Active Forced Convection Photovoltaic/Thermal Panel Efficiency Optimization
Analysis
by
Bradley Fontenault
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
Master of Engineering
in Mechanical Engineering
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Engineering Project Advisor
Rensselaer Polytechnic Institute
Hartford, CT
April, 2012
© Copyright 2012
by
Bradley Fontenault
All Rights Reserved
ii
CONTENTS
Active Forced Convection Photovoltaic/Thermal Panel Efficiency Optimization
Analysis……………………………………………………………………………….i
LIST OF TABLES ............................................................................................................ iv
GLOSSARY ...................................................................................................................... v
LIST OF FIGURES .......................................................................................................... vi
NOMENCLATURE ........................................................................................................ vii
ACKNOWLEDGMENT .................................................................................................. ix
ABSTRACT ...................................................................................................................... x
1. Introduction.................................................................................................................. 1
1.1
Background ......................................................................................................... 1
1.2
Project Scope ...................................................................................................... 6
2. Methodology/Approach ............................................................................................... 7
2.1
PV/T Test Model and Arrangement ................................................................... 7
2.2
PV/T Panel Thermal Model ................................................................................ 8
2.2.1
Assumptions ........................................................................................... 8
2.2.2
Theory and Governing Equations .......................................................... 9
2.3
Test Cases ......................................................................................................... 12
2.4
Meshing ............................................................................................................ 14
2.5
Material Properties............................................................................................ 15
2.6
Solving .............................................................................................................. 16
3. Results and Discussion .............................................................................................. 18
4. Conclusions................................................................................................................ 28
5. References.................................................................................................................. 30
Appendix A: Test Case Supplementary Data .................................................................... 1
iii
LIST OF TABLES
Table 1: Summary of test cases ....................................................................................... 13
Table 2: Initial conditions for test cases .......................................................................... 14
Table 3: PV/T panel materials and study-relevant properties ......................................... 15
iv
GLOSSARY
Ethylene Vinyl-Acetate
EVA
Finite Element Analysis
FEA
Functionally Graded Material
FGM
Coefficient of Performance
COP
Concentrated Photovoltaic
CPV
Photovoltaic
PV
Photovoltaic and Thermal
PV/T
Shockley-Queisser
SQ
v
LIST OF FIGURES
Figure 1: Solar irradiance per day given in kWh per square meter per day [5] ................ 3
Figure 2: PV/T system proposed by Yang et al. [4] .......................................................... 5
Figure 3: PV/T solar panel simulation test set-up ............................................................. 8
Figure 4: Thermal model of a PV panel [12] ................................................................... 10
Figure 5: PV/T solar panel meshed in COMSOL using the physics controlled mesh
sequence ................................................................................................................... 15
Figure 6: Laminar flow profile common to all test cases ................................................ 19
Figure 7: Test Case “1a” two-dimensional surface plot of temperature at steady state . 20
Figure 8: Test Case “2a” two-dimensional surface plot of temperature at steady stat ... 20
Figure 9: Test Case “3a” two-dimensional surface plot of temperature at steady state . 21
Figure 10: Test Case “1d” two-dimensional surface plot of temperature at steady state 21
Figure 11: Water Velocity Impact to Average PV/T Cell Surface Temperature – Inlet
Water Temperature, Tin = 298.15 K ........................................................................ 22
Figure 12: PV/T Average Surface Temperature Impact to Average PV/T Output
Efficiency – Inlet Water Temperature, Tin = 298.15 K ........................................... 23
Figure 13: Water Flow Velocity Impact to Average Water Outlet Temperature – Inlet
Water Temperature, Tin = 298.15 K ........................................................................ 24
Figure 14: Water Flow Velocity Impact to Average PV/T Thermal Efficiency – Inlet
Water Temperature Tin = 298.15 K ......................................................................... 25
Figure 15: PV/T Panel Average Total Efficiency vs. Flow Velocity of Coolant Water –
Inlet Water Temperature, Tin = 298.15 K ................................................................ 27
vi
NOMENCLATURE
Symbol
A
A flowpath
Cp
Description
Units
2
PV cell Area
m
Cross-sectional area of the reservoir (assuming unit m2
depth)
Heat capacity at constant pressure
J/(kg*K)
C pwater
Dh
Ein
E pv
Ewater
hc, forced
Specific heat of water
4.18 J/(g*C)
Hydraulic diameter
Total solar energy into the cell
Electrical energy
m
W
W
Thermal energy extracted by water
Forced convection heat transfer coefficient
W
W/m2
I mp
Maximum power point current
Thermal conductivity
Mass of water
Electrical power out of PV cell
Flow rate of water
Heat flux
Heat source
Convective heat loss
Heat flux going into PV cell
A
W/(m*K)
g
W
ml/s
W/m2
W/m2
W
W/m2
Heat or energy into PV cell
Longwave energy
Heat or energy out of PV cell
Shortwave energy flux
W
W
W
W/m2
Shortwave energy
Solar irradiance
W
W/m2
Reynolds Number
Temperature
Ambient temperature
Water inlet temperature
Water outlet temperature
Temperature of PV cell
[]
K
K
K
K
K
Reference temperature
K
Time
Inlet water flow velocity
Fluid velocity
seconds
m/s
m/s
k
mwater
Pout
Q
q''
q'''
qconv
''
qheat
qin
qlw
qout
''
qsw
qsw
q
''
rad
Re
T
Tamb
Tin
Tout
Tpv
Tref
t
Uwater
u
vii
Vmp
bref
e
h pv
h pv
htot
hth
hTref
m
r
s
u
Maximum power point voltage
Temperature coefficient at reference temperature
V
1/K
Surface emissivity
Average cell electrical efficiency
[]
[]
PV cell electrical efficiency
[]
Total PV/T panel efficiency
Thermal efficiency of the cell
PV cell electrical efficiency at reference temperature
[]
[]
[]
Dynamic viscosity
Density
Stefan-Boltzmann constant
Kinematic viscosity of water at 25 C
Pa*s
kg/m3
5.67e-8 W/(m2*K4)
9.137e-7 (m2/s)
viii
ACKNOWLEDGMENT
I would like to thank Rensselaer Polytechnic Institute for the resources and professionals
that have provided me with an invaluable education that I plan on using throughout the
rest of my career as an engineer. I would like to especially thank Dr. Ernesto GutierrezMiravete for all his help and patience he provided throughout the completion of this
project. Also, this couldn’t have been possible without the financial support of Electric
Boat Corporation. Most importantly, I would like to give my upmost thanks to my
family and to my wife, Katelyn, for providing endless and unconditional support
throughout my education program at RPI.
