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=0.15m, Do=0.17m) that is submerged in an adjoining body of water. The water temperature is nominally at T(infinity)=17 C and a convection coefficient of ho=1500W/m^2 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 volumetric flowrate of V=0.025 m^3/s, what pipe length L is needed to provide a discharge temperature of Tm,o= 21C?