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

fixed temperature by a gradual change over a small temperature interval should be
acceptable if (2∆T t )/ (T i -T s ) < 0.1. Through the use of Equation (4.63), the transient
model is applicable anywhere in the storage medium. This model removes the
necessity of tracking the moving phase change boundary and generally simplifies
the numerical solution.
4.5 Macro-dynamic performance analysis of the HDH system
4.5.1 Cooling tower performance
In comparison with the two phase flow in the PCM-packed columns (i.e. the
evaporator and condenser), the energy balance for a conventional cooling tower
which is packed with nonconductive media doesn’t include the solid sub-domain.
Thus, this results in two energy balance equations for both liquid and gas phases
instead of three for the case of PCM packing. Though the cooling tower theory is
basically different from the developed mathematical modeling approach, it is indeed
useful for defining and identifying the crucial indicative parameters for addressing the
system performance. Since operation and design theory of evaporative coolers and
direct contact condensers is closely related, these parameters can serve both of
them. The practical theory of cooling towers operation was, perhaps, first developed
by Merkel [54]. 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. Appendix (D) covers the theoretical development and
analysis of Merkel’s equation, which is extremely important to develop a common
understanding of the performance measures in the subsequent discussions.
4.5.2 Humidifier efficiency
The performance of a humidification column can be evaluated by Braun's [58]
effectiveness model for a counter flow cooling tower. This model was based on
Merkel's assumptions which neglect the effect of the water loss due to evaporation
and set the Lewis number to unity. Braun defines air-side effectiveness, ζ a as the
ratio of the actual heat transfer to the maximum possible air-side heat transfer that
would occur if the exiting air stream were saturated at the temperature of the inlet
hot water (i.e., h a2 = h s,w2 with reference to figure (4.1) for the present study);
Qg,
actual
Q
evap
(4.69)
Qg,max
imum mg
h
g,
actual
s,
w2
hg1 evap
where h s,w2 is the saturated air enthalpy at inlet water conditions, and h a1 is the
enthalpy of the inlet air. Analogously to a dry counter flow heat exchanger, Braun
92