ix
ABSTRACT
The electrical output efficiency of a photovoltaic (PV) cell, similar to any other
semiconductor, is negatively impacted as its temperature increases; however, they must
be arranged in direct sunlight to produce electricity. To optimize the capability of PV
panels and decrease accelerated PV cell wear by controlling their operating temperatures
measures must be taken. A preliminary design for a photovoltaic thermal (PV/T) solar
panel has been developed and analyzed to control the inherent temperature increase of
PV cells to increase electrical efficiency, while also carrying the absorbed heat away
from the panels for a myriad of applications. The cooling system consists primarily of a
thin rectangular aluminum reservoir that is mounted to the backside of PV/T panels
through which water flows. Several water flow rates and reservoir thicknesses were
analyzed to determine which combinations of these factors produced optimal PV/T panel
cooling results, thus the greatest PV/T panel electrical efficiency. Thermal efficiency of
the PV/T panel was also calculated and compared for the various combinations of flow
velocity and reservoir thickness. The total panel efficiency is resultantly an additive
efficiency of thermal and electrical efficiencies. It was found that the higher total
efficiencies were achieved in configurations utilizing the highest flow rates and largest
reservoir thickness. However, high flow rates translated to minimal net temperature
differences between the PV/T panel inlet and outlet, which is undesirable. Heat transfer
between the PV/T panels and the cooling reservoirs was modeled and simulated in
COMSOL.
x
1. Introduction
1.1 Background
Global warming, rising fuel oil prices, and other environmental factors in the world
today are influencing organizations to develop green energy technologies to be used by
corporations and individual consumers. One such technology was invented in 1894 by
Charles Fritts and is referred to as the photovoltaic (PV) cell [1]. PV cells convert
sunlight into electrical energy, which can be harnessed and supplied to the electrical
grid. The first PV cell created by Fritts was only 1% efficient; however, modern day
single junction solar cells have efficiencies up to 23% [2], which is approaching the
Shockley Queisser (SQ) Limit of 33% [3]. The SQ Limit was developed in 1961 by
William Shockley and Hans Queisser and represents the maximum theoretical efficiency
of a perfect solar cell using a p/n junction to extract electrical power at standard test
conditions.
New PV technologies have been shown to improve energy utilization efficiency, such as
multi-junction cells, optical frequency shifting, and concentrated photovoltaic (CPV)
systems, among others; however, these technologies are expensive both in acquisition
and maintenance costs and resultantly have not been utilized on a wide scale at this time
[4].
By visual inspection of the aforementioned SQ limit, most (67%) of solar energy is lost,
or unable to be harnessed to produce usable electricity. Of this 67% of lost energy,
approximately 47% can be attributed to solar energy being converted to heat, which
directly correlates to an increase in PV cell operating temperature. Approximately 18%
of photons pass through the PV cell, 2% of the solar energy is lost to other factors, and
the remaining 33% of solar energy accounts for maximum theoretical energy that can be
converted to electricity [3]. It should be noted that for the statements above to be valid, it
is assumed that there is only one semiconductor material be used per cell; only one P/N
junction per cell is employed; the sunlight is not concentrated or magnified; and all solar
energy is converted to heat from photons greater than the band gap of the semiconductor
1
material be utilized. Multi-junction PV cells, CPV systems, and other advanced PV
systems can exceed the SQ limit, thus it is not applicable to those types of systems.
The term band gap refers to the energy difference between the top of valence (outer
electron) band and the bottom of the conduction (free electron flow) band. In the valence
band, electrons are tightly held in their orbits by the nuclear forces of a single atom. In
the conduction band, electrons have enough energy to move freely and are not tied to
any one atom. Materials with a small band gap which behave as insulators (large band
gaps) at absolute zero but allow excitation of electrons into their conduction bands (at
temperatures below their melting point) are called semiconductors.
Electrical voltage is created when electrons flow from one band to the other (valence to
conduction), which is brought upon by an external force: photons from sunlight with the
energy required to cross the band gap [3]. Photons with energy less than the band gap
will pass through the PV cell. Photons with energy greater than the band gap energy do
excite electrons and make them flow to produce usable voltage, however, excess photon
energy is dissipated to generate heat.
PV cell semiconductor materials are chosen to be able to absorb most of the solar light
spectrum as possible, in order to generate the most amount of electricity possible, which
results in a low band gap. However, materials with larger band gaps produce more
voltage, which consequently relates to a narrower spectrum of sunlight that can be used.
Therefore, a balance between the amount of usable sunlight and voltage output must be
found when choosing PV cell semiconductor materials. PV cell semiconductor materials
with smaller band gaps may be more subject to higher operating temperatures, because
the energy content of photons above the material band gap will be generated into heat as
a byproduct [3]. Most solar cells today are made from silicon, the second most abundant
element in the earth's crust, which happens to have one of the lowest band gaps among
other materials used to make PV cells [2].
In commercial and residential applications, PV cells are assembled into modules, which
are then assembled into panels. PV panels are then assembled to form arrays. The most
2
applicable regions to use PV panels are in environments with plentiful amounts of sun
exposure, which most often are regions with warm climates (i.e. high ambient
temperatures). This is especially true for the United States, which is shown by Figure 1
below. Figure 1 graphically shows the average daily solar radiation in Kilowatt-hours per
square meter per day that falls on the United States.
Figure 1: Solar irradiance per day given in kWh per square meter per day [5]
PV panel temperature increases due to low solar energy-to-electricity efficiencies
because not all energy absorbed by PV cells can be converted to electrical energy;
therefore, to satisfy conservation of energy laws, the remaining energy must be
converted to heat. Also, regions with warm climates (i.e. high ambient temperatures),
where solar energy potential is at its greatest as shown above, reduce the efficiency of
PV panels by limiting the heat dissipation from the panels. Therefore, it is relevant and
essential to develop methods of cooling the PV cells to increase output efficiency. This
is especially true for CPV systems, which essentially magnify the solar illumination
being received by PV panels [6]. The temperature of adequately ventilated CPV systems
3
can reach upwards of 70 degrees Celsius, which can be harmful to the PV panels and
reduce their operating lifetime. Oh et al. [7] has found that poorly ventilated PV panels
in environments with high ambient temperatures can reach temperatures greater than 90
degrees Celsius. These conditions can be extremely dangerous to people who may be in
the vicinity of the panels and can also decrease the service life of the panels.
