Thermal modelling of parabolic trough collectors - Solar Energy Sciences and Engineering Applications - page 180

and if stainless steel 321H is chosen the thermal conductivity is calculated from:

k pipe = (0 . 0153)T pi-po + 14 . 775 (6.2.12)

Both equations were determined by linearly fitting data from Davis (2000).

6.2.3 Heat transfer from the receiver pipe to the glass envelope
As is mentioned before, between the receiver pipe and the glass envelope heat transfer
occurs by convection and radiation. Convection heat transfer depends on the annulus
pressure (KJC, 1993). At low pressures ( < 0.013 Pa), heat transfer is by molecular

conduction, whereas at higher pressures the heat transfer is by free convection. Radi-
ation heat transfer also occurs because there is a difference in temperature between
the outsider receiver pipe surface and the inside glass envelope surface. The radiation
heat transfer calculation is simplified by assuming gray surfaces, for which ( ρ

∼

α ) and
that the glass envelope wall is opaque to infrared radiation. All these are examined
separately in the following sections.

=

6.2.3.1 Convection heat transfer

As mentioned above, two heat transfer mechanisms are considered in the determina-
tion of the convection heat transfer between the receiver pipe and glass envelope wall
(q po-gi,conv ). These are the free-molecular and natural convection (KJC, 1993). The
cases of vacuum and pressure in the annulus are examined separately.

a) Vacuum in annulus When the annulus is under vacuum (pressure < 0.013 Pa),

the convection heat transfer between the receiver pipe and glass envelope occurs by
free-molecular convection (Ratzel et al., 1979) and is given by:

∼

q po-gi,conv = π D po h po-gi (T po − T gi ) (6.2.13)

where

k std

D po )) 4

b λ D po
D gi

1

h po-gi = For: Ra Dgi < (D gi / (D gi − (6.2.14)

D po
2ln D gi
D po

+

+

and

(2 − a)(9 γ − 5)

b = (6.2.15)

2a( γ + 1)

10 − 20 (T po-gi + 2 . 331 × 273)

λ = (6.2.16)

(P a δ

2 )

where: D po = outside receiver pipe diameter (m); D gi = inside glass envelope diam-

eter (m); h po-gi = convection heat transfer coefficient for the annulus gas at T po-gi

(W/m 2 - ◦ C); T po = outside receiver pipe surface temperature ( ◦ C); T gi = inside glass

envelope surface temperature ( ◦ C); k std =

thermal conductivity of the annulus gas at