A shell and tube heat exchanger with one-tube pass and one-shell pass has been designed to cool a hot oil on the shell side from 70°C to 40°C using cooling water that on the tube side entering at 20°C and leaving at 40°C. The product  for the oil is 1,500 W/K. The heat exchanger has100 tubes made of a metal alloy with k = 5.0 W/m K, each 2.0 m long, 0.02 m in outer diameter, and 0.015 m in inner diameter. The tube-side convective heat transfer coefficient is = 1,000 W/m² K. An automatic control system keeps the outlet temperature of the oil at the desired 40°C by adjusting the flow rate of the cooling water. When the heat exchanger is first put in service, it works exactly according to the design specifications.

However, after a few months in service, an engineer notes that, while the oil is being cooled to the correct temperature, the outlet temperature of the cooling water has dropped to 35°C. Fouling is suspected as the culprit. (a)

Determine the heat exchanger duty, the cooling water flow rate, and the overall heat transfer coefficient for the clean heat exchanger.

(b) Determine the cooling water flow rate and the fouling coefficient for the fouled heat exchanger.

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