To cool a summer home without using a vapor-compression refrigeration cycle, air is routed through a plastic pipe (k = 0.15 W/m ∙ K, Di = 0.15 m, Do = 0.17 m) that is submerged in an adjoining body of water. The water temperature is nominally at T∞ = 17°C, and a convection coefficient of ho ≈ 1500 W/m2 ∙ K is maintained at the outer surface of the pipe.

If air from the home enters the pipe at a temperature of Tm.i = 29°C and a volumetric flow rate of Vi = 0.025 m3/s, what pipe length L is needed to provide a discharge temperature of Tm,o = 21°C? What is the fan power required to move the air through this length of pipe if its inner surface is smooth?

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Air Tmo Plastic pipe k, Di, D. Water, T