Environmental Engineering Reference
In-Depth Information
Table 4.4.2
Details of the configuration, operating conditions
and thermal properties of the thermosyphon solar-
energy water-heater used in the sample calculation.
System parameters
A
c
= 2.0
(m
2
)
F
av
=
0.9
(
τα
)
e
=
0.72
U
L
=
3.5
(Wm
−
2
K
−
1
)
(WK
−
1
)
(
UA
)
s
=
3
N
=
8
M
2
=
297
(kg)
h
3
=
1.8
(m)
h
2
=
1.7
(m)
L
r
=
1
(m)
D
r
=
0.015
(m)
L
p
=
8.72
(m)
D
p
=
0.025
H
td
=
19.2
(M J m
−
2
)
Weather conditions
T
a
=
16
(
◦
C)
T
m
=
15
(
◦
C)
t
=
59,220
(s)
Hot-water demand
M
L
=
208
(kg)
T
L
=
46
(
◦
C)
(kg m
−
3
)
Fluid properties
ρ
w
=
998
µ
w
=
10
−
3
(Ns m
−
2
)
v
w
=
1.00
×
10
−
6
(m
2
s)
( J kg
−
1
K
−
1
)
C
w
=
4190
β
w
=
2.1
×
10
−
4
(K
−
1
)
of the applied conditions, whereas the Bailey number, K, is a function essentially of the
system design. However, all these dimensionless groups include information available
readily to a designer who, using the nomgram, can thus determine the Brooks number
X, and thus the solar fractions.
A worked example of using the correlations to predict the daily solar fraction The
component specifications of a thermosyphon solar- energy water heater and climatic
conditions (for a typical day in June) used in the following example are given in Table
4.4.2. Evaluating the parameters K, W, I and Z gives K
=
12, W
=
0.7, Y
=
20, and
Z
0.3 respectively. Also, since the thermal performance is being determined for the
reference month of June,
Z
J
=
=
0.3. A three-stage algorithm is used to determine
the dimensionless Brooks number, X, from which the solar fraction can be calculated.
Stage I is to determine the deviation,
m
J
(due to circulation number effects) of the
characteristic gradient from the maximum value,
m
j
,max
.
m
∗
=
Z
=
0.051. This stage corresponds to the first quadrant of
the nomogram shown in Figure 4.3.4. Stage two is to determine the maximum gradient,
m
J
,
max
for the system and subtract the gradient displacement,
m
, to give the actual
gradient,
m
J
of the characteristic curve.
m
J
,
max
,
0.055, giving
m
j
=
=
0.673, the actual gradient,
m
J
,is
then given by
m
J
=
m
J
,max
−
(
m
J
)
=
0
.
622
(4.4.21)
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