Environmental Engineering Reference
In-Depth Information
constant for black radiation, and
T
S
is the absolute temperature of the Sun surface.
Formally, it can be assumed that the energy emission of surface 1 is
E
1
=
I
.
It is assumed that the surfaces 2 and 3 have uniform temperatures
T
2
and
T
3
,
respectively, uniform reflectivities, respectively,
ρ
2
and
ρ
3
, different from zero, and the
emissivities of the surfaces,
ε
2
=
1
−
ρ
2
and
ε
3
=
1
−
ρ
3
. Thus, the emissions of surfaces
2 and 3 are:
A
2
ε
2
σT
2
E
2
=
(2.4.33)
A
3
ε
3
σT
3
E
3
=
(2.4.34)
The geometric configuration of the SCPC can be described by the value
ϕ
i
−
j
of the
nine mutual view factors for the three surfaces 1, 2 and 3.
The considerations are carried out only for the 1 m section of the SCPC length
which remains in thermal equilibrium. The known input data are:
-
outer diameter
D
of cooking pot and its geometric location,
-
dimensions of the parabolic reflector,
-
surfaces areas
A
1
,
A
2
,
A
3
, and all view factors,
φ
i
−
j
,
-
heat transfer coefficients (including conductivity)
k
2
and
k
3
, for surfaces 2 and 3,
-
emissivities
ε
2
and
ε
3
of surfaces 2 and 3,
-
reflectivities
ρ
2
and
ρ
3
(defined by respective emissivities
ε
2
and
ε
3
),
-
absolute temperature of the Sun's surface
T
S
=
6000 K,
-
absolute water temperature
T
w
(average of the inlet and outlet temperatures),
-
absolute environment temperature
T
0
=
293 K.
The unknown output data are:
-
emissions
E
2
,
E
3
and irradiation
I
,(
I
=
E
1
),
-
convective heat
Q
2,
c
from reflector to environment,
-
radiative heat
Q
2,
r
from outer side of reflector to environment,
-
convective heat
Q
3,
c
from surface 3 to environment,
-
radiosity of the three surfaces
J
1
,
J
2
and
J
3
,
-
absolute temperatures
T
2
and
T
3
of surface 2 and 3,
-
energy efficiency of the SCPC, expressed by the water enthalpy change
Q
3,
u
,
-
all respective quantities related to exergy.
The
energy analysis
is based on the following energy conservation equations for
each involved surfaces:
=
+
+
+
+
+
J
1
ϕ
2
−
1
J
2
ϕ
3
−
1
J
3
Q
2,
c
Q
2,
r
Q
3,
c
Q
3,
u
(2.4.35)
ε
2
(
ϕ
1
−
2
J
1
+
ϕ
2
−
2
J
2
+
ϕ
3
−
2
J
3
)
=
E
2
+
Q
2,
c
+
Q
2,
r
(2.4.36)
ε
3
(
ϕ
1
−
3
J
1
+
ϕ
2
−
3
J
2
+
ϕ
3
−
3
J
3
)
=
E
3
+
Q
3,
c
+
Q
3,
u
(2.4.37)
The magnitudes
J
1
,
J
2
and
J
3
are the radiosity values for surfaces 1, 2 and 3, respec-
tively, and the values of
ϕ
i
−
j
are the respective view factors. The radiosity expresses the
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