CFD Modelling of a Beam-Splitting Hybrid Solar Receiver

UNSW%AUSTRALIA%
%
%SCHOOL%OF%MECHANICAL%AND%MANUFACTURING%ENGINEERING%!
CFD%MODELLING%A%BEAM4
SPLITTING%HYBRID%SOLAR%
RECEIVER!
!
%
Yihan%Liu%
Z3468084
%
Master of Engineering (Mechanical)
Postgraduate Thesis Submission
Date of Submission (June 2015)
Supervisors: Dr Robert Taylor, Dr Victoria Timchenko
%

ii
Declaration
Certificate of Originality
I, Yihan Liu, hereby declare that this submission is my own work and to the best of my
knowledge it contains no materials previously published or written by another person,
or substantial proportions of material which have been accepted for the award of any
other degree or diploma at UNSW or any other educational institution, except where
due acknowledgement is made in the thesis. Any contribution made to the research by
others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in
the thesis.
I also declare that the intellectual content of this thesis is the product of my own work,
except to the extent that assistance from others in the project’s design and conception in
style, presentation and linguistic expression is acknowledged.
Signed ………………………………
Date ………………………………
1/06/2015

iii
Abstract!!
A three dimensional computational simulation is implemented to model the thermal
performance of a previously designed hybrid photovoltaic / thermal (PVT) solar
collector. This type of solar collector uses beam splitting to generate electrical and
thermal energy from the same compact package, the selective absorber filter out the
unwanted solar spectrum from PV cells and utilise them as energy source.
This project was done to validate the experimental result and to simulate four different
selective nanofluids configuration. The collector utilises a Linear Fresnel Lens that has a
concentration ratio of 8.3 and an absorbing fluid channel followed by PV cells
underneath.
The model is built in ANSYS-CFX, and a method of Monte Carlo ray tracing is adopted
to simulate the incident solar radiation landing on the collector. The fluid domain is
comprised of 6mm diameter inlet and outlet tubes connected to a rectangular chamber
(410mm×60mm×12mm) in which an absorbing fluid flows. As the spectral absorption
coefficient varies in different fluid, a different thermal output results from changing the
fluid.
In this study, four inlet temperature conditions are selected between 20 ºC to 100 ºC, in
order to determine the full efficiency curve as a function of mean operational
temperature. It was found that the efficiency of selective nanofluids is much higher than
water, and the efficiency decreases with higher temperature input.

iv
Acknowledgements!
This thesis would not have been possible without the support of several individuals.
Firstly, I would like to thank my supervisors, Dr Robert Taylor and Dr Victoria
Timchenko, their expertise provide me great insight of solar thermal energy and
computational fluid dynamics.
Secondly, I would like to thank Felipe Crisostomo, the PHD candidate who gave me the
opportunity on this thesis study, and offer me guidelines of all the confusion that I had
on this particular collector.
There are many other people that I would like to show my appreciation, Alexander
Booth, his thesis give me much help on radiation application, Justin Becker who
designed and built the collector.
Lastly, I would like to thank the individuals that gave some advice on my CFD model,
they are Dr Guan Yeoh, Yasitha Hewakuruppu, Qiyuan Li, Anthony Yuen and David
Fulker.

v
List!of!Figures!!
Figure 1 Global New Investment in Renewable Energy by Technology, Developed and
Developing Countries, 2013[1].........................................................................................2!
Figure 2 A Concentrating PV System Using Several Dichroic Mirrors Dividing the
Spectrum into Five Bands [14] .........................................................................................6!
Figure 3 a Concentrating PV Configuration With Less Optical Losses [16]....................7!
Figure 4 Selective Mirrors Reflect the Long Band to Si Cells and Transmit the Short
One to DSSC (Dye-Sensitised Solar Cell) [14] ................................................................8!
Figure 5 Thin-film Wave Interference Filter...................................................................10!
Figure 6 Spectral Splitting Using a Selective Absorber [14]..........................................11!
Figure 7 Proposed Collector with Couple Modelling [30]..............................................14!
Figure 8 Beam-splitting Solar Thermal Concentrator from Justin Becker ....................18!
Figure 9 Beam-splitting Components .............................................................................19!
Figure 10 Nanofluid Channel Assembly View ...............................................................20!
Figure 11 Boundary Parameters of the Fluid Domain ....................................................21!
Figure 12 ASTM G173-03 Standard Reference Spectra.................................................23!
Figure 13 Fresnel Transitivity in Different Wavelengths [32].......................................24!
Figure 14 Glass Transitivity in Different Wavelengths [33]...........................................25!
Figure 15 Absorption Coefficient of Four Types of Nanofluid .....................................29!
Figure 16 Engineering Drawing of Fluid Domain ..........................................................35!
Figure 17 Side View and Isometric View of the First Mesh...........................................36!
Figure 18 Created Blocks for Mesh C.............................................................................37!
Figure 19 Structured Mesh Generation Schematics........................................................37!
Figure 20 Side View and Isometric View of Mesh.........................................................38!
Figure 21 Mesh Convergence Determination .................................................................39!

vi
Figure 22 Setting Applied as Monte Carlo Ray Tracing Method ...................................41!
Figure 23 Major Changes of Nanofluid 4 Material Properties........................................42!
Figure 24 Absorption Coefficient Data Input (nanofluid 4) ...........................................43!
Figure 25 Top Glass Applied in Radiation .....................................................................44!
Figure 26 Momentum and Mass Solution Chart.............................................................48!
Figure 27 Heat Transfer Solution Chart..........................................................................48!
Figure 28 Efficiency Curves of Two Models..................................................................51!
Figure 29 Basic Geometries of The Model.....................................................................52!
Figure 30 Stream Line Plot in the Channel (water 20ºC) ...............................................53!
Figure 31 Velocity Vector of Fluid Domain (water at 20 ºC).........................................53!
Figure 32 Temperature Contour at the Central Plane (water 20ºC)................................54!
Figure 33 Stream Line of Water 40 ºC............................................................................55!
Figure 34 Vector of Velocity of Water at 40 ºC .............................................................55!
Figure 35 Temperature Contour of Water at 40 ºC.........................................................56!
Figure 36 Stream Line of Water at 60 ºC........................................................................56!
Figure 39 Stream Line of Water at 80 ºC........................................................................58!
Figure 42 Radiation Intensity Volume Rendering of Fluid Domain (water 20 ºC) ........60!
Figure 43 Radiation Intensity Volume Rendering of Fluid Domain (NF1 20 ºC)..........61!

vii
Figure 47 Efficiency Cure of All the fluids ....................................................................65!
Figure 48 Efficiency Curve of All Fluids .......................................................................67!
!

viii
List!of!Tables!!!
Table 1 Concentration Ratio of Each Type of Collectors...............................................16!
Table 2 Divided Bands and Their Radiation Flux...........................................................23!
Table 3 Fresnel and Glass Transmission Applied...........................................................25!
Table 4 Solar Flux into the Receiver, Concentration Ratio at 8.3 ..................................26!
Table 5 Reynolds Number Calculation...........................................................................34!
Table 6 Results From CFD Model..................................................................................49!
Table 7 Experiment Result by Felipe Crisostomo ..........................................................50!
Table 8 Temperature Results in All Fluids .....................................................................63!

ix
Nomenclature!!
ρ is density (kg/m3
)
u is flow velocity based on the actual cross section area of the duct or pipe (m/s)
µ is dynamic viscosity (Ns/m2
)
L is characteristic length (m)
ν is kinematic viscosity (m2
/s)
κ! is the absorption coefficient ! !!
∙ !
L is the participating medium thickness (m)
!! is spectral absorptivity
Qu is the instantaneous useful energy output from the collector (W)
Qi is the instantaneous incident solar energy on the collector (W)
ṁ is Mass flow rate (kg/s)
Cp is the specific heat capacity of the working fluid (J/kg·K)
To is the temperature at the outlet (°C)
Ti is the temperature at the inlet (°C)
A is the area of the collector (m2
)
G is incident radiation on the collector (W/m2
)
V is wind speed (m/s)
ℎ!"#$ is the convection heat transfer coefficient ! !!
∙ !

x
! is the emissivity of the surface
! is Stefan-Boltzmann constant, its value is 5.67×10!!
!! !!
∙ !!
!! is the surface temperature (K)
!!"## is the surrounding temperature (K)
ℎ!"# is convection heat transfer of air ! !!
∙ !
! is the thickness of the glass, (m)
k is the conduction heat loss coefficient
! !

xi
Contents!
Declaration ........................................................................................................................ii!
Abstract ........................................................................................................................... iii!
Acknowledgements..........................................................................................................iv!
List of Figures ...................................................................................................................v!
List of Tables................................................................................................................. viii!
Nomenclature ...................................................................................................................ix!
1.! Introduction...............................................................................................................1!
1.1 Background .............................................................................................................1!
1.2 Project Aims............................................................................................................2!
2.! Literature Review......................................................................................................4!
2.1! Introduction of Solar Energy..............................................................................4!
2.2! Beam Splitting....................................................................................................4!
2.3! Spectral Splitting in Hybrid PV/T Receivers .....................................................8!
2.3.1 Thin Film Filters Method.................................................................................9!
2.3.2 Nanoparticle Fluid Filter Method...................................................................10!
2.4! Mathematical and Theoretical Models .............................................................13!
2.5! Comparison of Different Types of Collectors..................................................16!
3.! Project Description..................................................................................................18!
3.1! System Design..................................................................................................18!
3.1.1 System Components.......................................................................................18!
3.1.2 Receiver Concept ...........................................................................................19!

