Environmental Engineering Reference
In-Depth Information
there being a maximum collector temperature
(
T
c
)
max
at which no heat is collected:
T
a
+
β
I
U
(
T
c
)
max
=
(7.3)
The fraction of the incident irradiance that is collected,
q
/
I
, is called the collector efficiency
η
:
q
I
=
β
−
U(
T
c
−
T
a
)
η
≡
(7.4)
I
The collection efficiency
I
, and the
heat collection rate
q
decreases with increasing collector temperature. The maximum collector
efficiency is
η
is a linearly decreasing function of the ratio
U(
T
c
−
T
a
)/
when heat is collected at ambient temperature. The efficiency falls to zero when
the collector temperature reaches
β
T
c
)
max
. Either of these limits of operation has no practical value
because either no heat is collected or it is collected at ambient temperature, which has no useful
function. Practical collector systems will function at intermediate conditions where
(
η<β
and
T
c
<(
T
c
)
max
.
Flat plate collectors operate at lower efficiency in winter than in summer. When we use typical
collector values of
5 W/m
2
K, winter and summer clear-day noontime values
β
=
0
.
8 and
U
=
870 W/m
2
,
T
a
70
◦
F (21
◦
C),
I
910 W/m
2
, and
T
a
32
◦
F(0
◦
C), and a collector
of
I
=
=
=
=
140
◦
F (60
◦
C) suitable for domestic water heating, the corresponding winter
and summer collector efficiencies are
temperature of
T
c
=
6%. At other hours, where
I
is
less than these noontime values, the collector efficiencies will be less. This will also be the case
when the sky is cloudy. Year-round collector efficiencies are likely to be in the range of 30-50%.
Because of the vagaries of solar irradiance from day to day, a solar collector, no matter how big,
can never completely satisfy the demand for year-round heat for domestic hot water or space heating,
and a backup supply must be available for satisfactory operation. The relationship between annual
heat collection and collector area is sketched in Figure 7.8(a). A very small collector accumulates
only a small amount of heat, whereas an oversized one collects enough heat to meet the daily
demand on all but a few very cold, cloudy days, when auxiliary heat must be supplied. The capital
cost of a collector system is plotted in Figure 7.8(b), showing how the cost increases with collector
area, but is finite for small areas because the storage, piping, and control system needed constitute
η
w
=
45
.
5% and
η
s
=
58
.
Annual demand
Area
Area
(a)
(b)
Figure 7.8
The characteristics of solar heat collection systems as a function of collector area: (a) annual
heat collection and (b) capital cost.
