Environmental Engineering Reference
In-Depth Information
Padilla et al. (2011) in their paper present a detailed one-dimensional numerical
heat transfer analysis of a PTC. The receiver and envelope were divided into several
segments and mass and energy balances were applied in each segment. The partial
differential equations developed were discretized and the nonlinear algebraic equations
were solved simultaneously. Finally, to validate the numerical results, the model was
compared with experimental data obtained from Sandia National Laboratory (SNL)
and other one-dimensional heat transfer models.
The model presented in this chapter takes into consideration all modes of heat
transfer: forced convection into the receiver pipe and from the glass cover to ambient
air (usual case when there is wind); natural convection in the annulus between the
receiver and the glass cover; conduction through the metal receiver pipe and glass
cover walls; and radiation from the metal receiver pipe to glass cover and from glass
cover to the sky.
6.2 THE ENERGY MODEL
Although for low-temperature applications a bare tube receiver can be used, as for
this kind of applications low technology collectors the flat-plate can be used, in this
chapter only a glazed receiver is considered, which is the usual case for PTCs. For the
annulus between the receiver and the glass cover two conditions are considered: the
vacuum, usually used in high temperature applications, and the air case, which is used
for lower temperature applications, and for cases when the vacuum is lost from the
former design.
The model is written in Engineering Equation Solver (EES) software (Klein 2002).
This is done for two reasons; the EES includes routines to estimate the properties of
various substances by specifying any two properties, such as temperature and pres-
sure, and EES can be called from TRNSYS which allows the development of a model
which can use the capabilities of both programs. The model is validated with known
performance of existing collectors, and subsequently is used to perform an analysis
of the collector installed at Archimedes Solar Energy Laboratory at Cyprus University
of Technology.
The collector performance model uses an energy balance between the fluid flowing
through the receiver, usually a heat transfer fluid (HTF), and the atmosphere. It includes
all equations necessary to predict the various expressions of the energy balance, which
depend on the ambient conditions and the collector receiver optical properties and
condition.
A cross-section of the collector receiver and the subscript definitions are shown
in Figure 6.2.1a whereas Figure 6.2.1b shows the energy balance of the receiver and
Figure 6.2.1c the steady-state thermal resistance model. The model assumes that all
temperatures, heat fluxes, and thermodynamic properties are uniform around the cir-
cumference of the receiver. This assumption is not very accurate as it is well known
that the radiation profile is not uniform, and the bottom part receives much higher
solar flux than the top part because of the radiation reflected by the parabolic mir-
ror. For small solar collectors however, this simplification does not introduce severe
inaccuracies. Additionally, all flux directions shown in Figure 6.2.1b are positive.
It should be noted that in the resistance model the incoming solar energy and optical
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