Chapter 7, Problem 7.140P

The thermal pollution problem is associated with discharging warm water from an electrical power plant or from an industrial source to a natural body of water. Methods for alleviating this problem involve cooling the warm water before allowing the discharge to occur. Two such methods, involving wet cooling towers or spray ponds, rely on heat transfer from the warm water in droplet form to the surrounding atmosphere. To develop an understanding of the mechanisms that contribute to this cooling, consider a spherical droplet of diameter D and temperature T, which is moving at a velocity V relative to air at a temperature $T_{\infty }$ and relative humidity ${\varphi }_{\infty }.$ The surroundings are characterized by the temperature $T_{\text{sur}}.$ Develop expressions for the droplet evaporation and cooling rates. Calculate the evaporation rate (kg/s) and cooling rate (K/s) when $D=3\text{mm,}V=7\text{m/s,}T=40°\text{C,}{T}_{\infty }=25°\text{C,}{T}_{\text{sur}}=15°\text{C,}$ and ${\varphi }_{\infty }=\mathrm{0.60.}$ The emissivity of water is ${\epsilon }_w=\mathrm{0.96.}$