To cool a storehouse in the summer without using a conventional air-conditioning system, t...

To cool a storehouse in the summer without using a conventional air-conditioning system, the owner decided to hire an engineer to design an alternative system that would make use of the water in the nearby lake. The engineer decided to flow air through a thin smooth 10-cm-diameter copper tube that is submerged in the nearby lake. The water in the lake is typically maintained at a constant temperature of 15°C and a convection heat transfer coefficient of 1000 W/m²·K. If air (1 atm) enters the copper tube at a mean temperature of 30°C with an average velocity of 2.5 m/s, determine the necessary copper tube length so that the outlet mean temperature of the air is 20°C.