Page 89 - Defrosting for Air Source Heat Pump

Modeling study on uneven defrosting 81

the retained water to the ambient air. The Nusselt number and the corresponding coef-
ficients of natural convective heat transfer were used [27]:

h c H 1 9 13
Nu L ¼ ¼ 0:13 GrPrÞ 3, for 10 < GrPr < 10 (4.25)
ð
λ a
where

ð
gβ T w T a Þ 3
Gr ¼ H (4.26)
ν 2
Furthermore, the heat transferred from the water layer to the frost layer for melting the
frost and to the ambient air was:

h w T w, j T tp A 0 ¼ L sf m f , j + h c,w T w, j T a A f a j ¼ 1 3ð Þ (4.27)

Third stage: Frost melting with water flowing away from a circuit Unlike in
Stages 1, 2, or 4, as shown in Fig. 4.2C, in this stage, there were differences for
the energy and mass flows in the three control volumes, as the melted frost started
to flow away from a circuit. For Circuit 1, no melted frost flowed into it as it was
at the highest level, but the melted frost in this circuit flowed down into Circuit 2.
For Circuit 2, the melted frost in this circuit flowed into Circuit 3. Finally, the melted
frost in Circuit 3 flowed into water-collecting Tray C and was collected by Cylinder C,
as shown in Fig. 4.1.
As shown in Fig. 4.2C1, energy conservation in Control Volume 1 (Circuit 1)
yielded:

dT w,1
q 1 ¼ L sf m f,1 + c p M w,max + c p m w,1 T w,1 + h c,w T w,1 T a ÞA f a + q Me
ð
dt
(4.28)
where M w, max is the maximum of the melted frost held on the surface of a refrigerant
circuit.
Mass conservation in this control volume was:

m w,1 ¼ m f,1 (4.29)

For the other two control volumes, as shown in Fig. 4.2C2 and C3, energy conserva-
tion yielded:

dT w, j
q j + c p m w, j 1 T w, j 1 ¼ L sf m f, j + c p M w,max + c p m w, j T w, j
dt

+ h c,w T w, j T a A f a + q Me j ¼ 2, 3Þ (4.30)
ð