Both active and passive methods of cooling PV panels have been researched and
analyzed to date. Conclusions of these studies have been made that controlling the
temperature increase of PV panels results in significant gains in electrical output of the
panels. In many of these investigations, the thermal energy extracted from the PV panels
has been utilized for a variety of low temperature applications (i.e. residential water
heating, radiant floor heating, swimming pool heating, etc.). These systems are referred
to as hybrid photovoltaic and thermal (PV/T) systems. Teo et al. [8] investigated an
active PV panel cooling system, in which the PV panels were cooled by forced
convection, with air being the heat carrying fluid, and resulted in a 4-5% efficiency
increase. Chen et al. [9] developed a hybrid PV/heat pump system using refrigerant fluid
R134a as the heat carrying fluid. The coefficient of performance (COP) of the heat pump
and electrical efficiency of the PV panel was measured at different condensing fluid flow
rates and temperatures. Bakker et al. [10] analyzed a PV/T panel array where heat was
extracted from the panels and stored underground in a heat exchanger. In winter, the
heat could be extracted from the ground via a heat pump and used to heat potable water
and support a floor heating system while increasing the electrical efficiency of the solar
panel.
The largest PV/T solar panel installation in the United States was brought online in
February 2012 in Rhode Island at Brown University’s Katherine Moran Coleman
Aquatics Center. In this application, 168-patented PV/T panels were installed on the
center’s roof, which under full sun exposure can provide enough electricity to light the
building and heat the one million gallon swimming pool inside of it [11].
Yang et al. [4] developed a functionally graded material (FGM) with copper water pipes
cast into it that was bonded with thermal paste to the backside of a PV/T panel. Cooling
4
water was pumped at various flow rates through the cast copper pipes to decrease the
PV/T panel temperature thus increasing PV/T panel electrical efficiency by up to 2%.
This study also analyzed the thermal efficiency of the FGM/copper tube design, and
reported that a combined thermal and electrical efficiency of 71% could be achieved,
compared to 53-68% total efficiency of other PV/T concepts. The system design
proposed by Yang et al. is shown below in Figure 2.
Figure 2: PV/T system proposed by Yang et al. [4]
This study leverages off work previously accomplished by Yang et al. [4], by utilizing
the identical PV/T panel and thermal glue properties; however, a thin rectangular
reservoir through which water will flow through and carry heat away from the panel will
be developed and analyzed in lieu of the FGM with cast copper water coolant pipes
explored by Yang. This is accomplished in COMSOL MultiphysicsTM finite element
software package. Increases in electrical efficiency of the panel at various operating
temperatures will be calculated from the subject PV/T panel thermal coefficient, bref .
5
1.2 Project Scope
The objective of this study is to investigate a preliminary PV/T panel design using finite
element analysis (FEA) to determine the anticipated gains in electrical efficiency that
can be achieved, as well as to quantitatively determine the amount of thermal energy that
can be captured. The subject design includes a reservoir that is mounted to the backside
of a predefined PV/T panel through which water will flow and carry heat energy away
from the panel. The electrical efficiency of the PV/T panel is expected to increase as the
cell operating temperature decreases, while the thermal energy carried away from the
PV/T panel be utilized for numerous applications (i.e. heating a swimming pool, heating
potable water, use in radiant floor heating systems, etc.). The scope of this project will
be limited to the analysis of the heat transfer between the PV panel and the reservoir
bonded to the panel, the resulting increase in PV/T panel electrical efficiency, and the
thermal energy extracted from the panel. The total PV/T panel efficiency will be
calculated as a function of both the electrical and thermal efficiency of the panel. This
study will not consider the entire recirculating water system that delivers water to the
panel reservoir and carries the heated water away from the panel; this project rather, is
focused primarily on the affect to electrical efficiency of the PV/T panel and the thermal
energy that can be extracted from it.
6
2. Methodology/Approach
In this project, a single PV/T panel will be evaluated using COMSOL MultiphysicsTM
FEA software, from which results could be extrapolated for an array of identical PV/T
panels. An aluminum reservoir will be modeled in COMSOL for the subject PV/T
panel, through which water at a predetermined inlet temperature will flow. Three
different reservoir thicknesses will be analyzed to determine the impact they have on
cooling the panel. As this study investigates forced convection using water as the
coolant, or heat carrying fluid, various water flow rates will also be analyzed for impact
to cooling performance with qualitative consideration given to the size of pump needed
for the flow rates (greater size correlates to more electricity needed to operate pump).
2.1 PV/T Test Model and Arrangement
As mentioned in Section 1.1, work being done in this study will utilize the PV materials
defined in the work done by Yang et al. [4], and will use the uncooled PV/T panel data
as a reference point since an experimental analysis of the subject PV/T design was not
feasible for this project.
The PV cells making up the PV panel assemble into an
approximate length, width, and thickness of 30.5 cm X 30.5 cm X 0.27 mm,
respectively. For simplicity, it is assumed that the whole panel is covered in PV cells,
with no packing material (material used to fill in gaps between the cells on a panel). The
PV cells are commercial grade monocrystalline silicon cells with electrical efficiency,
hT , of 13% and have a thermal coefficient, bref , of 0.54% [1/K] [4]. The thermal
ref
coefficient represents the degradation of PV cell output per degree of temperature
increase.
The cooling reservoir is bond to the back of the panel by a thermal paste with an
approximate uniform thickness of 0.3 mm over the whole surface area of the reservoir –
PV panel interface. The reservoir walls are approximately 1 mm in thickness and are
constructed from aluminum. Aluminum was chosen as the reservoir enclosure material,
due to its high thermal conductivity, which promotes heat transfer across its boundary,
its availability, and its relatively low cost in comparison to other conductive metals such
7
as copper. A cross section view of the assembly is shown below in Figure 3. Similar to
Yang et al. [4], it is also assumed that the conceptual PV/T panel being considered in
this project is not coated with a protective glass and/or a layer(s) of ethylene vinylacetate (EVA), both of which are typically used to protect PV cells in real world
applications.
