Environmental Engineering Reference
In-Depth Information
•
Non-participating gas in the annulus,
•
Long concentric isothermal cylinders, and
•
The glass envelope is opaque to infrared radiation.
These assumptions are not all completely accurate as the glass envelope wall is not
completely opaque for the entire thermal radiation spectrum and the glass envelope
wall and the selective coatings are not gray (Touloukian and DeWitt, 1972). However,
any errors associated with the assumptions are relatively small.
The radiation heat transfer between the receiver pipe and glass envelope (q
po-gi,rad
)
is estimated with the following equation, applied for infinitely long concentric cylinders
(Cengel, 2006):
D
po
(T
po
−
T
gi
)
σπ
q
po-gi,rad
=
1
ε
(1
(6.2.20)
− ε
gi
)D
po
po
+
ε
gi
D
gi
10
−
8
W/m
2
-K
4
);
where:
σ
=
Stefan-Boltzmann
constant
(
=
5.67
×
D
po
=
outside
receiver pipe diameter (m); D
gi
=
inside glass envelope diameter (m); T
po
=
outside
receiver pipe surface temperature (K); T
gi
=
inside glass envelope surface temperature
(K);
ε
po
=
receiver pipe selective coating emissivity; and
ε
gi
=
glass envelope emissivity.
6.2.4 Conduction heat transfer through the glass envelope
The anti-reflective treatment on the inside and outside surfaces of the glass envelope
is assumed not to introduce any thermal resistance or to have any effect on the glass
emissivity. This is reasonably accurate since the treatment is usually a chemical etching
which does not add any additional elements to the glass surface (Forristall, 2003).
The conduction heat transfer through the glass envelope uses the same equation as the
conduction through the receiver pipe wall described in Section 6.2.2. As in the receiver
case, the temperature distribution is assumed to be linear. Furthermore, the thermal
conductivity of the glass (k
glass
) is assumed constant - as explained in Section 6.2.1 -
with a value of 1.04, which corresponds to Pyrex glass (Touloukian and DeWitt, 1972).
In equation form this is given by:
2
π
k
glass
(T
gi
−
T
go
)
q
gi-go,cond
=
ln
D
go
D
gi
(6.2.21)
6.2.5 Heat transfer from the glass envelope to the atmosphere
The heat transfer from the glass envelope to the atmosphere occurs by convection and
radiation. Depending on whether there is wind the convection will either be forced or
natural. Radiation heat loss occurs due to the temperature difference between the glass
envelope and sky. All these are examined separately below.
6.2.5.1 Convection heat transfer
The convection heat transfer is determined by knowing the Nusselt number, which
depends on whether the convection heat transfer is natural (no wind) or forced (wind
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