Page 135 - Industrial Ventilation Design Guidebook

4.2 STATE VALUES OF HUMID AIR; MOLLIER DIAGRAMS AND THEIR APPLICATIONS 97

FIGURE 4.18 Water drop cooling in the air flow. Point (I) represents the air state surrounding the
water drop (2).

water will not cool further even though there is still water vaporization from the
drop surface. This is due to the fact that the temperature difference between the
air dry bulb temperature and drop surface is so large that the energy needed for
vaporization comes convectively from the air. This is illustrated in Fig. 4.18.
If the air dewpoint is higher than the water temperature (or more accu-
rately, the surface temperature of the drops), water vapor condenses from the
air on the surface of the water drops. Now the water warms up and the air
cools down and at the same time dries up; in other words, the cooling tower
recovers heat from the outlet air. We will now consider the operation of a
cooling tower more closely with the notations of Fig. 4.19.
The energy balance for a distance dL is

From Eqs. (4.112), (4.113), and (4.121), we have, when Le = 1, for vaporization
rify, = (a/Cp)(x'(O v) - x), and substituting this in the equation above, we get

FIGURE 4.19 Mathematical approach for a cooling tower.