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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