Page 83 - Defrosting for Air Source Heat Pump

Modeling study on uneven defrosting 75

4.2.1.1 Assumptions and calculation conditions

The two semiempirical models were developed based on the fundamentals of energy
and mass conservation and heat and mass transfer within each of the control volumes
at each stage of the defrosting process, and also using some of the experimental data
obtained in experimental studies previously reported. When establishing the two
models, the following was assumed:
i. The convective heat transfer between the frost and ambient air in the first two stages was
neglected. Therefore, the mass loss of frost due to sublimation during these two stages was
neglected.
ii. The thermal conductivities of the tubes and fins were much higher than those of the frost
and retained water, and hence their heat transfer resistances were neglected.
iii. The mass flow rate of refrigerant was evenly distributed into the three refrigerant circuits
during defrosting, and the frost was assumed to be uniformly accumulated over the coil
surface before starting defrosting. It is not the frost evenly accumulated on the surface of
circuit, but the total frost accumulations on different circuits’ surface are assumed to be
the same.
iv. The movement of the melted frost layer was considered to be a flowing boundary. Because
the velocity of the water flow was very small as observed during experiments, the melted
frost layer flowed in a laminar regime.
v. During the third stage, the retained water in each control volume was in a dynamic
equilibrium, i.e., the difference between the mass of the water entering into a control vol-
ume and that flowing away from the control volume was equal to the rate of frost melting
within the control volume.
vi. During defrosting, the melted frost infiltrated into the porous structure of the frost. The
contact area between the frost and the melted frost would increase as water flowed down-
ward, suggesting that the flow resistance was increased downward along the surface of the
outdoor coil. Therefore, the velocity of the water layer in each control volume was
decreased from top to bottom.
vii. There would be a thin water film between the frost and the surface of the fin, which is
shaped like a wedge. The upper end is thin while the lower is thick. But in this section,
it was assumed as a rectangle, so the water film surface contacting with frost is also par-
allel to the fin surface. And thus, the thermal conductivities between the fin and the water
layer and between the water layer and the frost are the same for the whole water film.
viii. During defrosting, there was no frost chip or debris flowing into a down circuit or a water-
collecting tray.
ix. During defrosting, the mass of melted frost left on the water-collecting trays or vaporized
from the water-collecting trays and cylinders was neglected.
x. In the process of the melted frost falling into a down-circuit or a water-collecting tray, the
heat dissipated from the melted frost to the ambient air was negligible because the falling
distance was small.
Furthermore, the following experimental data previously obtained were also used in
assisting the development of the two semiempirical models:
(a) The total mass of the frost was experimentally obtained at 1050 g, thus following Assump-
tion (iii), the mass of frost formed on the surface of each circuit, M f, j (j ¼ 1 3) , was 1050 /
3 g, or 350 g.