Chapter 8, Problem 8.31P

To cool a summer home without using a vapor compression refrigeration cycle, air is routed through a plastic pipe $\left(k=0.15W/m\cdot K,D_i=0.15m,D_o=0.17m\right)$ that is submerged in an adjoining body of water. The water temperature is nominally at $T_{\infty }=17°C$ , and a convection coefficient of $h_o\approx 1500W/m^2\cdot K$ is maintained at the outer surface of the pipe.

If air from the home enters the pipe at a temperature of $T_{m,i}=29°C$ and a volumetric flow rate of ${\stackrel{\dot{}}{\forall }}_i=0.025m^3/s$ , what pipe length L is needed to provide a discharge temperature of $T_{m,o}=21°C$ ? What is the fan power required to move the air through this length of pipe if is inner surface is smooth?