Evaluate the rate of heat loss per meter from pressurized water flowing at 200°C through a 10-cm-ID pipe at a velocity of 3 m/s. The pipe is covered with a 5-cm-thick layer of 85% magnesia wool which has an emissivity of 0.5. Heat is transferred to the surroundings at 20°C by natural convection and radiation. Draw the thermal circuit and state all assumptions.
GIVEN
? Pressurized water flowing through an insulated pipe
? Water temperature (Tw) = 200°C = 493 K
? Pipe inside diameter (Di) = 10 cm = 0.1 m
? Water velocity (V) = 3 m/s
? Magnesia wool insulation thickness (t) = 5 cm = 0.05 m
? Emissivity of the wool insulation (?) = 0.5
? Temperature of the surroundings (T?) = 20°C = 293 K
FIND
? The rate of heat loss per meter (q/L)
ASSUMPTIONS
? Steady state
? Pipe surface temperature can be considered constant and uniform
? Surroundings behave as a black body
? Pipe is horizontal
? Thermal resistance of the pipe is negligible
? Ambient air is still
? Pipe thickness is negligible
? Fully developed flow
SKETCH
Heat transfer coefficient on the water side:
The Reynolds number of the water flow is
Applying Equation
Heat transfer coefficient on the air side:
The natural convection heat transfer coefficient on the outside of the insulation is a function of the exterior temperature of the insulation (TI). For a first iteration, let TI = T? + 20° = 40°C. Evaluating the air properties from Appendix 2, Table 28, at the film temperature of 30°C
The Grashof number is
Applying Equation (8.20)
The insulation temperature (TI) can be determined by equating the heat transfer between Tw and TI to that from TI to T?
Checking the units then eliminating them for clarity
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