Question

Liquid, pumped through the inside of the pipe, is at a
temperature T_{i} = 400K and provides a convection
coefficient h_{i} = 450 W/m^{2}-K at the inner
surface of the pipe. The inside and outside radii of the pipe are
r1 = 0.25 m, r2 = 0.31 m. The thermal conductivity of the pipe is
240 W/m-K. The outside radius of the insulation, r3 = 0.35 m. The
thermal conductivity of the insulation is 20 W/m-K. The outside
surface is exposed to T_{o} = 300K and a convection
coefficient h_{o}= 200 W/m^{2}-K. Assume one
dimensional conduction with a pipe length L = 1m.

- Provide your sketch and state your assumptions (1 point)
- Sketch (clearly and neatly) the thermal resistance circuit of
the system from T
_{i}to T_{o}with new (not cracked) insulation and express all resistances in terms of the relevant variables (1 point) - Calculate all the resistance values with new (not cracked) insulation (0.5 point)
- Calculate the heat transfer, q between the fluid and the ambient air and provide the units with new (not cracked) insulation (0.5 point)
- Calculate the heat transfer, q between the fluid and the ambient air with no insulation at all. In this case, r3 does not exist (0.5 point)
- An engineer suggested to assume that 50% of the pipe is insulated due to the cracks. Using your results, estimate the heat transfer, q between the fluid and the ambient air with the cracked insulation. (0.5 point)
- Please write the following statement by hand: I have completed this work individually. I did not help anyone and did not receive help from anyone while doing this work. (4 points will be deducted if this statement is not provided)

Answer #1

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