One house owner with a pond on his property has decided to use the pond water to cool his house. His idea is to flow air through a thin smooth 10-cm-diameter copper tube that could be submerged into the pond. The water in the pond, at few meters below the surface is typically maintained at a constant temperature of 15°C. If he assumes the air (~1 atm) entering 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 that would be needed so that the outlet mean temperature of the air is 20°C. You may consider the convection heat transfer coefficient of 1000 W/m2·K on the outer surface of the copper tube, between the pond water and copper tube. Since the copper tube is thin, the conduction resistance of the tube wall may be neglected.

One house owner with a pond on his property has decided to use the pond water to cool his house. His idea is to flow air through a thin smooth 10-cm-diameter copper tube that could be submerged into the pond. The water in the pond, at few meters below the surface is typically maintained at a constant temperature of 15°C. If he assumes the air (~1 atm) entering 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 that would be needed so that the outlet mean temperature of the air is 20°C. You may consider the convection heat transfer coefficient of 1000 W/m2·K on the outer surface of the copper tube, between the pond water and copper tube. Since the copper tube is thin, the conduction resistance of the tube wall may be neglected.