However, while protecting the delicate silicon PV panels, these
encapsulation materials hinder the performance of PV panels by affecting the panel’s
absorptivity of solar irradiance. Teo et al. [8] found that the highest temperatures
experienced in a PV panel are on the backside of the panel due to the high thermal
conductivity of the silicon PV material; therefore, precedence exists for cooling the
panel from the backside rather than using water to cool the panel on the topside.
Figure 3: PV/T solar panel simulation test set-up
2.2 PV/T Panel Thermal Model
2.2.1
Assumptions
Several assumptions must be made to perform this study regarding the conceptual PV/T
panel construction, atmospheric conditions, water flow characteristics, and other factors,
which impact this thermal analysis.
8
1. The solar irradiance imparted on the entire surface of the PV/T panel is 1000
W/m2.
2. All solar irradiance that is not used to produce electricity in the PV/T panel
will be developed into heat.
3. The subject conceptual PV/T panel is not constructed with a glass and/or
EVA encapsulating layer, which would result in decreased PV/T absorption
of solar irradiance.
4. No dust or any other agent is deposited on the PV/T surface affecting the
absorptivity of the PV/T panel.
5. The coolant water at the inlet of the conceptual PV/T reservoir will have
uniform temperature.
6. The flow through the coolant reservoir is considered to be fully laminar and
incompressible.
7. The ambient temperature surrounding the PV/T panel is 298.15 K.
8. An average wind speed of 1 m/s exists throughout the simulations.
2.2.2
Theory and Governing Equations
All three modes of heat transfer are involved when considering a basic PV panel. Heat
is transferred within the PV cell and its structure by conduction and heat is transferred to
the PV/T panel surroundings by both free and forced convection. Heat is also removed
from the panel in the form of long-wave radiation [12]. Heat transfer by conduction to
the panel structural framework is often ignored due to the small area of contact points;
however, it will be considered throughout the COMSOL simulations from the PV/T
panel surface and through the reservoir casing. The heat conduction through from the
PV/T cell surface to the reservoir enclosure casing is given by Equation [1] below.
rCpDT = -Ñ× (kÑT)
The PV panel thermal model can be simply described by Equation [2] below
9
[1]
rCpDT = qin - qout + q'''
[2]
The heat source term, q''' , is zero since there is no heat generation within the PV cell. In
Figure 4 below, this is shown in a thermal model diagram of a PV panel and can be
mathematically described by the expression in Equation [3]. It should be noted that all
the terms in Equation [3] could be impacted by environmental factors such as cloud
cover, ambient temperature, wind, angle of the PV panel to the sun, and many other
factors. This study will keep these variables constant while systematically varying the
selected parameters already identified to determine the most optimal system design.
Figure 4: Thermal model of a PV panel [12]
rCpDT = qsw - qlw - qconv - Pout
[3]
The heat loss due to forced convection on the top and bottom surfaces of a PV cell is
given by Equation [4] below [12].
qconv = -hc, forced × A × (Tpv - Tamb )
[4]
In this study, forced convection does not only occur on the top surface of the PV panel,
but also through the reservoir mounted to the backside of the panel. Therefore, the total
convective heat transfer is a combination of the heat transfer at the top and bottom
surfaces of the PV/T panel and the heat transfer from the flowing water in the reservoir.
10
The FEA software being used in this study, COMSOLTM, contains a non-isothermal
laminar flow and conjugate heat transfer physics package, which is being used to model
the convective heat transfer in the water reservoir on the backside of the PV panel. This
package is appropriate for this study, because of the inhomogeneous temperature field
that is created as water flows from the inlet to the outlet of the reservoir. COMSOLTM
numerically solves the fully compressible continuity and momentum equations, which
are the governing equations for the fluid flow, and are shown below in Equations [5] and
[6], respectively [15].
Ñ× (ru) = 0
[5]
æ
è
(
)
2
3
ö
ø
ru × Ñu = -Ñp + Ñ × ç m Ñu + ( Ñu) - m ( Ñ × u) I ÷
T
[6]
The conduction-convection equation is also solved, which is shown in Equation [7].
rCpu× ÑT = Ñ× ( kÑT )
[7]
The longwave radiation heat loss can be calculated from Equation [8] below [12].
4
qlw = e × s × (Tpv4 - Tamb
)
[8]
The thermal model analyzed in this study is similar to that modeled by Jones and
Underwood [12], although the amount of energy applied to the PV cell that is converted
to heat energy is calculated using the same method Kerzmann and Schaefer [13] utilize.
The heat energy going into the PV cell is a function of the PV cell efficiency, h pv , as
shown below in Equation [9], which satisfies Assumption 2 above.
''
''
qheat
= qrad
× (1- h pv )
11
[9]
The PV cell electrical efficiency, h pv , is given by Equation [10] below as a function of
its efficiency at reference temperature, the PV cell temperature, and the PV cell thermal
coefficient [14].
h pv = hT éë1- bref (Tpv - Tref )ùû
ref
[10]
The PV cell electrical output efficiency can also be expressed as a function of PV cell
power output, solar irradiance, and the PV cell surface area as shown in Equation [11]
below [8].
h pv =
Vmp I mp
''
qrad
A
[11]
In Equation [10], hTref is the PV cell efficiency at reference conditions (i.e. Tref = 25°C ,
''
qrad
=1000
W
), and bref is the PV thermal coefficient.
m2
The thermal model of the PV/T system being analyzed is complex, in which the PV cell
temperature, PV cell electrical output efficiency, and the amount of energy being
converted into electricity and into heat to increase the PV cell temperature are all
interrelated. Similar studies such as the study being presented in this work have been
performed by Kerzmann and Schaefer [13], who numerically solved a similar PV/T
complex system, and Yang et al. [4], who analyzed another type of PV/T system using a
different commercial FEA software package, ABAQUS.
2.3 Test Cases
Numerous test cases will be simulated in COMSOL, in which water inlet velocity and
reservoir thickness will be varied to determine an optimal design for the PV/T system.
A constant ambient temperature of 298.15 K will be used for all test cases to simulate
laboratory test conditions and to concentrate the focus of performance impacts of the
12
aforementioned variables. A summary of the test cases is shown in below. It is shown
that for each test case, the flow was confirmed to be laminar to satisfy Assumption 6 by
confirming that the dimensionless Reynolds number, Re, was less than 2300. The
Reynolds number is given by Equation [12] below.