xii
4.! Solar Thermal Theory .............................................................................................22!
4.1! Solar Spectral Irradiance Derivations...............................................................22!
4.2! Transmission Loss of Fresnel Lens and Glass Plates.......................................24!
4.3! Heat Loss Calculation.......................................................................................27!
4.4! Nanofluid Absorptivity.....................................................................................29!
5.! Numerical Model ....................................................................................................31!
5.1 Governing Equations and Turbulence Models......................................................31!
5.1.1 Mass Conservation.........................................................................................31!
5.1.2 Momentum Equation......................................................................................32!
5.1.3 Energy Equation.............................................................................................32!
5.1.4 Flow Model Selection ....................................................................................33!
5.2 CFD Geometry Development ...............................................................................34!
5.3 Grid description and Refinement ..........................................................................36!
5.4 Boundary Conditions ............................................................................................40!
5.1.1! Selection and Settings of Domain.............................................................40!
5.4.2 Inlet ................................................................................................................43!
5.4.3 Outlet..............................................................................................................43!
5.1.4! Top and Bottom Glasses ...........................................................................44!
5.4.5 Side Walls ......................................................................................................45!
5.5 Schematics Applied...............................................................................................45!
5.5.1 Transient Analysis..........................................................................................45!

xiii
5.5.2 High-Resolution Schemes..............................................................................46!
5.5.3 The Discrete Transfer Model .........................................................................46!
5.5.4 The Monte Carlo Model.................................................................................47!
5.6 Convergence..........................................................................................................47!
5.7 Validation and Verification...................................................................................49!
5.7.1 Comparison of Results ...................................................................................49!
6.! Results.....................................................................................................................52!
6.1! Fluid Domain Flow Result ...............................................................................52!
6.2! Radiation Intensity with Different Fluids.........................................................60!
7.! Discussion of Results ..............................................................................................66!
7.1 Accuracy Discussion.............................................................................................66!
7.2 Comparison with Experimental Data....................................................................67!
7.3 Comparison of Different Fluid..............................................................................68!
8.! Conclusion and Suggestions ...................................................................................70!
9.! References...............................................................................................................72!
Appendix A…………………………………………………………………………….77
Appe ndix B ……………………………………………………………………………81
Appendix C……………………………………………………………………………. 85

1. Introduction!!
1.1!Background!
Energy collection is increasingly an issue that is a highly discussed topic. The demand
of global power is around 1.3×1013
W [1] and it is rising every year with the continued
economic and social development of economies around the world. With concerns of the
energy supply potentially under stress at some point in the future, many solutions have
been proposed, one of which is renewable energy development. Renewable power
capacity increased more than 8 percent in 2013, accounting for over 56 percent of net
additions and now has the potential to account for over a fifth of world electricity
generation. Globally, wind power accounts for the largest share of growth in
renewables-based generation (34%), followed by hydropower (30%) and solar
technologies (18%). As the share of wind and solar PV in the world’s power mix
quadruples, their integration both from a technical and market perspective becomes
more challenging, with wind reaching 20% of total electricity generation in the
European Union and solar PV accounting for 37% of summer peak demand in Japan [2].
As the problem of obtaining adequate energy resources is becoming more and more
serious, the potential of solar energy is more realistic than before. More importantly, as
the sun emits solar energy, the radiation that is striking earth in average is 1.8×1014
W,
with the right adoption of solar energy technologies, a potential of energy crises could
be averted. In the year of 2014, solar energy had the most investment among global
renewable energy projects (Figure 1).

2
Figure 1 Global New Investment in Renewable Energy by Technology, Developed and Developing
Countries, 2013[1]
Solar collectors are designed to utilise solar energy, and a solar thermal collector is a
device that transfers solar radiation into heat energy; while a photovoltaic solar collector
generates electrical energy directly from solar radiation. The combination of these two
collectors is called a Photovoltaic / Thermal Hybrid Solar System (PV/T System) which
is the subject of this thesis.
1.2!Project!Aims!
This project studies a particular solar beam-splitting hybrid solar system. The solar
collector was designed and built by Justin Becker as his thesis topic, and is located in
the solar lab in building K17 of the Kensington Campus of UNSW. The simulation is
carried out to predict the performance of this type of the solar collector through a
simulated efficiency test. An experimental study has also been done at the same time by
Felipe Crisostomo to validate the simulation results involving water and nanofluid heat

3
collection and transfer methods. The simulation model is employed in this project to
reduce the amount of time needed to analyse the performance of the collector.
The aim of the CFD project also involves an opportunity to demonstrate an
understanding of the fundamentals and use of ANSYS-CFX software, as well as to
introduce and explore the numerous applications within the software in a simulated
system.
! !

4
2. Literature!Review!
2.1 Introduction!of!Solar!Energy!
A universally recognised trend of human development is increasing energy
consumption. While solar energy is abundantly available and can be supplied without
environmental pollution, it has not yet achieved high levels of adoption. There are two
main mechanisms for capturing and transforming sunlight into usable energy in
commercialisation: photothermal and photovoltaic. Photothermal solar collection
involves using an absorbing medium to convert sunlight into useful heat. In 1878,
Augustin Mouchot developed the first photothermal system by using a solar thermal
collector to run a heat engine [3]. Photovoltaic collection employs semi-conductor
materials (e.g. silicon) which possess bandgaps in the optical or near infrared range. The
first photocell collector to convert sunlight into electricity was reported by Tyagi et al.
in the mid-1950s [4].
2.2 Beam!Splitting!!
PV cells are commercially viable with module efficiencies ranging from 14% and 43.5%
in laboratory measurements [5]. The cost of high efficiency PV cells (compared to
concentrators such as lenses and mirrors) is much higher, which is why multi-junction
PV cells are commonly used under concentrated solar radiation to shorten the payback
period [6]. Silicon cells, which are much cheaper, have relatively low efficiency
(turning a lot of solar energy into heat). To make matters worse these PV cells are
highly dependent on the temperature of the cell surface, and can even be physically
damaged in extreme cases [7]. As a result, cooling methods have been developed for
concentration Silicon PV systems, including “post-absorption” and “pre-absorption”

5
heat management methods. The “pre-absorption” method removes the wave lengths of
light that will not be converted to electricity, before they hit the cell. This method is
favourable to the other because thermal absorbers are able to capture the solar spectrum
effectively in each band, while PV cells have a fixed spectral response. It means that
photons with energies lower than the band wavelengths pass through the semiconductor
material and are absorbed as heat by the mounting at the back of the cell.
Semiconductor materials absorb high-energy photons; however, the excess energy is not
used by conventional single-junction PV cells, but is generally dissipated as heat. As a
result, wavelengths that higher or lower than the band gap incur heat losses, which
increases cell temperature and limits single semiconductor material efficiency at 30%
[8]. Therefore, a study of spectral beam splitting that directs some part of the solar
spectrum on to the PV cell has been developed. This means it reduces the heat load on
the cell and also converts additional solar spectra to thermal energy that is filtered out
from the cells, and at the same time, increases system efficiency.
A concept has been developed by Jackson in 1955 that involves separating spectral
sunlight into various wavelength bands and directing each band to the most efficient
receiver [9]; in addition, Moon et al. have demonstrated experimental fields which are
still being extensively used to solve the problem of spectral mismatch in solar cells [10].
Various sunlight spectral-splitting mechanisms have been proposed (Figure 2);
holographic concentrators can split sunlight into several bands along with concentrating
it. This mechanism has a great advantage on low concentration solar collectors. The PV
cells can alternatively be mounted with a thermal solar collector together as a PV/T
system; where the transmitted absorber can filter out part of the solar spectrum before it
reaches the cells, the most well-known of these methods is the thin-film wave
interference filter method [11] and selective absorbing/transmitting filter method [12].

6
!
Figure 2 A Concentrating PV System Using Several Dichroic Mirrors Dividing the Spectrum into
Five Bands [14]
1. SPECTRAL)SPLITTING)IN"PV"RECEIVERS#
The configuration of a typical concentrating spectral-splitting PV system includes a
concentrating device such as a lens or a dish which is combined with a spectral splitter
at the focal region of the concentrator. The splitter acts as a selective mirror to create
two different focal points. The splitter may have a curved surface rather than a flat one
to account for the effects associated with non-parallel rays on the wave interference
filters. One of the advantages of using curved mirrors is the shifting of the focal point of
the concentrating system to provide a suitable area for locating the receivers; otherwise,
the receivers may cause shadowing and therefore optical losses. [13]
Theoretically, dividing the spectrum into different bands and directing them to match
different PV cells can achieve very high solar conversion; however, it could be
challenging to use waveguides and various receivers in practice. The design should aim
at reducing wind loads, increasing light acceptance, minimising moving parts as much
as possible. Although the most challenging part is reduction of shadowing in order to

7
achieve high efficiency. [14] In 2006, Barnett et al. proposed and built a planar spectral
splitting concentrated PV system that has conversion efficiency of over 50% (Figure 3).
The total efficiency of such a configuration is the product of the optical plus the cell
module efficiencies. The system has achieved 39.1% as a maximum total efficiency out
of a concentration ratio of 30. [15]
Figure 3 a Concentrating PV Configuration With Less Optical Losses [16]
From a concentrating device, a significant portion of sunlight is not collected (in the
form of diffused sunlight). Some literature also discussed developing solutions to
capture diffuses sunlight by using selective mirrors in 2011. Such mirrors can be short-
pass mirrors and transmit shorter wavelengths which are mainly the diffused component,
so that these parts of sunlight can be absorbed by a high band gap collector which is
mounted behind the mirror (Figure 4). [17]

8
!
!
Figure 4 Selective Mirrors Reflect the Long Band to Si Cells and Transmit the Short One to DSSC
(Dye-Sensitised Solar Cell) [14]
2.3 Spectral!Splitting!in!Hybrid!PV/T!Receivers!
Hybrid PV/T solar collectors are devices that are able of converting solar energy into
both electricity and heat; it combines PV cells with a thermal receiver to maximize the
power conversion and efficiency from incident solar irradiation. On the other hand,
thermal receivers also filter the spectrum so that only wavelengths where the PV cell
works most efficiently are used. The aim is that instead of capturing the whole spectrum
on PV cells, the system reduces undesirable heating as much as possible. Maghanga et
al. have introduced a cut-off mirror made of TiO2: Nb and Al2O3 on an Aluminum
substrate. The mirror reflects 75.6% of sunlight below 1100nm and 28% of sunlight
above the 1100nm wavelength. The bands that are not reflected can be absorbed and

