Chapter 7, Problem 7.148P

Consider an air-conditioning system composed of a bank of tubes arranged normal to air flowing in a duct at a mass rate of ${\stackrel{.}{m}}_a\left(\text{kg/s}\right).$ A coolant flowing through the tubes is able to maintain the surface temperature of the tubes at a constant value of $T_s<T_{a,i},$ where $T_{a,i}$ is the inlet air temperature (upstream of the tube bank). It has been suggested that air cooling may be enhanced if a thin, uniform film of water is maintained on the outer surface of each of the tubes.

1. Assuming the water film to be at the temperature $T_s,$ develop an expression for the ratio of the amount of cooling that occurs with the water film to the amount of cooling that occurs without the film. The amount of cooling may be defined as $T_{a,i}-T_{a,o},$ where $T_{a,o}$ is the outlet air temperature (downstream of the tube bank). The upstream air may be assumed to be dry, and the driving potentials for convection heat and mass transfer may be approximated as $\left(T_{a,i}-T_s\right)$ and ${\rho }_{A,sat}=\left(T_s\right),$ respectively. Note: The total rate of heat loss from the air may be expressed as $q={\stackrel{.}{m}}_a{c}_{p,a}\left(T_{a,i}-T_{a,o}\right).$ Estimate the value of this ratio under conditions for which $T_{a,i}=35°\text{C}$ and $T_s=10°\text{C}\text{.}$
2. Consider a tube bank that is 5 rows deep, with 12 tubes in a row. Each tube is 0.5m long. with an outside diameter of 8 mm, and a staggered arrangement is used for which $S_T=S_L=24\text{mm}\text{.}$ Under conditions for which ${\stackrel{.}{m}}_a=0.5\text{kg/s,}V=3\text{m/s,}{T}_{a,i}=35°\text{C,}$ and $T_s=10°\text{C,}$ what is the value of $T_{a,o}$ if the tubes are wetted? What is the specific humidity of the air leaving the tube bank?