Thermal modelling of parabolic trough collectors - Solar Energy Sciences and Engineering Applications - page 178

q gi-go,cond + q go,SolAbs = q go-a,conv + q go-s,rad (6.2.4)

q HeatLoss = q go-a,conv + q go-s,rad (6.2.5)

It should be noted that the solar absorption at the outside pipe, q po,SolAbs and out-
side glass, q go,SolAbs surfaces are treated as heat flux expressions, which simplifies the
solar absorption expressions as it considers the heat conduction through the receiver
pipe and glass envelope wall to be linear. Actually, the solar absorption in the glass
envelope wall (semitransparent material) and receiver pipe (opaque metal material)
are volumetric phenomena. However, it is well known from heat transfer textbooks
(Cengel 2006) that most of the absorption in a metallic surface (receiver pipe) occurs
very close to the surface (within a few µ m) and although solar absorption occurs
throughout the thickness of the glass envelope wall, its absorptance is very small
( α

0.02). Thus, the error in treating solar absorption as a surface phenomenon is
very small.
The various heat transfer interactions are analysed in different sections below,
starting from the heat transfer fluid inside towards the ambient air and sky outside the
receiver assembly.

=

6.2.1 Convection heat transfer between the HTF
and the receiver pipe
Newton's law of cooling states that the convection heat transfer from the inside surface
of the receiver pipe to the HTF is given by hA(T s -T ∞ ). Therefore in the case of the
PTC model and using the nomenclature adopted in Figure 6.2.1:

h f π D pi T pi T f

q f-pi,conv = − (6.2.6)

The convection heat transfer coefficient at the inside pipe diameter, h f is given by:

k f
D pi

h f = Nu D pi (6.2.7)

=

HTF convection heat transfer coefficient at T f (W/m 2 - ◦ C); D pi

=

where: h f inside

=

diameter of the receiver pipe (m); T pi inside surface temperature of receiver pipe

( ◦ C); T f mean (bulk) temperature of the HTF ( ◦ C); Nu Dpi

= = Nusselt number based

thermal conductivity of the HTF at T f (W/m- ◦ C).
In Equation 6.2.6, both T f and T pi are independent of angular and longitudinal
directions of the receiver. The same applies for all temperatures and properties in the
energy model.
The Nusselt number depends on the type of flow through the receiver pipe.
Although the flow in the receiver pipe is well within the turbulent flow region at
typical operating conditions, the model includes conditional statements to determine
the type of flow. When the Reynolds number is lower than 2300, laminar flow exists
in the receiver pipe and the Nusselt number is constant. For pipe flow, the constant
value, assuming constant heat flux, as in the case of a PTC, is equal to 4.36 (Cengel
2006). Turbulent and transitional cases occur at Reynolds number > 2300. Therefore,

on D pi ; and k f =