Table 1: Summary of test cases
In Table 2 below, the invariable initial conditions for the test cases are shown. Many of
the initial values shown in the table have been discussed thus far. One however, that has
not, is the heat transfer coefficient used for the heat convection occurring at top and
bottom of the PV/T panel. Jones and Underwood [12] source values for the forced
convection heat transfer coefficient at a nominal wind speed of 1
a PV panel from various sources, which range from 1.2
m
on the top surface of
s
W
W
to 9.6 2
. Similar
2
m ×K
m ×K
correlations were made for heat transfers coefficients on the bottom side of a PV panel.
An average of the subject values of approximately 6.5
W
for forced convection will
m2 × K
be used in this study for convection occurring at the top and bottom surfaces of the PV/T
panel, which satisfies Assumption 8 above.
13
Table 2: Initial conditions for test cases
2.4 Meshing
The PV/T solar panel was meshed in COMSOL using the built-in physics controlled
mesh sequence setting. As shown in Figure 5 below, the number of mesh elements
increase at each boundary so that the heat transfer and flow fields can be resolved
accurately. A normal mesh setting was used in this study to decrease the physical time
of running all of the required simulations in COMSOL, while ensuring that accurate
results were obtained. Finer meshes were experimented with but were found to increase
simulation time reasonably, while subtle changes were observed in the solutions for cell
and cooling water temperatures for the same initial conditions.
14
Figure 5: PV/T solar panel meshed in COMSOL using the physics controlled mesh sequence
2.5 Material Properties
The materials used to construct and analyze the conceptual PV/T system shown above in
Figure 3, consist of silicon, silicone thermal paste, aluminum, and water for the PV/T
cell, binding agent, reservoir enclosure, and coolant fluid, respectively. Below, in Table
3, the properties of these materials that are relevant to this study are shown. The values
shown for water that are indicated to be temperature dependent are actively provided by
COMSOL at each time step while it is resolving the simulation.
Table 3: PV/T panel materials and study-relevant properties
15
2.6 Solving
As mentioned in this paper previously, the FEA software package, COMSOLTM, was
used to simulate and solve the flow and heat transfer model described thus far using
various equations defined in Section 2.2 of this paper. All of the simulations run were
steady state studies solved in two dimensions as shown by Figure 5, in which the
conjugate heat transfer and laminar flow physics packages were utilized. It was verified
that all the flow velocities used would produce laminar flows, rather than turbulent
flows, by calculating the Reynolds number, Re, from Equation [12] shown below. For
this study, the flow in the channel can be characterized by flow between parallel planes,
in which the hydraulic diameter, Dh , becomes twice the plate spacing [16].
Re =
Uwater Dh
[12]
u
The software modeled the flow through the PV/T reservoir by solving the formulations
of the continuity and momentum equations.
At each time step in the simulations
performed, the PV cell efficiency, h pv , is calculated from Equation [10] from the user
input values for bref , hTref , Tref , and from the COMSOL solved value for the cell
''
''
temperature, Tpv . The amount of solar irradiance, qrad , that is goes to heat, qheat , is then
calculated from Equation [9]. Similarly, values for the thermal efficiency of the cell
were calculated iteratively by COMSOL using Equations [13], [14], and [16] below.
Convergence of the steady state solution was monitored throughout the simulation,
which on average, converged in approximately 30-40 seconds (real time).
Post processing of the data recorded in the simulations is required to calculate the
thermal efficiency, hth , of the PV/T panel [4]. First, the total amount of energy (solar
irradiance) into the cell must be calculated, which is given by Equation [13] below.
16
''
Ein = qrad
×A
[13]
Next, the thermal energy of the extracted by the water per second must be calculated
from Equation [14].
·
Ewater = mwater Cpwater (Tout - Tin )
[14]
·
The mass flow rate of the water,
m water
, passing through the reservoir can be calculated
from the density and flow rate of the water, assuming unit depth of the reservoir. For
three-dimensional analysis, the depth could be extrapolated to any desired depth. The
mass flow rate is given by Equation [15] below.
·
m = rQ = rUwater A flowpath
[15]
The thermal efficiency is simply given by Equation [16].
hth =
Ewater
Ein
[16]
Similarly, the quantity of the total input energy converted to electrical energy can be
approximated from the solution data by obtaining the average electrical efficiency of the
PV/T panel, a COMSOL derived value taken across the top layer of the model, and
multiplying it by the total energy into the panel,
Ein
. This is shown by Equation [17].
E pv = h pv × Ein
[17]
The total efficiency of the PV/T panel is then computed from Equation [18].
htot =
(E
water
+ E pv )
Ein
[18]
17
3. Results and Discussion
Using the initial values shown in Table 2, each of the test cases in Table 1 was simulated
in COMSOLTM, which solved the governing equations for the PV/T system discussed in
Section 2.2.2, above. Data extracted from COMSOLTM following each simulation for
post processing included the average cell surface temperature, Tpv , average water outlet
temperature, Tout , average PV/T panel thermal efficiency, hth , and the average PV/T
panel electrical efficiency, h pv . The values for hth after each simulation were also
manually calculated in Microsoft Excel using Equations [14] and [16] and the extracted
values for Tout . Comparison of the manually calculated values for thermal efficiency
and the COMSOL calculated values differed significantly. This is due to the fact that
the average water temperature at the outlet was used to calculate the thermal efficiency;
however, COMSOL iteratively solved for the thermal efficiency at each time step in the
simulation, which is a more accurate method.
For the remainder of this paper,
discussion of thermal efficiency values will correspond to values calculated by the
software. Using the data extracted from the COMSOL solutions, the results in the
following sections were compiled.
The simulations performed assumed that the water inlet temperature was of uniform
temperature equal to 298.15 K (25 °C), which is the same temperature specified for the
ambient temperature. This water temperature was chosen to imitate a scenario in which
the cooling water may reach ambient air temperature before entering the cooling
reservoir to carry heat away from the PV/T panel. For the remainder of this section,
flow reservoir thickness and flow channel thickness are to be considered interchangeable
terms.
In Figure 6, the velocity profile of the water in the flow channel is shown. A similar
laminar flow profile was achieved in each of the test cases and is only shown once here
for information. One can see the no-slip boundary condition invoked on the interior
walls of the reservoir, and the parabolic flow profile that is created. As expected, the
maximum flow velocity is at the center of the flow channel.
