TABLE OF CONTENTS Jaber and Webb developed the equations necessary to apply the Effectiveness-NTU method to counterflow or crossflow cooling towers. The approach is useful in crossflow and simplifies the method of solution when compared to a more conventional numerical procedure.
Consider the equation for the enthalpy transfer in an evaporative process given by Equation 4.2.12, which may be written as
With the assumption of Merkel that the Lewis factor is equal to unity, Equation 4.4.1 reduces to
where ( i masw ?i ma) is the enthalpy driving potential used by the Effectiveness-NTU method in the case of evaporative cooling.
For the control volume shown in Figure 4.2.1, it follows from Equations 4.2.14 and 4.2.21 that
It is convenient to relate dQ to the slope of the saturated air enthalpy ( i masw) water temperature ( T w) curve. Equation 4.4.3 is written as
from which it follows that
It follows from Equation 4.4.3 that di ma = dQ/m a. Subtract this relation from Equation 4.4.5, and find
From Equations 4.4.6 and 4.4.2, it follows that
This equation, applicable in an evaporative system, will correspond to the heat exchanger design determined in Equation 3.5.4 if one defines the air capacity rate (cold fluid) as m a and the water capacity rate (hot fluid) as m w c pw/( di masw/ dT w).
The maximum theoretical amount of enthalpy that can be transferred, is Qmax...
