Question

# Liquid, pumped through the inside of the pipe, is at a temperature Ti = 400K and...

Liquid, pumped through the inside of the pipe, is at a temperature Ti = 400K and provides a convection coefficient hi = 450 W/m2-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 To = 300K and a convection coefficient ho= 200 W/m2-K. Assume one dimensional conduction with a pipe length L = 1m.

• Sketch (clearly and neatly) the thermal resistance circuit of the system from Ti to To 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)

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