18
Figure 6: Laminar flow profile common to all test cases
In Figure 7 through
Figure 9 below, two-dimensional plots for the steady state solution of the temperature
distribution for test cases 1a, 2a, and 3a are shown. As specified in Table 1, the only
difference between these cases is the reservoir flow thickness, while the inlet flow
velocity is invariable. As shown in the figures below, the reservoir flow thickness has a
19
large impact on the overall temperature of all materials that the PV/T system is
comprised of. From inspection of the figure legends, it can be deduced that the greater
the flow channel thickness at low flow velocities, the cooler the system will remain. A
compilation of temperature gradient plots and additional results data for all test cases run
are displayed in Appendix A.
As shown below, for the largest flow channel thickness of 0.015 m, the maximum
temperature reached on the PV/T surface is approximately 319 K, while the maximum
temperature reached for the thinnest flow channel is approximately 327 K.
As
anticipated, one can see that the water temperature is warmest towards the top of the
flow channel and almost linearly decreases as distance from the top of the channel
increases.
Figure 7: Test Case “1a” two-dimensional surface plot of temperature at steady state
20
Figure 8: Test Case “2a” two-dimensional surface plot of temperature at steady stat
Figure 9: Test Case “3a” two-dimensional surface plot of temperature at steady state
In Figure 10 below, the temperature gradient across the PV/T system is shown for a high
flow velocity test case. In comparison to low velocity temperature gradient plots, one
can see the effect velocity has on the temperature gradient of the cooling water.
21
Figure 10: Test Case “1d” two-dimensional surface plot of temperature at steady state
This phenomenon is shown further by visual inspection of the raw data extracted from
the COMSOL solutions to develop Figure 11, which represents the results obtained from
Test Cases “1a” through “3d” shown in Table 1. From Figure 11, it is also inferred that
the higher the cooling water velocity, the lower the average PV/T surface temperature
will be. This was also expected, as the faster the cooling water travels through the PV/T
system, the less time it has to dwell in the reservoir to collect additional heat, thus
increasing its temperature. As the water temperature increases in the reservoir, the
difference in temperature between the PV/T surface and the water decreases, resulting in
decreased heat transfer across the reservoir-thermal paste interface.
From the data
shown in Figure 11, it is shown that the average PV/T surface temperature can approach
temperatures of approximately 318 K, when it is equipped with the narrowest flow
channel thickness of 0.005 m at the lowest flow velocity of 0.0002 m/s. However, the
surface temperature can be expected to approach 312 K when the PV/T panel is
equipped with the largest flow reservoir at the lowest flow velocity analyzed in this
study. At the highest flow velocity examined, the PV/T surface temperature actually
reaches the lowest temperature when the narrowest reservoir is utilized. Therefore, it is
shown that large flow channels at high velocities result in higher average surface
temperatures. Appendix A contains plots of the steady state surface temperature as a
function of the length of the PV/T panel for each of the cases simulated.
22
Water Flow Velocity Impact to Average PV/T Cell Surface Temperature
Water Temperature at Inlet Tin = 298.15 K
320
318
316
314
312
PV/T Cell Average 310
Surface Temperature
308
(K)
Flow Channel = .015 [m]
Flow Channel = .01 [m]
Flow Channel = .005 [m]
306
304
302
300
298
0
0.002
0.004
0.006
0.008
0.01
0.012
Inlet Flow Velocity, Uwater (m/s)
Figure 11: Water Velocity Impact to Average PV/T Cell Surface Temperature – Inlet Water Temperature,
Tin = 298.15 K
From a cell electrical output efficiency standpoint, the cooler the PV/T surface is, the
greater the efficiency will be, which is shown in Figure 11 and
. By visual inspection, it is shown that a cell output efficiency of approximately
11.2% can be expected from the PV/T system with the smallest reservoir thickness
with water flowing at the lowest inlet velocity examined. For this case, the output
efficiency of the PV/T panel is comparative to the output efficiency of an uncooled
(i.e. negligible flow velocity) PV/T panel, which was shown to reach a saturated
average temperature of approximately 328 K (55 °C), resulting in an output efficiency
of 10.9%. It should be noted that the simulated uncooled average PV/T surface
temperature of 328 K corresponds well to the uncooled PV/T surface temperature
obtained by Yang et al. [4].
23
PV/T Average Surface Temperature Impact to Average PV/T Output Efficiency
Water Temperature at Inlet Tin = 298.15 K
14
13
12
PV/T Cell Average
Output Efficiency,
ηpv(%)
11
Flow Channel = .015 [m]
Flow Channel = .01 [m]
10
Flow Channel = .005 [m]
NTOC Efficiency at 298.15 [K]
9
PV/T Efficiency Without Cooling
8
295
300
305
310
315
320
PV/T Average Surface Temperature (K)
Figure 12: PV/T Average Surface Temperature Impact to Average PV/T Output Efficiency – Inlet Water
Temperature, Tin = 298.15 K
As previously mentioned, the smallest reservoir thickness at the high inlet velocity
results in the lowest average PV/T surface temperature, thus the highest PV/T output
efficiency of approximately 12.9%, which approaches the NTOC PV output efficiency
of 13%. It should be noted, however, that the difference in cell efficiency and surface
temperature at the three higher flow velocities is minor, and a significant difference is
only given at the lowest flow velocity of 0.0002 m/s. Individual plots of PV/T output
efficiency for each of the cases simulated are shown in Appendix A.
24
325
A similar trend for the PV/T surface temperature shown in Figure 11 is displayed in
Water Flow Velocity Impact to Average Water Outlet Temperature
Inlet Water Temperature, Tin = 298.15 K
330.00
325.00
320.00
315.00
Water Average Outlet
Temperature (K)
310.00
Flow Channel = .015 [m]
Flow Channel = .01 [m]
Flow Channel = .005 [m]
305.00
300.00
295.00
0
0.002
0.004
0.006
0.008
0.01
0.012
Inlet Flow Velocity, Uwater (m/s)
Figure 13 for the cooling water outlet temperature. For low water flow velocities and
narrow reservoir thicknesses, the outlet temperature is much warmer than larger flow
channels. This is due to the larger volume of fluid in the thicker reservoirs, which
naturally heats up slower than the smaller volume in the narrower reservoirs. However,
at high velocities the outlet temperature for the narrower flow thickness is slightly cooler
than the largest flow thicknesses, although the temperature of the fluid hardly increases
from inlet temperature. It is shown that the maximum water outlet temperature obtained
was approximately 326 K, which occurred during the simulation of the narrowest flow
channel and the slowest flow velocity. In Appendix A, plots are shown for the water
outlet temperature as a function of the flow channel thickness for all cases run.
