Experimental and Numerical Analysis of a PCM-Supported ...

Appendix D
D1. Cooling tower theory and performance
D.1.1 Merkel’s equation
The practical theory of cooling towers operation was, perhaps, first developed by
Merkel [3]. This theory has been presented and discussed in detail throughout
numerous heat and mass transfer textbooks as the basis of most cooling tower
analysis and design rating. Excessively large number of scientific research and
publications cover the theoretical and experimental analysis of wet cooling towers
over its long history which has led to a common understanding and technical
maturity. Baker [53] presented a complete review on the technical papers dealing
with cooling tower and assessed different suggestions of coupling heat and mass
transfer in a single driving force.
Merkel’s theory has lumped both sensible and
latent heat transfer due to interface-bulk
temperature and humidity differences in a
single driving force for total heat transfer and
equivalent single transfer coefficient. This
driving force is the difference between the
enthalpy of the saturated air at the interface
and the enthalpy of the bulk humid air.
Considering a small element of the packing
region in counter flow as illustrated in figure
D.1, the heat transfer rate from water to air
can be expressed as [56]:
dQ lg
q lg
aedV
(D.1)
Figure D.1: Counter flow
through an element of the
packing region [5]
where a e is the specific (per unit volume) water-air interfacial area, dV is the element
volume, and q lg
is the heat flux at the interface, given by:
where
qlg h g ,int
h g
(D.2)
h g,int = the specific enthalpy of moist gas at the interface
h g = the specific enthalpy of the local bulk moist air
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