It is proposed to heat process water (15C, 0.05 kg/s, 4184 J/kg-K) to 90C ing a hot gas (150C, 1000 J/kg-K) available at a rate of 0.25 kg/s. The heat exchanger ed is a one-shell pass and four-tube and in a counter-current operation. The water flows inside the tubes made of copper (ID - 2.5 cm, OD - 3.0 cm). The heat transfer coefficient at the gas side is 120 W/m2-K. A scale on the water side offers an additional thermal resistance of 0.005 m2-K/W.
a. Determine the overall heat transfer coefficient based on the outer tube diameter
b. Determine the appropriate mean temperature difference for the heat exchanger
c. Estimate the required tube length