Environmental Engineering Reference
In-Depth Information
Table 2.4.5
Results of the energy and exergy calculations of the solar cell.
Term
Related symbol
Energy %
Exergy %
INPUT:
solar radiation
e
S
,
b
S
100
100
Subtotal
100
100
OUTPUT:
reflection
(
ρ
C
)
5
5
convection
q
k
,
b
k
6.21
0.62
radiation
q
r
,
b
r
12.43
0.67
useful heat
q
c
,
b
c
,(
η
E,q
,
η
B,q
)
65.88
6.61
electricity
E,
(
η
E,el
,
η
B,el
)
10.48
11.16
irreversibility loss
δ
b
-
75.94
Subtotal
100
100
b
r
=
ρ
C
b
S
(vi)
q
k
1
T
0
T
C
b
k
=
−
(vii)
ε
C
σ
3
(3
T
C
+
T
0
−
4
T
0
T
C
)
b
0
=
(viii)
q
C
1
T
0
T
C
b
C
=
−
(ix)
The exergy loss
δb
can be calculated by completion of equation (2.4.112). From
the exergetic viewpoint the solar cell can be evaluated by: the exergy electric efficiency
η
B
,
el
=
E/b
s
, the exergy heating efficiency
η
B
,
q
=
b
c
/b
s
, or the exergy cogeneration
efficiency
η
B
,
cog
b
c
)
/b
s
.
As the solar radiation energy is always larger than the solar radiation exergy
(
q
S
> b
S
), and the electrical exergy and electrical energy are equal, thus the energy elec-
trical efficiency of the solar cell is always smaller than the exergy electrical efficiency,
(
η
B
,
el
>η
E
,
el
).
=
(
E
+
Example 2.4.5.1
A1m
2
surface of the photovoltaic cell at temperature
T
c
=
318 K,
emissivity
ε
C
=
0
.
95, (reflectivity
ρ
C
=
0
.
05), generates
E
=
152 W of electrical energy.
The temperature of the Sun is assumed
T
S
=
5800 K. The convective heat transfer
3 W/(m
2
K).
The results calculated with the formula of the present paragraph are shown in
Table 2.4.5. The values of the solar radiation energy and exergy:
e
S
=
coefficient
k
=
1386 W/m
2
and
1294 W/m
2
, were respectively assumed as the 100% in the energy and exergy
balances.
The instant energy electric efficiency
η
E
,
el
=
b
S
=
10
.
48% is smaller from the exergy
electric efficiency
η
B
,
el
=
11
.
16%, however the energy cogeneration efficiency
η
E
,
cog
=
10
.
48
+
65
.
88
=
76
.
36% is significantly larger than the exergy cogeneration efficiency
η
B
,
cog
=
17
.
77%. Table 2.4.5 illustrates also that the low temperature
heat (convection, radiation and useful heat) has small exergy value.
11
.
16
+
6
.
61
=
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