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/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 T_o = 300K and a convection coefficient h_o= 200 W/m²-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