25
Water Flow Velocity Impact to Average Water Outlet Temperature
Inlet Water Temperature, Tin = 298.15 K
330.00
325.00
320.00
315.00
Water Average Outlet
Temperature (K)
310.00
Flow Channel = .015 [m]
Flow Channel = .01 [m]
Flow Channel = .005 [m]
305.00
300.00
295.00
0
0.002
0.004
0.006
0.008
0.01
0.012
Inlet Flow Velocity, Uwater (m/s)
Figure 13: Water Flow Velocity Impact to Average Water Outlet Temperature – Inlet Water Temperature,
Tin = 298.15 K
From Figure 14 it is shown that highest thermal efficiency for any PV/T test case is
achieved by the largest reservoir thickness, at the fastest flow velocity. However, as
26
shown
above
in
Water Flow Velocity Impact to Average Water Outlet Temperature
Inlet Water Temperature, Tin = 298.15 K
330.00
325.00
320.00
315.00
Water Average Outlet
Temperature (K)
310.00
Flow Channel = .015 [m]
Flow Channel = .01 [m]
Flow Channel = .005 [m]
305.00
300.00
295.00
0
0.002
0.004
0.006
0.008
0.01
0.012
Inlet Flow Velocity, Uwater (m/s)
Figure 13, the temperature increase from the inlet to the outlet of the PV/T panel is
minimal. If the user of such a PV/T system prefers higher temperature water, a
slower flow velocity would be desired so that a significant change in water
could be realized. Even with a slower water velocity, an increase in the PV/T average
electrical efficiency is achieved, compared to a PV panel without a cooling feature as
shown in
. A noticeable dip in the efficiency is also shown for flow channels of 0.01 m and 0.005
m, which is due to the slight change in temperature from the inlet to the outlet of the flow
channel. At higher velocities, the temperature change is still small, however, an increase
in the velocity (i.e. mass flow rate) results in an increase in the thermal efficiency of the
PV/T system.
27
Water Flow Velocity Impact to Average PV/T Panel Thermal Efficiency
Inlet Water Temperature Tin = 298.15 K
90
80
70
60
PV/T Cell Average 50
Thermal Efficiency,
ηth (%)
40
Flow Channel = .015 [m]
30
Flow Channel = .005 [m]
Flow Channel = .01 [m]
20
10
0
0
0.002
0.004
0.006
0.008
0.01
0.012
Inlet Flow Velocity, Uwater (m/s)
Figure 14: Water Flow Velocity Impact to Average PV/T Thermal Efficiency – Inlet Water Temperature
Tin = 298.15 K
In Figure 15 the combined efficiency of the PV/T panel is plotted with respect to the inlet
flow velocity, which shows that the largest reservoir thickness, combined with the highest
flow velocity is the most efficient option with a water inlet temperature equivalent to the
ambient temperature of 298.15 K. As mentioned previously, however, this option does not
result in an optimal water outlet temperature that would be useful for a secondary
application, such as heating potable water, heating a swimming pool, or other functions.
All options, except for the smallest flow channel at the lowest flow velocity, yield a
measurable gain in PV/T electrical output efficiency.
Also worth noting is the relatively high thermal efficiency of the 0.01 m and 0.015 m flow
channel configurations at higher water flow velocities. This is mainly due to Assumptions
1 - 4 stated in Section 2.2.1 and the extreme sensitivity of thermal efficiency to
temperature change at high flow velocities. It was conservative to assume that all solar
irradiance energy not converted to electrical energy would be developed into heat. It is
28
reasonable to consider that a functional PV/T panel would not absorb a percentage of the
solar irradiance imparted on the panel due to the fact some of the solar irradiance is of the
incorrect wavelength for any given PV cell material. Also, after being in use for a period
of time, the surface of the PV/T panel would likely get dirty or dusty, which would impact
the absorptivity of the panel. With that mentioned, a proportional reduction in thermal
efficiency could be expected with a decrease in the absorptivity of the panel. Although a
different type of PV/T application was analyzed, Kerzmann and Schaefer [13] employed
an absorptivity reduction constant of 15% in their work to account for unabsorbed solar
irradiance, which would otherwise contribute heat to their application.
PV/T Panel Average Total Efficiency vs. Flow Velocity of Coolant Water
Inlet Water Temperature,Tin = 298.15 K
100
80
Flow Channel = .015 [m]
60
PV/T Panel Average
Total Output
Efficiency, ηtot (%)
Flow Channel = .01 [m]
Flow Channel = .005 [m]
Max Efficiency
40
20
0
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Inlet Flow Velocity, Uwater (m/s)
Figure 15: PV/T Panel Average Total Efficiency vs. Flow Velocity of Coolant Water – Inlet Water
Temperature, Tin = 298.15 K
The thermal efficiency of the PV/T panel at high flow velocities (i.e. high mass flow
rates) was found to be extremely sensitive with calculated values of the difference in
water temperature at the inlet and outlet of the panel. As mentioned previously, the
average temperature calculated in COMSOL was used to determine the thermal
29
efficiency of the panel. Using Equation [14], it was found that at the highest flow
velocity evaluated (0.01 m/s) and largest flow channel thickness (0.015 m), variations in
the outlet temperature, Tout , as small as 0.1 K resulted in a 20% difference in thermal
efficiency.
30
4. Conclusions
In this work, a conceptual photovoltaic thermal panel design was modeled and analyzed
using a commercial finite element software package, COMSOL Multiphysics: Version
4.2a. The PV/T panel evaluated consisted of a monocrystalline silicon PV cell that was
bound with a silicone thermal paste to an aluminum reservoir through which coolant
water flowed. Numerous simulations were completed to model the heat transfer across
the PV/T panel and ultimately to determine the PV/T electrical output and thermal
efficiencies of the panel. Water flow velocity and flow channel thickness were varied
and analyzed to determine which combinations yielded not only the highest total PV/T
efficiency, but also the most useful thermal and electrical output.
