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

The apparent heat capacity method is adopted in this study, since the temperature
field is the primary dependent variable that can be derived directly from the solution.
The apparent heat capacity assumes that the phase change occurs over a small
temperature interval rather than at a sharp melting temperature. However, in the
present study, all the three types of PCM packing media have a melting temperature
interval of 2°C around the specified melting points according to the manufacturer’s
data. Civan and Sliepcevich [18] have formulated the energy equation for a twophase
system of a pure substancea in a semi-infinite media undergoing phase
change, as depicted in figure (4.7), as follows:
h
h
h
2
T
2
hV h V
k
k
k
T
0
1
1
1
1
T
2
1
2
2
2
T
2
2
1
1
2
h h
1
1
1
2
2
d1
T
dT
t
Dp
Dt
(4.60)
The energy equation in the
form of equation (4.60) is
called an apparent heat
capacity formulation in which
the quantities enclosed in the
braces preceding T/t
represent an "apparent"
volumetric heat capacity.
Since the volumetric latent
heat effect of phase change,
(ρ 1 h 1 –ρ 2 h 2 ), is included in the
apparent volumetric heat
capacity definition, this
formulation allows for a
continuous treatment of a system involving phase transfer. In addition, it doesn’t
require the solution of separate, single-phase equations for each of the phases.
For simplification Civan and Sliepcevich [18] assumed that the pressure is
constant, the phases are isotropic and homogeneous, the phase densities are equal,
and there is no motion in either of the phases. Accordingly, equation (4.60) reduces
to:
in which
Figure 4.7: Schematic of a semi-infinite
domain undergoing phase change
T
T
c
k
(4.61)
t
x
x
90