9
delivered as useful heat. A problem of the solar power tower is the effect of significant
variation of angle incidence on the heliostats area receiver. It could be solved by
dividing the beam splitter into small segments and optimizing each one according to the
weighted mean angle of incidence [18]. Similar to dish concentrators, they can provide
a high concentration ratio but on small scales. Shou et al. has developed a spectrum-
splitting hybrid dish concentrating system [19]. The major problem of such a hybrid
dish concentration system is the slow response of positioning engines to transient
conditions. This problem can be addressed by replacing the engine with a thermoelectric
generator. However, current techniques related to thermoelectric generators have low
efficiencies compared to other electric generators.
There are two approaches that carry out spectral selectivity in hybrid systems by beam
splitting. The first is a more classical approach, which involves solid optical coatings on
substrates, and at the same time, a number of multilayer designs are described. Another
concept employs specially-formulated liquids that play the roles both the absorber and
the heat-transfer material.
2.3.1!Thin!Film!Filters!Method!
It is well-established that using a dialectic thin-film interference filter to split the solar
spectrum is a preferred option for beam splitting method. As illustrated in figure 3, the
thin-film filter reflects the selected spectrum bands and transmits the other wavelengths
of light based on the light interference between the layers of thin film filters. Osborn
aimed to get a high reflectance by using a multilayer filter [20], while Imenes focus on
the design and optimisation process of two types of filter as a hybrid PV/T central
receiver system study. [21] (Figure 5)

10
!
Figure 5 Thin-film Wave Interference Filter
As in multilayer filters, approaching an ideal rectangular profile requires a large number
of layers. However, issues related to new materials, and optical problems emerge to
undermine system performance. Therefore, this involves balancing the advantages and
disadvantages in performance and cost from the addition of each subsequent layer to the
model. On the other hand, a great flexibility is offered by the thin-film optical filter
approach in terms of tailoring the spectral window to the quantum process.
2.3.2!Nanoparticle!Fluid!Filter!Method!
While thin-film filters have been developed, selective absorber filters remain relatively
underdeveloped. Nanofluids are fluids that contain nanoparticles (particles with
diameters < 100nm) suspended in conventional base fluids. The concept of selective
absorption by heat transfer liquids for hybrid PV/T solar collectors was originally
proposed by Chendo et al in 1986 [21]. In a selective absorber model, the system
employs a liquid or a solid layer which is transparent to some wavelengths (suitable for
PV cells) and highly absorbing of the rest (see Figure 6). The working fluid can also act
as the heat transfer fluid.

11
!
Figure 6 Spectral Splitting Using a Selective Absorber [14]
By adding particles, a fluid could change from being transparent over most of the
optical spectrum to highly absorbing fluid. For a given particle, there is a natural
plasmon resonance frequency whereupon incoming photons cause large oscillations in
the electrons. This phenomenon can potentially be utilized to produce optical filters. [22]
An appropriate liquid-filter material must meet some requirements, such as adequate
refractive index and absorption coefficients, optical constants that determine a
satisfactory spectral response, solubility and stability in both cold and hot environments,
and satisfactory resolution of safety issues. [23]
Chendo et al. [18] proposed the concept of selective absorption by heat transfer liquids
for hybrid solar PV/T collectors in 1986. Numerical studies referring to heat transfer
and radiation model to optimise absorption properties in selective absorbing hybrid
solar collector are presented in recent years [24,25]. Nanofluids are able to achieve

12
tuneable optical properties [26]. Taylor et al indicates the possibility of producing
nanofluids at low nanoparticle volume fractures at a low cost [27,28].
In addition to providing optical filtration benefits, the nanoparticle-based fluids are also
able to act as the heat transfer fluid in the thermal receiver of the hybrid collector
system. Otanicar, Taylor et al point out that although it is relatively simple to design
nanoparticle suspensions with highly uniform broadband solar absorption, creating
selective optical filters through nanoparticle suspensions is more challenging. Further
issues involve the stability of the nanoparticle solutions under various conditions. As a
result of high surface area, numerous nanoparticle-nanoparticle collisions, and strong
van der Waals forces; untreated nanoparticles tend to agglomerate over time. Two
approaches are suggested for stabilisation of the solutions follows:
a) Give the particles repulsive surface charges
b) Make the particles attracted to the base fluid
The most common and practical methods for achieving both a) and b) are either adding
various surfactants or by using chemical functionalisation of the particles.
Nanofluids can be easily pumped or controlled in and out of the system, which is ideal
for dynamic optical switching within the system. Another advantage is that with a
nanofluid filter, de-coupling the PV and Thermal system is achievable so that nanofluid-
based filter can be adopted as heat transfer or thermal storage media to operate at an
optimum temperature. Taylor et al also investigated the absorption of nanofluids
towards solar spectrum by comparing model predictions to spectroscopic measurements.
It was pointed out that over 95% of sunlight is absorbable when the thickness of the
nanofluid is above 100mm and the volume fraction of the fluid is less than 1×10-5
.

13
A major disadvantage of such systems is the lack of available liquids with suitable
optical properties; however, nanofluid-based heat transfer liquids which incorporate
nanoparticles to achieve tuneable optical properties have shown potential in addressing
this issue. [27, 28] Also, nanofluids can be produced at low nanoparticle volume
fractions which indicate that it may be possible to design nanofluid filters at low cost.
The advantage of the concept of selective absorber fluid filters is that the thermal part of
the system is separated, which allows the photovoltaic and thermal components to
operate at significantly different temperatures. In addition, by using a fluid filter, it is
easy to remove heat from the thermal side, relatively speaking.
2.4 Mathematical!and!Theoretical!Models!
Mittal et al [29] has carried out a numerical study that selective nanofluids absorption
can significantly reduce heating of PV cells and consequently raise efficiency overall
other collector efficiencies. He also studied thermal and overall efficiency of Cu and Ag
as nanofluids, which can be used in Si PV cells.
On the other hand, Otanicar [30] investigated the performance of nanofluids and thin-
film-based filters within a concentrating hybrid PV/T system by using a theoretical
method. The results demonstrate that nanoparticle based filters have a performance
efficiency slightly lower than conventional thin-film filters. The reason is that the
nanofluids have a lower transmission performance when compared to the PV cell.
However, nanoparticle filters are able to achieve a higher thermal efficiency of up to 4%
when compared to thin-film filters, due to the fact that such filters have a significantly
reduced thickness which favours higher optical performance and a lower cost design.

14
Figure 7 shows the proposed collector design by Otanicar with both the optical and
thermal fluxes. The solar flux enters the top of the collector through glazed glass and
separated via a vacuum barrier to a transparent glass tube which contains a nanofluid
filter. Below the heat transfer fluid, there is another vacuum and PV cell. It is assumed
that the fluid will absorb the appropriate energy from the incoming solar radiation,
while multiple reflections from interfaces are not considered. It is shown in this
schematic that the thermal system and PV system have minimal thermal coupling.
Figure 7 Proposed Collector with Couple Modelling [30]
The final PV efficiency was calculated from the followed equation

15
!!"
∗
=
!!"!!"!!
!!!"#$%
Equation 1
The thermal efficiency was determined from the followed equation
!!! =
!!! !!"# − !!"
!" ∗ ! ∗ !
Equation 2
The overall efficiency of the hybrid photovoltaic/thermal system was determined from
the followed equation
!! = !!" + !!!! 1 −
!!"#
!!!",!"#
Equation 3
Where:
K = fraction of the Carnot efficiency, 0.5
Monte-Carlo Method
Lately, the direct simulation Monte Carlo method (DSMC) has been proposed in
addition to the LBM for the computation of fluid dynamics because of the practical
scientific and engineering importance of solving high-Knudsen-number (Kn) flows.
DSMC is a direct particle simulation method based on kinetic theory. The fundamental
idea behind the method is to track a large number of statistically representative particles.
The particles’ motion is later used to modify their positions, velocities, or even chemical
reactions in reacting flows.

16
The core of the DSMC procedure consists of four primary processes. First, the
simulated particles are moved within a time step. Boundary conditions are enforced
through modeling of molecule–surface interactions, which may include physical effects,
such as chemical reactions, three-body collisions, and ionized flows. Second, indexing
and cross-referencing of the particles are performed. This is a prerequisite for the next
two steps: simulating collisions and sampling the flow field. The key to practical DSMC
for large-scale processing is the accurate and fast indexing and tracking of the particles.
Third, the step of simulating collisions sets DSMC apart from other deterministic
simulation methods, such as molecular dynamics. The sub-cell method ensures that
collisions occur only between near neighboring particles by calculating local collision
rates based on individual cells but it restricts possible collision pairs to sub-cells. Fourth,
sampling of the particles provides information on macroscopic flow properties. The
spatial coordinates and velocity components of molecules in a particular cell are used to
calculate macroscopic quantities at the geometric centre of the cell.
2.5 Comparison!of!Different!Types!of!Collectors!
According to the collector types, there is a list of different type pf collectors and their
concentration ratio, which are found in the literatures and listed in Table 1.
Table 1 Concentration Ratio of Each Type of Collectors

17
Type of Collector Concentration Ratio
Flat plate collector 1
Evacuated tube collector 1
Parabolic through collector (PTC) 15-45
Linear Fresnel reflector (LFR) 10-40
Parabolic dish 100-1000
Solar photovoltaic (PV) 10
Solar PV / Thermal Technology 10
!

