Page 219 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

7.2 Cooling tower 217

where
dQ ¼ Heat transferred by convection and evaporation for cooling of water in volume dV per unit
plan area
K ¼ Equivalent heat transfer coefficient.
3
2
a ¼ Area of contact (m /m ) between air and water.
The contact area ‘a’ cannot be determined, and this is combined with K as Ka which refers to the
unit volume of the fill.
The transfer of heat dQ to air is equal to the loss of sensible heat by water. Mathematically,
dQ ¼ LC p dT (7.14)
2
where L ¼ water flow rate per unit area of the tower (kg/m hr)
C p ¼ specific heat (kJ/kg C)

3
2

dT ¼ differential change in temperature ( C) across the volume (dV,m /m of plan area)

Equating Eq. 7.13 and 7.14 for C p ¼ 1 kJ/kg C
0
LdT ¼ Kaðh hÞdV (7.15)
The integrated form of the thermal balance equation is -
KaV Z T h dT
¼ (7.16)
L h h
0
T c
where
3
2
V ¼ active fill volume/plan area (m /m ) and KaV ¼ tower characteristic
L
The equation assumes L and G to be constant, but due to evaporation, this is not true in practice;
however, at normal temperature levels, the error from this assumption is not significant.
A standard psychrometric chart is shown in Fig. 7.6. Based on the data from the psychrometric
chart, the cooling tower thermal balance plot (Fig. 7.7) is drawn with temperature as abscissa and
enthalpy per unit mass of dry air as ordinate. The plot in Fig. 7.7 is based on data of the Design
Illustration in Section 7.3. Line CD is the air operating line obtained from the thermal balance of heat
2
lost by the cooling water (L) and the same picked up by air (G, kg/hr m ) in counterflow. This line has a
slope of ðL=GÞ and the coordinate of point C is ðT c ; h c Þ. For a known ðL=GÞ ratio, point D can be
located as ½T h ; h c þðL=GÞRŠ. Assuming that the thin film of air surrounding the water droplets is
always saturated, line AB is the saturated air enthalpy (h) versus air temperature plot, which is the
same as the 100% RH curve on a humidity (psychometric) chart. One may note that the driving force at
any cross-section through the fill is the vertical distance between the two lines (BA and CD), which is
the difference between the total heat of air bulk and air film against temperature. The integral in the
right-hand side of Eq. 7.16 can be numerically evaluated from the graph.
In a design problem, the ambient wet-bulb temperature (T amb;WBT ) is known and h c is the saturated
air enthalpy corresponding to T amb;WBT . Cooling of water continues as long as the operating line re-
mains below the line of saturated air.