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

l
l
l
c c v k h aT
T
(4.8)
l
l
l
T
t
l
l
l
l
T
z
l
l
2
T
2
z
ls,
eff
In equations (4.7) and (4.8), subscripts s, l are standing for solid, and liquid
respectively, while v denotes the interstitial flow velocity and a is the total specific
surface area per unit volume of the packed column. The symbol ε s , and ε l denote the
solid fraction and the liquid holdup in the bed respectively where the total porosity in
the bed is ε = ε l =1- ε s .
In the above heat balance equation of the liquid phase (i.e. equation (4.8)), the first
term on the left hand side represents the accumulation of energy in the fluid, and the
second term represents the energy carried away by the fluid. On the right hand side,
the first term represents the energy gain by conduction through the fluid, while the
second term stands for the energy transfer with the solid phase. Similarly, for the
heat balance of solid phase, the first term on the left hand side accounts for heat
accumulation. On the right hand side, the first term accounts for heat gain by
conduction through and between solid particles, and the second term accounts for
heat gain from the fluid phase.
Generally, all PCM have low thermal conductivity (k). Paraffin waxes have thermal
conductivity of the order of 0.2 W/m.K while hydrated salts have higher thermal
conductivity but still relatively lower than 1.0 W/m.K. If the packing used are large
spheres, the overall heat and mass transfer coefficients will be low due to the high
internal thermal resistance in the PCM spheres (r/k). The thermal conduction
resistance inside the PCM beads is included implicitly by introducing the Jefferson
degradation factor [14] in the fluid-solid heat transfer coefficients in a onedimensional
CS model [section 4.3.3.5]. The effective heat transfer coefficients
between gas/liquid and the PCM beads are then given by:
hfs, eff
hfs
/(1.0 0.2Bi)
(4.9)
where Bi hfsdball
/( 6ks)
is the Biot number and the term 1/(1 0.2Bi)
represents the
Jefferson degradation factor. This effect of temperature gradient inside the particles
has to be considered in all the system components due to the relatively large size
and low thermal conductivity of the PCM beads. In this analysis a readily
encapsulated commercial PCM candidates were used as a packing media in the
evaporator, condenser, and the external thermal buffer. Table (A1) in the Appendix
presents the thermo-physical properties of the selected PCM candidates.
Pressure drop: It has been shown by Dullien [51] that the pressure drop in a porous
bed can be calculated as a function of the flow rate by using the Ergun’s equation
[52], when the flow rate is outside the range of validity of Darcy’s law (i.e. Re > 10).
The Ergun equation, which is based on the particle's model, is suitable to calculate
l
s
70