18
3. Project!Description!!
3.1 System!Design!
3.1.1!System!Components!!
The beam-splitting solar thermal concentrating collector is designed and built by Justin
Becker in his thesis. The dimensions for this model are based on his design. Figure 8 is
the solar concentrator that was built by Justin Becker that mounted on a tracking rig.
Figure 8 Beam-splitting Solar Thermal Concentrator from Justin Becker
A linear Fresnel lens was built on the top as a concentrator; the solar radiation is
concentrated onto the nanofluid channel and generates heat; and then spectrally
transmitted to the PV cells arrayed below to generate electricity. The collector design is
essentially composed of the following three systems: the Linear Fresnel Lens, the Beam

19
Splitting Channel and the PV Cells. See Figure 9 for the dimensions of the non-simulated
part. The concentration ratio of this Fresnel lens to channel is 8.3 according to the design.
Figure 9 Beam-splitting Components
The collector is also enclosed to prevent significant forced convection phenomena from
affecting the efficiency, as shown in Figure 8.
3.1.2!Receiver!Concept!!
For a hybrid PV/T system, the receiver includes two parts: the thermal part and PV cell
part, in this project, only the thermal receiver is under study for a thermal efficiency.
Therefore only the beam splitting channel is being modelled.
In the original design, the channel is designed in an acrylic rectangular chamber with a
dimension of 410mm×60mm×12mm assembled with bolts and sealed with a rubber ring.
The inlet and outlet are designed with Aluminium tubes as shown in Figure 10.

20
Figure 10 Nanofluid Channel Assembly View
As the project progressed, some alterations have been made:
Firstly, Inlet and outlet have been changed to the midpoint of the channel, from the
simulated flow; the mixture of the fluid is not optimal at the original designed point.
Secondly, the top and bottom of the channel has changed from acrylic to glass. The
reason of changing this is that glass is the most widely used cover material as it has the
best weather resistance, high short wave length transmission and low long wave
radiation transmission characteristics, while acrylic has a disadvantage of UV
degradation. Moreover, the sides are Aluminium and cotton insulation, results in low
transmission on the side walls and less conductivity heat loss has been generated due to
this change.
The updated boundary conditions and dimensions of the outside of the fluid are shown
in Figure 11.

21
Figure 11 Boundary Parameters of the Fluid Domain
For the simplicity of the model, there are two types of walls are set for this model:
Aluminum with wool insulation on all the side walls and 5.5mm thick glass on top and
bottom walls.
!

22
4. Solar!Thermal!Theory!!
4.1 Solar!Spectral!Irradiance!Derivations!
The optical performance of the system is an important part of the complete simulation
model. Absorbance, reflectance, and transmittance of solar energy are different in
different materials. As solar optical properties are normally functions of wavelength, a
specific description of the solar spectrum is needed and a derivation is required for the
data input of this simulation. Therefore a spectral distribution of the solar flux is needed
for the simulations in this project to produce accurate and reliable results.
The solar spectral irradiance is also different from the time of the day, the angle of the
sun, cloud cover and ozone layer thickness. In this project, a reference solar spectral
irradiance ASTM G173-03 has been chosen. It is a standard spectrum reference
developed by the American Society for Testing and Materials (ASTM). It stands for the
average spectral conditions across the United States over a calendar year. There are
some assumptions for this reference that also apply to the project model: [31]
It is assumed that the 1976 U.S Standard Atmosphere (from this the average
temperature, pressure, air density and other factors are used). It is also assumed at Solar
Zenith angle of 48.19° (or 41.81° from horizon).
The spectral irradiance of ASTM G173-03 in different wavelength is plotted in Figure
12.

23
Figure 12 ASTM G173-03 Standard Reference Spectra
According to this standard reference spectra data, the solar spectrum has been integrated
between 300 and 4000nm to apply total solar flux and was separated into 13 bands
between the wavelengths. As the irradiance peak for the smaller wavelengths, smaller
bands were applied in comparison to the larger wavelengths. The divided bands and
their radiation flux are shown in Table 2.
Table 2 Divided Bands and Their Radiation Flux
Banded wavelength range (nm) Radiation Flux(W/m2
)
280-390 24.92394275
390.5-500 120.718275
501-625 166.6506
626-750 147.71174
751-875 116.1214
876-1000 73.306505
1001-1125 68.332198
1126-1250 44.2861
0!
0.2!
0.4!
0.6!
0.8!
1!
1.2!
1.4!
1.6! 300!
328!
356!
384!
424!
480!
536!
592!
648!
704!
760!
816!
872!
928!
984!
1040!
1096!
1152!
1208!
1264!
1320!
1376!
1432!
1488!
1544!
1600!
1656!
1755!
2035!
2315!
2595!
2875!
spectral%Irradiance%W/m2%
wavelength%(nm)%
ASTM%G173403%

24
1251-1500 37.76048876
1501-1750 55.012985
1751-2000 8.410757374
2001-2500 29.0558345
2501-3000 0.426127728
total 892.7169541
4.2 Transmission!Loss!of!Fresnel!Lens!and!Glass!Plates!
The Fresnel lens of the concentrator has transitivity properties related to the solar
spectrum, and should be applied on the solar irradiation derivation. The Fresnel lens of
the concentrator is purchased from Nihon Tokushu Kogaku Jushi. Figure 13 is the
transitivity of the Fresnel in different wavelengths [32].
Figure 13 Fresnel Transitivity in Different Wavelengths [32]
According to the Fresnel spectral transitivity, the transmission of the Fresnel is high in
short wavelengths and low in long wavelengths, it even drops to 0 at 2500nm, which
results in the last band having a value of 0.
0!
10!
20!
30!
40!
50!
60!
70!
80!
90!
100!
spectral%transiQvity%%%
wavelenght%nm%
Fresnel%Spectral%TransiQvity%

25
There is also a glass plate on the top of the fluid chamber, as a container of the fluid and
it also serves the function of transmitting radiation. Although the transmission of glass
is very high, it is still should not be neglected. The glass material transitivity data is
obtained online from SCHOTT glass optical properties [33]. Figure 14 is the transitivity
property of the glass that was used in this model.
Figure 14 Glass Transitivity in Different Wavelengths [33]
The losses associated with the transmission of the Fresnel and glass plate are applied to
banded radiation. The integrated radiation derivations from Table 2 are multiplied by
the optical transmission. Table 3 shows the radiation with both transmissions applied.
Table 3 Fresnel and Glass Transmission Applied
Banded
wavelength
range (nm)
Radiation
Flux(W/m2
)
Glass
transmission
%
Fresnel
Transmis
sion%
Flux after Glass
and Fresnel (w/m2
)
300-390 24.92394275 84.53162107 22.000 4.635
390.5-500 120.718275 91.99193989 90.204 100.173
501-625 166.6506 92.42760162 91.000 140.168
626-750 147.71174 92.24253649 91.000 123.990
0!
10!
20!
30!
40!
50!
60!
70!
80!
90!
100!
2500!
2424!
2348!
2272!
2196!
2120!
2044!
1968!
1892!
1816!
1740!
1664!
1588!
1512!
1436!
1360!
1284!
1208!
1132!
1056!
980!
904!
828!
752!
676!
600!
524!
448!
372!
Spectal%transiQvity%%%
Wavelength%nm%
Glass%Spectral%TransiQvity%

26
751-875 116.1214 91.92479379 91.333 97.493
876-1000 73.306505 91.73717846 91.000 61.197
1001-1125 68.332198 91.67638846 91.000 57.006
1126-1250 44.2861 91.90651138 82.700 33.660
1251-1500 37.76048876 91.83951352 75.500 26.183
1501-1750 55.012985 92.54752794 48.000 24.438
1751-2000 8.410757374 92.41481651 44.333 3.446
2001-2500 29.0558345 85.57816345 12.500 3.108
2501-3000 0.426127728 75.3167 0.000 0.000
total 892.7169541 - - 675.4984865
From the table of transmission solar flux, band wavelength 2500-3000 is appearing to
be 0 as energy input due to the transmission of Fresnel, also can be seen that the
transmission of the Fresnel has a great influence on the solar flux.
As for the radiation received on the fluid, a concentration ratio needs to be applied for
the model. In this model, the concentration ratio is 8.3 for the design. It is multiplied by
the radiation flux from Table 3. Table 4 shows the solar flux into the receiver.
Table 4 Solar Flux into the Receiver, Concentration Ratio at 8.3
Banded wavelength
range (nm)
Flux after Glass and
Fresnel (w/m2
)
Flux after Glass and Fresnel to
receiver (w/m2
)
300-390 9.325 38.47128705
390.5-500 105.136 831.433443
501-625 140.143 1163.397296
626-750 123.949 1029.119329
751-875 97.374 809.1933928
876-1000 136.682 507.9341088
1001-1125 56.781 473.1538427
1126-1250 33.772 279.3812909
1251-1500 58.084 217.3162617
1501-1750 21.418 202.8380201

27
1751-2000 0.664 28.60126153
2001-2500 0.624 25.7979039
2501-3000 0.000 0
total 675.4984865 5606.637438
The data in Table 4 is applied to solar ray trancing model in ANSYS-CFX.
4.3 Heat!Loss!Calculation!!!
From the boundary conditions of this model, heat transfer is an energy loss that should
not be neglected. For the purpose of simplicity of this simulation, a combined
convection and radiation heat transfer is applied on the top and bottom glass of this
model. Conduction is assumed to happen on the side walls of the fluid model.
For combined heat transfer the coefficient ℎ!"#$%&'( is used, which includes the effects
of both convection and radiation is expressed as follow [34]:
ℎ!"#$%&'( = ℎ!"#$ + ℎ!"# = ℎ!"#$ + !" !! + !!"## !!
!
+ !!"##
!
Equation 4
Where:
! = 5.67×10!!
!! !!
∙ !!
, which is Stefan-Boltzmann constant
Emissivity of glass is between 0.92 - 0.94[33], and here we assume it is 0.92
The convection heat transfer coefficient on the glass is calculated as follows [1]:
ℎ!"#$ =
1
1
ℎ!"#
+
!
!!"#$$
Equation 5
Where:

