Page 85 - Defrosting for Air Source Heat Pump

Modeling study on uneven defrosting 77

Also in Eq. (4.4), h w , the average coefficient of convective heat transfer caused by
water flow inside a control volume, was evaluated by:

ð j +1ÞH
ð
ð
h w ¼ h w,x dx=Hj ¼ 1 3Þ (4.5)
jH

where the convective heat transfer coefficient due to water flow downward was eval-
uated by [22]:

λ 1 1
2
h w,x ¼ 0:332 Re x Pr 3 (4.6)
x
To evaluate h w, x , it was necessary to evaluate the velocity of the water layer in each
control volume, which, based on Assumption (vi), would decrease from top to bottom
within a circuit, and could be estimated by [24]:

H j 1
v j ¼ 0:85 ð j ¼ 1 3Þ (4.7)
t d,1

where t d,1 is the defrosting duration in Circuit 1, and an experimentally obtained value
168 s was used for t d,1 . H is the height of a refrigerant circuit.
Furthermore, q Me is the energy used to heat the metal of the outdoor coil and can be
evaluated by [25]:

ΔT Me
q Me ¼ c PMe m Cu + m Al Þ (4.8)
ð
Δt
where ΔT Me is the average temperature difference of the outdoor coil metal and was
evaluated by [25]:
(4.9)
ΔT Me ¼ T t T 0
1
T 0 ¼ ð T in,0 + T e,0 Þ (4.10)
2
1
T t ¼ ð T in,t + T e,t Þ (4.11)
2

where T 0 and T t are the average temperatures of the outdoor coil metal at the start and
end of a defrosting process, and T in and T e are the inlet and outlet tube surface tem-
peratures of the outdoor coil, respectively. In Eq. (4.8), c PMe is the average specific
heat of metal (copper and aluminum) and can be evaluated by:

m Cu c Cu + m Al c Al
c PMe ¼ (4.12)
m Cu + m Al