lanes (M) = 2 ? 15 = 30
The number of squares per lane (N) = 5
Therefore, the shape factor is
Equation (2.85) can be used to find the rate of heat transfer per unit length
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