It was found that the highest total PV/T panel efficiencies were achieved for test cases
involving combinations of high flow velocity and large flow channel thicknesses. The
highest total cell efficiency obtained of 95.7% was obtained from Test Case “1d”, in
which the flow thickness was 0.015 m and the inlet flow velocity was 0.01 m/s. Test
Case “3c” was found to be the least efficient configuration, which recorded a total
efficiency of 27.5% and consisted of a flow channel thickness of 0.005 m and inlet flow
velocity of 0.005 m/s. The highest efficiency obtained is unrealistic, which is due
conservative assumptions and the extreme sensitivity of thermal efficiency to
temperature change at high water flow velocities. It was deduced that at high flow
velocities (i.e. high mass flow rates), slight changes in temperature result in drastic
differences in thermal efficiency; therefore, precise temperature measurement is
essential for accurate results.
It was also concluded that the PV/T system with the highest efficiency is most likely not
the most desirable configuration for practical use. Although high inlet velocities result
in the lowest PV/T surface temperatures, thus the highest electrical efficiency, the
coolant water exiting the panel experiences no significant temperature change.
Therefore, it would not be entirely beneficial to utilize the water exiting the PV/T panel
for any practical application, such as heating a swimming pool, for use in a radiant floor
31
heating system, etc. A cost savings study would be required to determine the optimal
balance of electrical efficiency and thermal efficiency; however, that is beyond the scope
of this study. Future study of this PV/T system could include work evaluating the
performance of this system in different climates, utilization of different coolant fluids,
and evaluation of various inlet water temperatures.
32
5. References
[1] Nelson, Jenny. The Physics of Solar Cells. London: Imperial College Press,
2003.
[2] Turner, Wayne and Steve Doty. Energy Management Handbook: Sixth Edition.
Lilburn: The Fairmont Press, 2007.
[3] “Solar Cell Central: Four Peaks Technologies Inc., Scottsdale, AZ,” Design
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validation of heat transfer in a novel hybrid solar panel, International Journal of
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[5] “Arizona Solar Center, Inc.,” Copyright 1999-2012,
<http://www.azsolarcenter.org>
[6] Li Zhu, Robert F. Boehm, Yiping Wang, Christopher Halford, and Yong Sun,
Water immersion cooling of PV cells in a high concentration system, Solar
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of PV Modules Per ANSI/UL 1703 and IEC 61730 Standards, Conference Record
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[8] H. G. Teo, P. S. Lee, and M. N. A. Hawlader, An active cooling system for
photovoltaic modules, Applied Energy 90 (2012) 309-315.
[9] H. Chen, Saffa B. Riffat, Yu Fu, Experimental study on a hybrid photovoltaic/heat
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[10] M. Bakker, H. A. Zondag, M. J. Elswijk, K. J. Strootman, M. J. M. Jong,
Performance and costs of a roof-sized PV/thermal array combined with a ground
coupled heat pump, Solar Energy 78 (2005) 331-339.
[11] Sharp, Rowan. “Brown’s Hybrid Solar Panels a First for RI.” Eco RI News:
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<www.ecoRI.org>.
[12] A.D. Jones and C.P. Underwood, A Thermal Model For Photovoltaic Systems,
Solar Energy 70 (2001) 349-359.
[13] Tony Kerzmann and Laura Schaefer, System simulation of a linear concentrating
photovoltaic system with an active cooling system, Renewable Energy 41 (2012)
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page 106.
33
Appendix A: Test Case Supplementary Data
1. Test Case 1a
Figure A - 1: Test Case 1a two-dimensional temperature plot
Figure A - 2: Heat flux into PV/T panel vs. panel length
1
Figure A - 3: Cell electrical output efficiency vs. panel length
2. Test Case 1b
Figure A - 4: Steady state solution two-dimensional temperature plot of PV/T panel
2
Figure A - 5: Heat flux into PV/T panel vs. panel length
Figure A - 6: Cell electrical output efficiency vs. panel length
3
3. Test Case 1c
Figure A - 7: Steady state solution two-dimensional temperature plot of PV/T panel
Figure A - 8: Heat flux into PV/T panel vs. panel length
4
Figure A - 9: Cell electrical output efficiency vs. panel length
4. Test Case 1d
Figure A - 10: Steady state solution two-dimensional temperature plot of PV/T panel
5
Figure A - 11: Heat flux into PV/T panel vs. panel length
Figure A - 12: Cell electrical output efficiency vs. panel length
6
5. Test Case 2a
Figure A - 13: Steady state solution two-dimensional temperature plot of PV/T panel
Figure A - 14: Heat flux into PV/T panel vs. panel length
7
Figure A - 15: Cell electrical output efficiency vs. panel length
6. Test Case 2b
Figure A - 16: Steady state solution two-dimensional temperature plot of PV/T panel
8
Figure A - 17: Heat flux into PV/T panel vs. panel length
Figure A - 18: Cell electrical output efficiency vs. panel length
9
7. Test Case 2c
Figure A - 19: Steady state solution two-dimensional temperature plot of PV/T panel
Figure A - 20: Heat flux into PV/T panel vs. panel length
10
Figure A - 21: Cell electrical output efficiency vs. panel length
8. Test Case 2d
Figure A - 22: Steady state solution two-dimensional temperature plot of PV/T panel
11
Figure A - 23: Heat flux into PV/T panel vs. panel length
Figure A - 24: Cell electrical output efficiency vs. panel length
12
9. Test Case 3a
Figure A - 25: Steady state solution two-dimensional temperature plot of PV/T panel
Figure A - 26: Heat flux into PV/T panel vs. panel length
13
Figure A - 27: Cell electrical output efficiency vs. panel length
10.Test Case 3b
Figure A - 28: Steady state solution two-dimensional temperature plot of PV/T panel
14
Figure A - 29: Heat flux into PV/T panel vs. panel length
Figure A - 30: Cell electrical output efficiency vs. panel length
15
11.Test Case 3c
Figure A - 31: Steady state solution two-dimensional temperature plot of PV/T panel
Figure A - 32: Heat flux into PV/T panel vs. panel length
16
Figure A - 33: Cell electrical output efficiency vs. panel length
12.Test Case 3d
Figure A - 34: Steady state solution two-dimensional temperature plot of PV/T panel
17
Figure A - 35: Heat flux into PV/T panel vs. panel length
Figure A - 36: Cell electrical output efficiency vs. panel length
18