28
ℎ!"# is convection heat transfer of air, it is chosen to be 5 (natural convection)
!!"#$$ is the conduction coefficient of the glass surface, it is 1.14 ! !!
∙ !
! is the thickness of the glass, 5.5mm
ℎ!"#$ =
1
1
5 +
0.0055
1.14
ℎ!"#$ = 4.882226981! ! !!
∙ !
In the convection heat loss process, an assumption is made that the glass to air
convection is natural convection, because the channel is enclosed by a box. But the heat
transfer from inside of the box to the ambient is neglected, because the temperature
difference is forecasted to be less than 3 degrees.
For conduction heat transfer coefficient, there are Aluminium walls and Aluminium
walls with insulation covered. The thermal conductivity of wool is 6×10!!
!!/! ∙ !.
Thermal conductivity of Aluminium is !205!/! ∙ ![34]
Heat transfer coefficient with insulation is calculated as follows:
ℎ!"#$ =
1
!!""#
!!""#
+
!!"
!!"
=
1
0.02
6×10!! +
0.03
205
= 0.2999986829
Equation 6
The entire heat transfer coefficient will be applied on the ANSYS-CFX boundary
conditions. (Application detail in chapter 5)

29
4.4 Nanofluid!Absorptivity!!
Nanofluid solution that consists of nanoparticles suspended in transparent solution. In
this project, Silver-silica core-shell nanodiscs were suspended in water to allow
nanoparticles to absorb short wavelength and water to absorb long wavelength.
Four kinds of nanofluids were simulated in the CFD model, with four concentrations of
the resulting nanofluid. In this project, they are referred as nanofluid1-4, where
nanofluid 4 has a relatively high concentrated nanofluid. And each nanofluid has its
own optical properties. Among the four nanofluids that were studied, most of the
thermal properties are as same as water; however, the optical absorptivity varies
significantly between samples. Different spectral absorption coefficients are shown in
the following figures. (Figure 15)
Figure 15 Absorption Coefficient of Four Types of Nanofluid
The spectral absorptivity is calculated as
1!
10!
100!
1000!
10000!
300!
367!
434!
501!
568!
635!
702!
769!
836!
903!
970!
1037!
1104!
1171!
1238!
1305!
1372!
1439!
1506!
1573!
1640!
1707!
1774!
1841!
1908!
1975!
2042!
2109!
2176!
2243!
2310!
2377!
2444!
AbsorpQon%Coefficient%(1/m)%
wavelength%(nm)%
AbsorpQon%coefficient%of%four%types%of%nanofluid%
NF4!
NF3!
NF2!
NF1!

30
!! = 1 − !!!!!
Equation 7 [34]
Where:
L is the participating medium thickness
Therefore absorption coefficient is calculated from the followed formula
κ! =
!" !! − 1
!
Equation 8
!

31
5. Numerical!Model!!
5.1!Governing!Equations!and!Turbulence!Models!!
CFD is fundamentally based on the governing equations of fluid dynamics. The
governing equations represent mathematical statements of the conservation laws of
physics, where the following physical laws are adopted:
• Mass is conserved for the fluid.
• Newton’s second law: The rate of change of momentum equals the sum of
forces acting on the fluid.
• First law of thermodynamics: The rate of change of energy equals the sum of the
rate of heat addition to the fluid and the rate of work done on the fluid. [35]
5.1.1!Mass!Conservation!
The conservation law considers fluid traveling through an element, whereby the mass
flow rate ‘in’ must be equal to the mass flow ‘out’. This motion can be split into
Cartesian coordinates. The equation below shows the mass conservation law.
!"
!"
+
!"
!"
+
!"
!"
= 0
Equation 9 [35]
Since the fluid is assumed to be incompressible, therefore density ρ is constant;
therefore the equation above is used.

32
5.1.2!Momentum!Equation!
The momentum equation follows Newton’s second law of motion, which states that the
sum of forces acting on the fluid element equals the product of its mass and the
acceleration of the element. The following equations are three scalar relations along the
x, y, and z directions of the Cartesian frame for which the fundamental law can be
invoked.
!"
!"
!""#$#%!&'()
=
!"
!"
!"#$!!!""#$#%!&'()
+!
!"
!"
+ !
!"
!"
+ !
!"
!"
!"#$%&'()
= −
1
!
!"
!"
!"#$$%"#!!"#$%&'(
+
!
!!
!
!!!
+ !
!!
!
!!!
+ !
!!
!
!!!
!"##$%"&'
!"
!"
!""#$#%!&'()
=
!"
!"
!"#$!!!""#$#%!&'()
+!
!"
!"
+ !
!"
!"
+ !
!"
!"
!"#$%&'()
= −
1
!
!"
!"
!"#$$%"#!!"#$%&'(
+
!
!!
!
!!!
+ !
!!
!
!!!
+ !
!!
!
!!!
!"##$%"&'
!"
!"
!""#$#%!&'()
=
!"
!"
!"#$!!!""#$#%!&'()
+!
!"
!"
+ !
!"
!"
+ !
!"
!"
!"#$%&'()
= −
1
!
!"
!"
!"#$$%"#!!"#$%&'(
+
!
!!
!
!!!
+ !
!!
!
!!!
+ !
!!
!
!!!
!"##$%"&'
Equation 10[35]
5.1.3!Energy!Equation!
The equation for the conservation of energy is derived from the consideration of the
first law of thermodynamics that the rate of change of energy is equal to the sum of the
rate of heat and work added through an element.
!!!
!"
!"
=
!
!"
!
!"
!"
+
!
!"
!
!"
!"
+
!
!"
!
!"
!"
+
!"
!"
+ !
Equation 11[35]

33
5.1.4!Flow!Model!Selection!
In the flow model, a flow type is defined by Reynolds number. When the Reynolds
number is under 2300, the flow type is laminar; while Reynolds number that above
4000 is turbulence flow.
The Reynolds Number calculation:
!" =
!!!
!" !
= !"# !
= !" !
Equation 12 [35]
Where:
µ is dynamic viscosity (Ns/m2
)
ν is kinematic viscosity (m2
/s)
For a pipe or duct the characteristic length is the hydraulic diameter. The Reynolds
Number for a duct or pipe can be expressed as:
!" =
!"!!
!
=
!!!
!
Equation 13
Hydraulic Diameter of a Circular Tube or Duct
!! =
4!!!
2!"
= 2!
Equation 14
Hydraulic Diameter of Rectangular Tubes or Ducts is

34
!! =
4!"
2 ! + !
=
2!"
! + !
Equation 15
The Reynolds number for both inlet and main channel are listed in Table 5
Table 5 Reynolds Number Calculation
Part mdot (kg/s) ρ (kg/m3
) Area (m2
) u (m/s) Dh (m) v (m2
/s) Re
inlet 0.011667 1000 2.8274×10-5
0.412625 0.006 1.004×10-6
2466
channel 0.011667 1000 0.00072 0.016204 0.02 1.004×10-6
323
According to the Reynolds number above inlet flow is transient; however for channel
flow it is laminar. The flow that I am researching is in the channel, therefore laminar
flow has been chosen in this model.
The software that I used is ANSYS-CFX with ICEM for meshing. The reason that I am
using ICEM is demonstrated in the next section. The solving computer was in Tyree
computer lab G17, windows 7 ANSYS workbench 14.5 parallel model.
5.2!CFD!Geometry!Development!!
The geometry of the model is shown in engineering drawing Figure 16. In this project,
only the fluid domain is generated for the simulation, according to CFX user guide, all
the conditions around the fluid can be applied in setups, therefore the fluid domain
geometry as presented.

35
Figure 16 Engineering Drawing of Fluid Domain
The inlet and outlet are at 6 mm diameter, 32.5mm length tubes are selected. Between
the tubes is a rectangular channel with a diameter of 410mm×60mm×12mm. the
position in the design model is shown in the isometric view, where the top glass is the
surface facing up. The top glass is exposed under the concentrated solar spectrum and
transmits radiation to the bottom glass.
This fluid domain is built in CATIA and was imported to ANSYS as a CATIA part file,
only one fluid domain has been generated, and one part file has been imported.
!

36
5.3!Grid!description!and!Refinement!!
The first mesh was done using an ANSYS default mesh model. The initial plan was to
slice the part into three to provide a simple geometry and sweepable surfaces. The mesh
quality was fine but inlet and outlet was cut-off from the main body and elements are
lack of consistency between them. As a result, the mesh was generated as one part of the
geometry. Many meshing methods have been applied due to the complexity of the part,
such as hex domain, face mapping, and edge sizing. Also a refinement was required for
the edges by using bias edge sizing, because for a turbulence flow, the boundaries are
required to be finer than the inside of the domain.
Figure 17 shows the screen shots of the side view and isometric view of the first mesh,
which has 114,838 elements.
`
Figure 17 Side View and Isometric View of the First Mesh
From the side view of the first mesh, it is very obvious that the mesh is not symmetrical
at the inlet. Additionally, from the results that I gained from this model, the symmetry
problem has a great influence on the flow stream. Therefore I used ICEM to generate
my mesh model. After a thorough study of ICEM tutorials, another mesh was generated
by creating blocks for the model. 21 blocks were created as a structured mesh model.

37
The ‘O-Grid’ method has been used for the inlet and outlet tube to create a symmetric
inflation.
The followed Figure 18 shows the blocks that I created for the model.
Figure 18 Created Blocks for Mesh C
To create such blocks, some steps have been taken, the schematics of the structured
mesh generation is shown in
Figure 19:
Figure 19 Structured Mesh Generation Schematics
Create a 3D block for the main channel
Cut the block in three by using absolute
dimensions
O-grid action to separate the middle block
Extend the middle block to cover both inlet and
outlet.
O-grid action to separate the extended block.

38
The following figures are the views of the mesh that has been generated in ICEM, finer
boundaries; gradual size change and Hex domain have been applied on the mesh
structure. The quality of the mesh is also coloured in the Figure 20.
Figure 20 Side View and Isometric View of Mesh
From the coloured mesh figure, shows that most of the mesh cubes are in very good
quality in blue, the surrounding of inlet and outlet has some green colour mesh but still
of an acceptable quality. This structured mesh has been checked statistically in ICEM,
and the critical data are shown below:
• Aspect ratio is between 1.0 and 8.6
• Determinant 2×2×2 is in the range of 0.7 to 1.0
A grid independence study has been conducted to verify the number of elements. The
determination of the convergence was chosen before the heat transfer model was
applied, and this is due to the fact that Monte Carlo method may contribute on the
fluctuation of the solution. Therefore the velocity of the central line of the fluid has

39
been chosen for the grid independence study. 10 points were selected along the central
line to determine the mesh convergence. Figure 21 is the chart with the velocity at each
point plotted.
Figure 21 Mesh Convergence Determination
It can be seen that the velocity of a model with mesh count smaller than 229,499 varies
dramatically at most points. However, the velocity of flow within a model with a mesh
count greater than 229,499 is smooth and steady. This indicates that a mesh count below
this number cannot describe the flow character accurately, and mesh count above this
number is suitable for further simulation study. For the purpose of simplicity and
resource management, a minimally acceptable number of mesh was set at 229,499 for
this simulation.
0!
0.1!
0.2!
0.3!
0.4!
0.5!
0.6!
28,869! 85,337! 104,159!144,587!179,564!210,001!229,449!270,609!307,071!
Velocity%m/s%
Element%count%
POINT!1!
POINT!2!
POINT!3!
POINT!4!
POINT!5!
POINT!6!
POINT!7!
POINT!8!
POINT!9!
POINT!10!

40
5.4!Boundary!Conditions!
5.4.1 Selection!and!Settings!of!Domain!
Fluid domain set as the geometry that has chosen in section 5.2. The material selection
is water since it is what was available in the experiment lab and can directly use for
validation. It is set as continuous fluid in 1 atmosphere with no buoyancy. The flow
model is chosen in laminar (see section 5.1.4).
In the energy application, a heat transfer is applied to the fluid domain, in the drop
menu of thermal energy in ANSYS, an Energy Transport Equation is solved which
neglects variable density effects. It is suitable for low speed liquid flow with constant
specific heats. An optional viscous dissipation term can be included if viscous heating
is significant. Moreover, a Monte Carlo radiation multiband method was applied on the
fluid domain under the thermal energy. An assumption of the radiation application is
that the radiation is evenly applied on the fluid, which may be hard to control in the
same distribution in the experiment case, but this is the ideal scenario. The screen shot
of the fluid domain thermal radiation is shown in Figure 22. A CEL code is applied for
this multiband method which is attached in Appendix B.

41
Figure 22 Setting Applied as Monte Carlo Ray Tracing Method
As in the nanofluids simulation, the material properties are set in water data, constant
fluid properties, with an applied function of spectral absorption coefficient, scattering
coefficient is set at 0, and also some other thermal properties. The major settings of
material properties are shown in Figure 23, where nanofluid 4 is presented. In the
absorption coefficient data input, more than 4000 data pairs are presented since it is the
most important parameter that is involved in the study. The data input screen shot is
shown in Figure 24, the CEL codes are attached in appendix C.

42
Figure 23 Major Changes of Nanofluid 4 Material Properties

43
Figure 24 Absorption Coefficient Data Input (nanofluid 4)
5.4.2!Inlet!!
The mass flow rate of inlet is 0.0116667kg/s as acquired from experimental data, inlet
fluid is at a static temperature which varies in different cases, it has been chosen at 20
Degree Celsius, 40 Degree Celsius, 60 Degree Celsius and 80 Degree Celsius.
5.4.3!Outlet!!
The average static pressure sets at 0 pa because the fluid domain is assumed to be
incompressible fluid, the mass flow rate is the same from inlet to outlet.

44
5.4.4 Top!and!Bottom!Glasses!
Both glass boundaries are sets at no slip wall with heat flux in the model, the heat loss is
discussed in section 4.3 that convective and radiation combined heat loss is applied. An
expression is applied to describe the heat flux which attached blow.
-((stefan)*0.92*((T^4)-(298.15^4)[K^4])+((4.882226981*(T*1[K^-1]-
298.15)))[kg s^-3])
Top glass is also applied with a source of radiation, where are the expressions named
“SpectralProp” that are attached in appendix A. Figure 25 shows the screen shot of this
radiation source.
Figure 25 Top Glass Applied in Radiation

45
5.4.5!Side!Walls!
It is assumed to be only one condition on all the sides, including inlet and outlet
boundary surfaces. They are set at no slip wall with heat flux, the expressions used in
CFX as a CEL code is:
-(0.2999986829*(T*1[K^-1]-298.15)[kg s^-3])
Those expressions for applied heat losses were associated with the various temperature
of the surface and ambient temperature at 298.15 Kelvin (25°C). These expressions in
ANSYS are solved numerically until the change in heat flux is minimised.
5.5!Schematics!Applied!!
5.5.1!Transient!Analysis!!
Iteration or convergence errors occur due to the difference between a fully converged
solution of a finite number of grid points and a solution that has not fully achieved
convergence. The majority of commercial CFD codes solve the discretised equations
iteratively for steady-state solution methodologies. For procedures requiring an accurate
intermediate solution at a given time step, the equations are solved iteratively in
transient methods. It is expected that progressively better estimates of the solution are
generated as the iteration step proceeds and ideally satisfies the imposed boundary
conditions and equations in each local grid cell and globally over the whole domain. [35]

46
5.5.2!HighTResolution!Schemes!
High-resolution schemes are used in the numerical solution of partial differential
equations where high accuracy is required in the presence of shocks or discontinuities.
They have the property of higher order spatial accuracy in smooth parts of the solution,
free spurious oscillations or wiggles solution, high accuracy around shocks and
discontinuities.
5.5.3!The!Discrete!Transfer!Model!
This model is based on tracing the domain by multiple rays leaving from the
bounding surfaces. The technique was developed by Shah (1979) and depends
upon the discretization of the equation of transfer along rays. The path along a
ray is discretized by using the sections formed from breaking the path at
element boundaries. The physical quantities in each element are assumed to be
uniform.
These rays have to be traced through the domain in the same way that the
photons would be tracked in the Monte Carlo model. Therefore, the model
description for both Monte Carlo and Discrete Transfer is identical.
For the results to be accurate the elements must be chosen so that the radiation
field is reasonably homogeneous inside them. This means, for example, that
they must be small enough that the scattering optical depth is less than unity
across each element.
Non-gray models are dealt with by treating each band as a separate calculation
(possible because scattering and reflection are assumed to be coherent).

47
Tracking is done only once, and the results for the bands are combined to give
the total radiative heat transfer
5.5.4!The!Monte!Carlo!Model!
The underlying processes of target systems (the physical interactions between photons
and their environment) are simulated by the Monte Carlo method. In this method, an
individual photon is selected among photon source. It will be tracked through the
system before its weight falling below some minimum. Every time when the photon
experiences a surface intersection, scattering or absorption etc., the physical quantities
of interest will be updated. A complete record is created for the photon in the system
during the process. Many photon records are necessary to estimate physical quantities of
interest in one system. Each band of Photon sources is treated independently for non-
gray models and Photon sources can be selected based on emitted radiation.
In CFX, the photons track across the domain is tracked by the main computational
overhead which can be utilised to generate the record. Therefore, a balanced description
of the domain to efficiently track the photons is essentially to be created. It can be
achieved by a rough mesh for the radiation field, rather than any other transport
variables. As a result, if there is no emit, absorb, and scatter radiation for the domain
material, it is not necessary to create a mesh in the volume since the radiation transfer is
only between the boundary surfaces.
5.6!Convergence!!
The convergence criteria is residual target at 10-4
, since the method of analysis is of the
transient type, so the iteration operated from 2-10 loops to keep the residual target under

48
10-4
. The momentum and mass curve kept under 10-4
from the iteration, and heat
transfer converges from 0.01 to 10-4
; at time step 500, the residual number reaches the
target value. The transient analysis requires a long computational time; therefore each
temperature condition takes around two days to compute. The momentum and mass and
Heat transfer solution chart is shown in Figure 26 and Figure 27.
Figure 26 Momentum and Mass Solution Chart
Figure 27 Heat Transfer Solution Chart

49
From the solution charts of momentum, it is clear that the solution variable value stays
below 10-4
which means in this part the solution is always converged within the
expected convergence criteria. On the other hand, a fluctuation is appeared in the chart,
it is only because the iteration is done automatically by 2-10 loops each time step and
the solution varies each time step, the chart connect each solution linearly so that some
jumps are on the curve.
In the solution curve of heat transfer chart, a convergence curve is appeared in the figure.
It can be explained by as the time goes by, the heat transfer happens dramatically at first
and reaches below 10-4
, then it can be explained as the heat transfer is still happening
but can be iterated within each time step.
5.7!Validation!and!Verification!!
5.7.1!Comparison!of!Results!
The CFD model is built in the same physical conditions as in the experiment, the
purpose of this project is to compare simulated results with the experimental results and
therefore verify the model in future studies of more conditions with the same principles.
Moreover, it is possible to make alterations from CFD model to save experiment time
and expenses. The result from the CFD model with water as the working fluid is shown
in Table 6.
Table 6 Results From CFD Model
Tm%(C)% Qu%(W/m)% Efficiency%(%)%
20.3674% 86.98602! 19%!
40.3422% 80.90954! 18%!
60.3017% 71.37979! 16%!
80.2474% 58.62867! 13%!

50
The efficiency is calculated from the followed equation.
! =
!!
!!
=
!!! !! − !!
!"
Equation 16
Where,
G = Incident radiation on the collector (W/m2
)
The validation data are the experimental data recorded by Felipe Crisostomo in the pre-
designed solar concentrator, located in the solar lab at UNSW. The data are also
recorded with water as the working fluid, which is as follows in Table 7.
Table 7 Experiment Result by Felipe Crisostomo
Tm%(C)% % Qu%(W/m)% Efficiency%(%)%
30% ! 80.12159! 18%!
40% ! 73.26763! 16%!
50% ! 65.73517! 15%!
60% ! 57.52418! 13%!
70% ! 48.63468! 11%!
80% ! 39.06667! 9%!
90% ! 28.82014! 6%!
100% ! 17.89509! 4%!
Since this project chose a different mean temperature from the experiment results, these
tables cannot clearly verify the result; see Figure 28 for a better comparison.

51
Figure 28 Efficiency Curves of Two Models
Figure 28 shows that both data sets are in a similar range, the curve at 0 (K·m2
/W) is
almost at the same point. As temperature increases, both efficiency curves are dropping
at a similar rate. The difference between them is that the slope, which makes the curves
deviate along the axis growth. The difference will be discussed in Chapter 7, but the
overall result is acceptable.
0!
0.02!
0.04!
0.06!
0.08!
0.1!
0.12!
0.14!
0.16!
0.18!
0.2!
0! 0.01! 0.02! 0.03! 0.04! 0.05! 0.06! 0.07! 0.08! 0.09! 0.1!
Efficiency(ŋ)
∆T/ G
Experiment%and%CFD%comparison%
CFD!model!
experiment!model!
Trendline!CFD!
Trendline!Experiment!!

52
6. Results!
6.1 Fluid!Domain!Flow!Result!
Some fundamental geometry of the CFD model is demonstrated before obtaining the
results. The Inlet and Outlet position are shown in Figure 29, solar radiation are applied
on the top glass directing to Z axis negative , and a default gravity direction in CFX is
also Z axis negative. A horizontal central plane is generated (Figure 29) to represent
some of the fluid characters, which is located on xy plane when z=0.
Figure 29 Basic Geometries of The Model
The model was simulated in different fluid materials; these are water and four selective
nanofluid. The absorption coefficient is different in different fluids as discussed in
section 4.4, but the fluid stream is similar from each other. Figure 30 shows the stream
line plot in the channel in global range when the fluid is water at 20ºC.

53
Figure 30 Stream Line Plot in the Channel (water 20ºC)
Figure 31 is when the fluid is used as water at 20ºC, the vector of velocity contour in
global range.
Figure 31 Velocity Vector of Fluid Domain (water at 20 ºC)
The velocity vector shows that velocities from inlet and outlet are significantly larger
than the fluid inside the chamber, but there is a relatively high region where the velocity

54
vectors are around 0.3m/s inside the chamber. The vectors in this region are pointing to
many directions that implicates the fluid fluctuate at this region.
Figure 32 is when the fluid is used as water at 20ºC, the temperature contour on
horizontal central plane.
Figure 32 Temperature Contour at the Central Plane (water 20ºC)
From the water temperature contour above, it can be seen that the cold water flows into
the system; it stays cold until passes the middle of the chamber and mixes with the rest
of the fluid. The corners of the chamber near the inlet have the peak temperature at
300K which can be explained as is bad mixture in the corner results in heat stagnation.
Figure 33 is the stream line of water at temperature of 40ºC. The inlet and outlet are
identified in the figure.

55
Figure 33 Stream Line of Water 40 ºC
Figure 34 is the vector plot of velocity of water at temperature of 40 ºC.
Figure 34 Vector of Velocity of Water at 40 ºC
The velocity vectors, it can be seen that outlet velocity are higher in some regions than
inlet, this is because after the flow mixes in the chamber, the outlet is not as evenly
distributed as inlet. The relatively high velocity region inside the chamber is similar
with water at 20 ºC.
Figure 35 is the temperature contour of water at temperature of 40 ºC.

56
Figure 35 Temperature Contour of Water at 40 ºC
The stagnation temperature point is at similar region which are near the inlet corners,
however, there is also a cold temperature region at the other corner. This also shows the
bad mixture in the channel.
Figure 36 is the stream line of water at temperature of 60 ºC. The inlet and outlet are
shown in the figure.
Figure 36 Stream Line of Water at 60 ºC

57
Figure 37 is the vector of velocity of water at temperature of 60 ºC in global range at
z=0 plane. The inlet and outlet still have the highest velocity of the whole domain; it
peaks at some part of the outlet. The high velocity region inside the channel is still
similar with other temperature conditions, which is in the middle and pointing to
different directions.
Figure 38 is the vector of velocity of water at temperature of 60 ºC on the horizontal
central plane.

58
The temperature contour of the central plane shows that the cold fluid comes in from
inlet and mix with the hot fluid inside the chamber, a fluctuation appears around the
middle part of the channel. However, the peak temperature appears at one side before
the fluctuation part. And the corners near the inlet are relatively cold compare to other
parts of the channel.
Figure 39 is the stream line of water at temperature of 80 ºC.
Figure 39 Stream Line of Water at 80 ºC
Figure 40 is the vector of velocity of water at temperature of 80 ºC.

59
From the vector of velocity of water at 80 ºC, it is similar from pervious velocity
vectors. It peaks at outlet which means the different velocity at different point of outlet,
a massive increase inside the channel that mix up the fluid around the midpoint.
Figure 41 is the temperature contour of water at temperature of 80 ºC.
It can be seen that the temperature mixture of water at 80 ºC is better than other
temperature conditions, but there are still cold points in the corners near inlet.

60
6.2 Radiation!Intensity!with!Different!Fluids!
The radiation intensity of fluid domain is shown in Figure 42 to Figure 46 different
tested fluid (water and four nanofluids) the screen shots are all in a similar position
where top glass is face up with inlet on the left side and outlet on the right.
Figure 42 shows the radiation intensity in water when inlet temperature is 20 ºC.
.
Figure 42 Radiation Intensity Volume Rendering of Fluid Domain (water 20 ºC)
Top glass is face up in this screen shot. It can be seen that inlet and outlet are
transparent which means no radiation in the volume. Top glass has the highest radiation,
while the intensity decreases as the radiation propagates through the channel. A problem
in this figure is that the top glass radiation is not evenly divided, and this may result in
solution error.

61
Figure 43 shows the radiation intensity in nanofluid 1 when inlet temperature is 20 ºC.
Figure 43 Radiation Intensity Volume Rendering of Fluid Domain (NF1 20 ºC)
The radiation intensity of nanofluid 1 has a similar distribution of radiation to water.
However, due to the nanofluid has a higher absorption coefficient, it has less intensity
of radiation than water. From Figure 43, it can be seen that the radiation intensity on the
top glass peaks at 858.1W/m2
sr and most of it is around 600 W/m2
sr. As a comparison
in water condition, most of the regions on top glass is at the peak radiation intensity of
951.5 W/m2
sr.

62

63
From all the radiation intensity volume rendering, the distrubution of incidence is
similar from on to another. A trend from these radiation intensity in differnet fluids is
that with a higher absobtion coefficient, comes with a lower radiation intensity. This can
be explain as such as nanofluid 4, a higher proportion of radiation is absorbed by the
fluid so that its intensity get lower. However all the figures have a inbalance intensity
on the top glass, this may happen because the velocity in the middle is higher or because
the CFD model is faulty.
Table 8 Temperature Results in All Fluids
%
Inlet%Temperature%(K)% Outlet%Temperature%(K)%
Water%
293.152! 293.8828!
313.152! 313.8324!
333.152! 333.7514!
353.152! 353.6428!
Nanofluid%1% 293.15! 293.9657!

64
313.15! 313.9246!
333.15! 333.8367!
353.15! 353.7269!
Nanofluid%2%
293.15! 293.975!
313.15! 313.933!
333.15! 333.849!
353.15! 353.7446!
Nanofluid%3%
293.15! 294.002!
313.15! 313.9519!
333.15! 333.867!
353.15! 353.765!
Nanofluid%4%
293.15! 294.0563!
313.15! 313.999!
333.15! 333.912!
353.15! 353.795!
All the fluid types are simulated in four inlet conditions, which are 20°C, 40°C, 60°C,
and 80°C. It can be seen from the temperature results table that the outlet temperature is
higher than inlet temperature, and higher outlet temperature in nanofluids especially in
nanofluid 4.
With the same energy input, the higher temperature difference means the higher
efficiency. All the temperature data are plotted in an efficiency curve which is shown in
Figure 47.

65
Figure 47 Efficiency Cure of All the fluids
!
0!
0.05!
0.1!
0.15!
0.2!
0.25!
C0.01! 0! 0.01! 0.02! 0.03! 0.04! 0.05! 0.06! 0.07!
Efficiency%(η)%
ΔT/G%
Efficiency%curve%of%all%fluids%
Water!
NF1!
NF2!
NF3!
NF4!

66
7. Discussion!of!Results!
7.1!Accuracy!Discussion!
Flow Stability
In the resulting output, the transient analysis method has been chosen instead of the
steady state method; the reason being is that steady state was not giving a satisfactory
result. In steady state, the convergence criteria for the residual target cannot reach 10-3
due to fluctuation of flow in the channel; and this has been verified by employing the
transient analysis type of flow stream animation that is recorded from 0s to 10s. The
fluctuations produced by the steady state analysis type results in an imprecise solution.
However, transient analysis not only calculates the solution in each time step, but also
iterates the solution until it reaches the residual target, as discussed in section 5.5, the
iterations are around 2-10 with system adaptation, and time step are also adaptive from
10-2
s to 10-3
s.
However, the transient analysis model still behaves unsatisfactorily if the iterative
process is terminated prematurely, where errors arise. Convergence errors therefore can
occur either because of the user being too impatient to allow the solution algorithm to
complete its progress to the final converged solution or because of the user applying
excessive convergence tolerances to halt the iteration process when the CFD solution
may still be considerably far from its converged state.
Physical Modelling Error
Physical modelling errors occur due to the uncertainties of the formulation in the
mathematical models. For example, the Monte Carlo method in radiation application
could be a significant reason to create more uncertainties on top of the fluctuating flow;

67
therefore physical modelling errors could be the other source of error in the simulation
model.
It can be seen from different temperature in water condition, the flow stream are differ
from one to another, so that the accuracy of this model has its limitation.
!
7.2!Comparison!with!Experimental!Data!
Figure 48 Efficiency Curve of All Fluids
As the description of Figure 48, the efficiency curve of both the CFD model and the
experiment shows that when ∆!/! = −0.005, the efficiency of the CFD model and the
experiment are almost the same. The curve diverged significantly after that and reached
up to 40% divergence. The reason of the difference could be explained by the following:
0!
0.05!
0.1!
0.15!
0.2!
0.25!
0! 0.02! 0.04! 0.06! 0.08! 0.1! 0.12!
Eﬃciency%(η)%
ΔT/G%
Eﬃciency%Curve%of%All%Fluids
Water!
NF1!
NF2!
NF3!
NF4!
Experimental!
Data!
Trendline!
Water!
Trendline!
NF1!
Trendline!
NF2!
Trendline!
NF3!

68
a) The emissivity is assumed to be the same from the CFD model, but actually
emissivity is highly depend on surface temperature.
b) The convection loss is assumed to be natural convection from the enclose area,
although in the experiment, the design is not fully enclosed and the roof of K17
could experience strong wind. The wind speed related to convection heat loss
coefficient is described in the following equation:
ℎ!"#$ = 3.8 + !
Equation 17
Where,
V= wind speed (m/s)
From the equation above, it can be seen that the convection heat loss coefficient
is highly depended on the wind speed, for instance, a 5m/s wind can bring the
hconv to 8.8 W/m·K. in the setup of CFD model, it was assumed to be natural
convection with a value of 5 W/m·K.
c) A higher heat transfer coefficient can result in a significant slope of efficiency
decrease.
7.3!Comparison!of!Different!Fluid!!
As in the description of Figure 48, the efficiency curve of all the fluids shows that
nanofluids have a higher efficiency than water, and nanofluid 4 has the highest
efficiency of all. The reason can be explained from the following:
Nanofluids have higher absorptivity, so the energy results in a correspondingly higher
increase of fluid temperature. With the same inlet temperature and increasing outlet
temperature, the temperature difference increases so that efficiency increases. However,

69
higher temperature also increases heat loss, so the slope is more significant in high
absorbance (e.g. nanofluid 4).

70
8. Conclusion!and!Suggestions!
The efficiency curve shows that nanofluids have better absorbance of radiation, so that
it is better to choose nanofluids when compared to water. On the other hand, the
efficiency curve is not the only determinant in the matter of fluid choice, since the PV
cell underneath receives the highest percentage of sunlight, and a good nanofluid should
also be able to filter out the wavelength that is not needed by the PV cell. This project is
intended to determine if the fluid is a good absorber, and to serve this purpose,
nanofluid 4 is the best among all the fluids studied.
In terms of future work the following points are to be taken into consideration:
• Future development of simulation is suggested to processed on ANSYS-Fluent,
so that the wall properties and materials can be defined more specifically. The
problem of CFX is that the wall boundaries cannot set as semi-transparent;
therefore there is no grantee of the wall that does not absorb heat.
• Future simulation is suggested to focus on radiation development, such as
attempt on Discrete Transfer Model. Application of radiation is yet to be studied
comprehensively.
• The geometry of the inlet tube to the channel should be gradual. From the
temperature contour, the corners of the rectangular channel are either high
temperature than surrounding areas or result in fluctuations in the flow.
Therefore the geometry should be redesigned to accommodate the flow stream
for effectively.
• Utilise a turbulent flow type within the simulation. Turbulent flow results in a
better mixture within the chamber and a more even temperature contour
throughout. In this project, the efficiency is not as high as expected because

71
without a good mixture, the temperature ‘hot points’ due to stagnant areas of
flow will escape by heat loss, and some other stream will leave to the outlet
without efficient absorption of radiation.
• A higher concentrated nanofluid can be adoped in the future to
• Since the efficiency curve drops suddenly in the experiment, a better insulation
is suggested for the enclosure of the device.
• Future development is needed on the PV cell part to optimise the efficiency of
the whole device.
• For a future design, a better procedure is start from simulation with designing at
the same time. By the time of a satisfactory result has been found in simulation,
then build up the rig and run an experimental test to compare with simulation
result.

72
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77
Appendix!A!
CEL Code of Expressions Input
SpectralProp = (prop1 * int1 + prop2 * int2 + prop3 * int3 + prop4 * int4 +
prop5 * int5 + prop6 * int6 + prop7 * int7 + prop8 * int8 + prop9 * int9 +
prop10 * int10 + prop11 * int11 + prop12 * int12 + prop13 * int13 )
Wavl1 = 0.390 [micron]
Wavl4 = 0.750[micron]
WavlHigh = 3.000 [micron]

78
WavlLow = 0.300 [micron]
heatout = -((stefan)*0.92*((T^4)-(298.15^4)[K^4])+((4.882226981*(T*1[K^-1]-
298.15)))[kg s^-3])
heatoutWOOL = -(0.2999986829*(T*1[K^-1]-298.15)[kg s^-3])
heatoutsidesAL = -(6833.3333*(T*1[K^-1]-298.15)[kg s^-3])
int1 = step(wavl1 -wavldim)
int10 = (step(wavl10 -wavldim)-step(wavl9-wavldim))
int13 = (step(wavlHigh-wavldim)-step(wavl12-wavldim))

79
prop1 = 38.47128705 [W/m^2]
prop10 = 202.8380201 [W/m^2]
prop11 = 28.60126153 [W/m^2]
prop12 = 25.7979039 [W/m^2]
prop13 = 0 [W/m^2]
prop2 = 831.433443 [W/m^2]
prop3 = 1163.397296 [W/m^2]
prop4 = 1029.119329 [W/m^2]
prop5 = 809.1933928 [W/m^2]
prop6 = 507.9341088 [W/m^2]
prop7 = 473.1538427 [W/m^2]
prop8 = 279.3812909 [W/m^2]
prop9 = 217.3162617 [W/m^2]
wavl1 = Wavl1 * 1[m^-1]
wavl10 = Wavl10 * 1[m^-1]
wavl11 = Wavl11 * 1[m^-1]
wavl12 = Wavl12 * 1[m^-1]
wavl2 = Wavl2 * 1[m^-1]

80
wavl3 = Wavl3 * 1[m^-1]
wavl4 = Wavl4 * 1[m^-1]
wavl5 = Wavl5 * 1[m^-1]
wavl6 = Wavl6 * 1[m^-1]
wavl7 = Wavl7 * 1[m^-1]
wavl8 = Wavl8 * 1[m^-1]
wavl9 = Wavl9 * 1[m^-1]
wavlHigh = WavlHigh * 1[m^-1]
wavlLow = WavlLow * 1[m^-1]
wavldim = wavelo * 1[m^-1]
END

81
Appendix!B!
Monte Carlo Band Derivation CEL Code:
SPECTRAL MODEL:
Option = Multiband
SPECTRAL BAND: a0300 to 0390
Option = Wavelength in Vacuum
Wavelength Lower Limit = WavlLow
Wavelength Upper Limit = Wavl1
END
Wavelength Lower Limit = Wavl1
END

82
END
END
END
END

83
END
END
END
END

84
END
END
Wavelength Upper Limit = WavlHigh
END

85
Appendix!C!
Nanofluid absorption coefficient function code
Nanofluid 1
LIBRARY:
CEL:
&replace FUNCTION: MatSpectralAbsorption1
Argument Units = [s^-1]
Option = Interpolation
Result Units = [m^-1]
INTERPOLATION DATA:
Data Pairs =
999308193333333,19.0782552412645,997645450915141,18.9600513919767,9
95988232558139,18.74407450755,994336510779436,18.5065931686984,9926
90258278146,18.297391560061,991049447933884,18.0892314987312,989414
052805280,17.8600077305814,987784046128501,17.6105127196866,9861594
01315789,17.4041619488983,984540091954023,17.2414571826729,98292609
1803279,17.095641859849,981317374795417,16.9285345258851,9797139150
5114……
Extend Max = On

86
Extend Min = On
Option = One Dimensional
END
END
END
END
Nanofluid 2
LIBRARY:
CEL:
INTERPOLATION DATA:
Data Pairs =
999308193333333,23.9226326805108,997645450915141,23.7003984977551,9
95988232558139,23.3792962602227,994336510779436,22.9818739594868,99
2690258278146,22.6691016703381,991049447933884,22.3095627363144,989

87
414052805280,21.9862788314584,987784046128501,21.6321523249703,9861
59401315789,21.3152473984989,......
Extend Max = On
Extend Min = On
END
END
END
END
Nanofluid 3
LIBRARY:
CEL:
INTERPOLATION DATA:

88
Data Pairs =
999308193333333,36.2764832108842,997645450915141,35.9583413568017,9
95988232558139,35.4465991321792,994336510779436,34.8950279423495,99
2690258278146,34.3608012514318,991049447933884,33.818972818931,9894
14052805280,33.2971701552953,9877840……
Extend Max = On
Extend Min = On
END
END
END
END
Nanofluid 4
LIBRARY:
CEL:

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