Page 90 - Defrosting for Air Source Heat Pump

82 Defrosting for Air Source Heat Pump

Mass conservation was:

m w, j ¼ m f, j + m w, j 1 j ¼ 2, 3ð Þ (4.31)

Fourth stage: Water layer vaporizing In this stage, the surface of the outdoor coil
was free of frost, and the vaporization of the retained water took place. As illustrated in
Fig. 4.2D, energy conservation in Control Volume j yielded:

dM w, j T w, j
q j ¼ c p + h c,w T w, j T a A w a + h c,d T r, j T a A d a
dt
+ m v, j L v + q Me j ¼ 1 3Þ (4.32)
ð
where h c, w (T w, j T a )A w a is the heat transferred to low-temperature ambient air
from the water layer in Control Volume j, and h c, d (T r, j T a )A d a is the heat trans-
ferred to the ambient air from the high-temperature dry coil surface in Control
Volume j.
Mass conservation in Control Volume jwas:

ð t
M w, j ¼ M w,max m v, j dt j ¼ 1 3ð Þ (4.33)
0
where m v, j is the mass flow rate of the retained water vaporized from Circuit j and was
proportional to the difference in vapor pressure between the exposed water surface and
ambient air, as described by Mills [28], expressed as:

m v, j ¼ h D A w a ρ ρ ð j ¼ 1 3Þ (4.34)

vsj va
In Eqs. (4.32) and (4.34), A w a is the effective wetted airside surface area of a refrig-
erant circuit. As the vaporizing process went on, the area was diminishing. The rela-
tionship between the effective wetted airside surface area and the equivalent airside
surface area of a refrigerant circuit was [8,14]:

1:5
M w, j
A w a ¼ A 0 (4.35)
M w,max
Then, the effective dry airside surface area of a refrigerant circuit in this stage,A d a ,
was:

(4.36)
A d a ¼ A 0 A w a
Moreover, the coefficient of convective mass transfer, h D , was related to the coeffi-
cient of natural convective heat transfer, h c , according to the Lewis Analogy [29,30]: