Paneles Solares Hibridos Collins-FinalReport

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HYBRID SOLAR PANEL EFFICIENCY OPTIMIZATION WITH A

LABYRINTH FIN ARRANGEMENTby

Robert P. Collins

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

Major Subject: Mechanical Engineering

Approved:

_________________________________________

Ernesto Gutierrez-Miravete, Project Adviser

Rensselaer Polytechnic InstituteHartford, Connecticut

December 11, 2013


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Copyright 2013

by

Robert P. Collins

All Rights Reserved


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CONTENTS

ACKNOWLEDGMENT .................................................................................................. iii

LIST OF TABLES ............................................................................................................ vi

LIST OF FIGURES ......................................................................................................... vii

TABLE OF SYMBOLS ................................................................................................. viii

KEYWORDS ..................................................................................................................... x

ABSTRACT ..................................................................................................................... xi

1. INTRODUCTION/BACKGROUND .......................................................................... 1

1.1 Solar Photovoltaic Cells ..................................................................................... 1

1.2 Solar Hot Water Heater ...................................................................................... 4

1.3 Hybrid Solar Panel (PV/T) ................................................................................. 5

2. METHODOLOGY/APPROACH ................................................................................ 7

2.1 Materials ............................................................................................................. 8

2.2 Model Arrangement ........................................................................................... 9

2.3 Test Arrangements ........................................................................................... 13

2.4 Model Theory and Relevant Equations ............................................................ 13

2.5 Finite Element Model ....................................................................................... 17

2.6 Expected Results .............................................................................................. 18

2.7 Model Limitations and Mesh Studies .............................................................. 18

3. RESULTS AND DISCUSSION ................................................................................ 20

3.1 PV/T Module Results ....................................................................................... 20

3.2 PV/T Array Results .......................................................................................... 30

3.3 Other Considerations ........................................................................................ 32

4. CONCLUSIONS ....................................................................................................... 33

REFERENCES ................................................................................................................ 34

APPENDIX A: CONSERVATION OF ENERGY CALCULATION ............................ 36

APPENDIX B: ELECTRICAL EFFICIENCY VERIFICATION .................................. 37


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LIST OF TABLES

Table 1: PV/T Model Materials ......................................................................................... 9

Table 2: Module Parameters ............................................................................................ 11

Table 3: Model Variables ................................................................................................ 12Table 4: Fin Test Arrangements ...................................................................................... 13

Table 5: Coarser Mesh Solution Data and PC Specifications...................................... 18

Table 6: Mesh Result Heat Balance and Accuracy ......................................................... 19

Table 7: Module Results .................................................................................................. 26

Table 8: Array Results ..................................................................................................... 32


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LIST OF FIGURES

Figure 1: Electrons Absorbing Incident Sunlight [1] ........................................................ 1

Figure 2: Band Gap [2] ...................................................................................................... 2

Figure 3: PV Array Hierarchy [6] ...................................................................................... 3Figure 4: Active Secondary Loop Solar Hot Water Heater System [8] ............................ 4

Figure 5: Hybrid Solar Panel Control Volume .................................................................. 7

Figure 6: Model Isometric Cross Section View ................................................................ 8

Figure 9: Hybrid Panel Cross Section View .................................................................... 10

Figure 7: Fin Labyrinth .................................................................................................... 10

Figure 8: PV/T Module Landscape View ........................................................................ 10

Figure 10: Model Boundary Conditions .......................................................................... 12

Figure 11: Hydraulic Diameter ........................................................................................ 15

Figure 12: Rectangular Orifice [16] ................................................................................ 16

Figure 13: Averaged Streamlines and Contours of Turbulent Kinetic Energy [16] ........ 17

Figure 14: Coarser Mesh.............................................................................................. 17

Figure 15: Mesh Accuracy............................................................................................... 19

Figure 16: No Fin Velocity Profile .................................................................................. 21

Figure 17: Fin Velocity Disruption .................................................................................. 21

Figure 18: Velocity Distribution in a Labyrinth Arrangement ........................................ 22

Figure 19: No Fin Temperature Distribution ................................................................... 23

Figure 20: Temperature Distribution Around a Fin ......................................................... 23

Figure 21: Temperature Contours in a Labyrinth Arrangement ...................................... 24

Figure 22: PV Surface Temperature Distribution ............................................................ 25

Figure 23: PV/T Module Thermal and Electrical Efficiency Correlation ....................... 27

Figure 24: Top Fin Arrangement Efficiency ................................................................... 28

Figure 25: Bottom Fin Arrangement Efficiency .............................................................. 29

Figure 26: Labyrinth Arrangement Efficiency ................................................................ 29

Figure 27: All Fin Arrangements ..................................................................................... 30

Figure 28: PV/T Array [6] ............................................................................................... 31
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TABLE OF SYMBOLS

Symbol Description Units

Collector Area Exposed to Solar Radia-tion

Flow Cross Sectional Area Constant Volume Specific Heat Constant Pressure Specific Heat Hydraulic Diameter

Radiative Power Per Unit Area

h Heat Transfer Coefficient

Flow Path Height m Current Thermal Conductivity

Mass Flow Rate

Electric Power Out of Panel

Thermal Power Out of Panel Energy Imparted on the Fluid Energy Radiated to the Atmosphere Re Reynolds Number

Ambient Air Temperature Cell Surface Temperature K

Inlet Working Fluid Temperature

Average Outlet Working FluidTemperature

Room Temperature 25 Cu Fluid Velocity at a Point


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Average Inlet Flow Velocity Voltage w Panel Width m

PV Cell Temperature Coefficient Emissivity

Panel Electrical Efficiency Panel Electrical Efficiency at Room

Temperature

Panel Overall Efficiency Panel Thermal Efficiency Dynamic Viscosity

Kinematic Viscosity

Density

TheStefan-Boltzmann Constant Gradient


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KEYWORDS

Hybrid Solar Panel

Energy Conversion Efficiency

Heat Transfer

LowReynolds Number Turbulent Flow

Solar Energy

Finite Element Method


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ABSTRACT

A photovoltaic (PV) cell is coupled with a solar hot water heater in an arrangement

called a hybrid solar panel, or PV/Thermal (PV/T) panel. This hybrid solar panel

concept explores the used of fins perpendicular to the flow direction to increase convec-tion and reduce boundary layer thickness at a low Reynolds number in order to increase

heat transfer between the PV cells and solar hot water heater while achieving a useful

temperature rise. The hybrid panel is designed with solar cells attached to a copper

reservoir using a thermal paste, with an insulated boundary between the bottom of the

fluid reservoir and the atmosphere. A two dimensional (2-D) finite element model is

used to simulate the temperature distribution and the outlet water temperature in the

PV/T module, where the number of fins and the flow rate in the reservoir are varied.

The module efficiency is compared, with the highest efficiency module arrangement

consisting of many, large fins, in a labyrinth arrangement. The model of the highest

efficiency PV/T module is run three times, with the outlet water temperature carried

from one model to the next in order to simulate a larger, PV/T array, resulting in a water

temperature rise of 16.5C, and an overall efficiency of 78.0%, 4.8% more efficient than

the PV/T array modeled with no fins.


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given material and temperature. Materials with small or no band gap are classified as

conductors, whereas materials with a large band gap are classified as insulators. Materi-

als such as silicon, which have an intermediate band gap, are semiconductors. Figure 2,

shows a schematic representation of the band structure of a semiconductor [2].

Figure 2: Band Gap [2]

This band gap is the step, or wall, that the electrons must overcome to move from the

valence band to the conduction band. In other words, the electrons need to be excited by

photons of a certain, minimum energy to jump the band gap. The band gap can be

considered proportional to the open circuit voltage of the semiconductor. With an

increase in temperature, the electrons have a higher resting energy state, effectively

reducing the band gap. With a reduction in band gap, the open circuit voltage of the

semiconductor of the PV cell decreases, while the current remains largely the same.

Because of Watts Law, P , the power output of the semiconductor, or PV celldecreases for the same amount of power in from solar radiation. The electrical efficien-

cy of a PV Cell is therefore decreased, as shown by the below equation [3], where the

current and voltage are measured at the maximum power point operation of the cell.

This phenomenon of a decrease in electrical efficiency with rising temperature is well

documented, with the relationship between temperature and efficiency explored by

Skoplaki, and Palyvos [4], which for some models, predicts a 0.41drop in efficiency
http://www.rpi.edu/dept/phys/ScIT/InformationProcessing/semicond/sc_glossary/scglossary.htmhttp://www.rpi.edu/dept/phys/ScIT/InformationProcessing/semicond/sc_glossary/scglossary.htmhttp://www.rpi.edu/dept/phys/ScIT/InformationProcessing/semicond/sc_glossary/scglossary.htmhttp://www.rpi.edu/dept/phys/ScIT/InformationProcessing/semicond/sc_glossary/scglossary.htm


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above room temperature. In hot, high sunlight conditions, temperatures of 50C can be

reached, severely dropping the efficiency of the panel, and also risking permanent

structural damage to the PV cell from the thermal stress [4].

The efficiency of the most common types of solar panels, mono-crystalline silicon PV

cells, typically ranges from 13-20% at room temperature [5], with that percentage of

power in sunlight converted into electrical power. The rest of the energy reflected off

the PV cells, or converted into heat. If that atmosphere is unable to accept the heat from

the PV cells, the temperature of the PV cells rises. As the temperature of the cells rise,

the efficiency of the cells decreases, and on hot, sunny days, PV cells can have a drop in

efficiency of up to 10%. Several methods are therefore used to cool PV cells in order to

maintain their electrical efficiency.

In practice, PV cells are arranged in modules, which are then combined to form PV

arrays; Figure 3 shows this hierarchy. This array is typical of the arrangement used for

the hybrid solar array used in this study.

Figure 3: PV Array Hierarchy [6]

PV Modules

PV Cells


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1.2 Solar Hot Water Heater

A solar collector in a solar hot water heater is an enclosed volume that the working fluid

flows through to collect the suns energy in the form of heat. This volume is very

insulated and optimized to capture solar radiation. Solar hot water heaters have a greaterefficiency when the collector volume is hot, and there is a large driving temperature

delta between the collector and the working fluid flowing through the collector. The

working fluid is typically water in a single loop solar hot water heater, which directly

feeds water for household usage. Water and other fluids such as a water/propylene

glycol mix are used to transfer the heat to the household water supply through a second-

ary heat exchanger in a secondary loop solar hot water heater. The working fluid can be

supplied actively, with a pump, or passively using natural convection of the fluid as it is

heated. Passive, natural convection flow is typical of primary loop solar hot water

heaters, whereas active loops are used in both primary and secondary solar hot water

heaters. An active, secondary solar hot water heating arrangement, typical to the ar-

rangement used in this study, is shown below in Figure 4. [7]

Figure 4: Active Secondary Loop Solar Hot Water Heater System [8]


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The thermal efficiency of a solar hot water heater is given by the below equation [3]:

1.3

Hybrid Solar Panel (PV/T)

In order to avoid the PV cells drop in efficiency, and capture the majority of the waste

heat from the PV cells, the PV cells are coupled with a solar hot water heater in a hybrid

solar panel, or PV/T panel. This design provides a novel method for cooling the PV

cells, whose efficiency diminishes with increasing temperature, and uses the heat ex-

tracted from the PV cells to heat household or commercial hot water as an alternative totraditional hot water heaters powered by fossil fuels. The efficiency of the hybrid solar

panel is the sum of the efficiency of the PV cells and the solar hot water heater [3].

Hybrid solar panels, also known as PV/T panels, have been explored in several previous

studies. In a similar study Fountenault [9] varied flow rates and flow channel thickness-

es in a laminar flow, hybrid solar panel. The exploration showed that, when all else was

constant, the average driving temperature difference between the PV cells and the fluid

in the flow channel drives both the thermal and electrical efficiencies. A large tempera-

ture delta was achieved by using a high mass flow rate of water in a large channel, which

led to lower temperature changes in the fluid when compared to lower flow rates in

smaller channels. As a result of a lower temperature change in the fluid, a larger average

temperature delta between the PV cells and the working fluid was maintained, and less

heat was lost to the atmosphere.

A study by Yang et al. [10] explored a model and prototype hybrid solar panel with a

functionally graded material (FGM). The FGM is a material with a property gradient.

In this case, the thermal conductivity of the material is higher, 1.13

, near the interface


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2. METHODOLOGY/APPROACH

A hybrid solar panel is designed, with a set control volume that encapsulates the panel as

shown below in Figure 5. The sunlight and the cold working fluid will be the two

defined inputs into the control volume, and therefore solar panel. Heat will be trans-ferred from the panel with the mass flow rate of the hot working fluid out, convectively

to the ambient air, and through reflection/radiation from the body of the body of the

panel. There is a current and voltage across the PV cell, which is also accounted for, and

a total electrical power out.

The net energy balance for the hybrid solar panel control volume used in this study is:

Within the control volume that is the hybrid solar panel, there is heat transfer between

the different material layers. Conduction heat transfer exists between and within the

solid layers of hybrid solar panel which will be constrained by the material conductivity.

Choice of highly conductive materials, such as copper will maximize the heat transfer

away from the solar panel to the walls of the cooling fluid reservoir. The heat transfer

out to the atmosphere is also minimized with a layer of insulation added to the bottom of

the hybrid solar panel.

Convective Heat

Transfer

HYBRID SOLAR

PANEL

Cold Primary Fluid Hot Primary Fluid

SunlightRadiation

Figure 5: Hybrid Solar Panel Control Volume


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Heat is conducted from the PV cells through highly conductive solids until it reaches the

solid/liquid boundary, where the heat is transferred to the working fluid in the fluid

reservoir. With known solid and liquid properties, the limiting factors explored in this

model are the surface area at the solid liquid boundary, boundary layers, and the convec-

tion in the flow path. Boundary layers form in duct flow, creating a hot layer of the

working fluid along the solid/liquid interface, where the bulk fluid temperature is much

lower. In a fluid such as water, conduction is a slower method of heat transfer than

convection. In order to increase the surface area, minimize boundary layer formation,

and increase heat transfer within the fluid by inducing mixing, or convection, sharp

edged fins are added perpendicular to the flow. A cross sectional unit thickness (not to

scale) of the model is shown below in Figure 6, which shows the material layers, and the

orientation of the fins to the flow.

2.1

Materials

Hybrid solar panel materials vary from the standard materials used by Fontenault [9] to

the FGM panel explored by Yang et al. Commonly available materials and those that

maximize heat transfer within the panel were chosen for this study. The materials used

in the model are listed below, with their reference and relevant material properties also

shown. COMSOL Multiphysics has built in materials, which are used for water, copper,

and silicon. All material properties below are constant in the model except for the

properties of water, which vary with temperature, with the water properties shown in

Table 1 are taken at 25C.

- PV Cells

- Thermal Paste

- Copper

Working Fluid

- Copper

- Insulation

Figure 6: Model Isometric Cross Section View


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Table 1: PV/T Model Materials

Material Property Value Reference

PV Cell 2329 COMSOLSilicon

k 130

700 .60 [11]

Thermal Paste 3500 [12]

k 2.87

.7Copper 8700 COMSOLCopper

k 400

385

Water 997.1 COMSOLWater @ 25Ck .611

= 4.184 902 x 10-6

2.2

Model Arrangement

A 2-D model of this scenario is created in COMSOL Multiphysics in order to simulate

this hybrid solar panel design. The number of fins on the top wall (0, 9, or 18), the

number of fins on the bottom of the wall (0, 9, or 18), and the fin length ( , , or flow path height) are tested for a single flow rate to see their effect on the efficiencyof the hybrid solar panel. The fins on the top of the flow path are expected to have a

two-fold effect on the heat transfer; increased flow mixing and increased surface area for

heat transfer on the hot wall. Fins on the bottom of the flow path do not increase the

surface area for heat transfer on the hot wall, but are instead tested for their ability to

disrupt boundary layer flow along the top wall and increase convection. Top and bottom

fins are also be tested together, as shown in Figure 7, which creates a labyrinth design,

which will effectively increase the flow path in the reservoir. For the labyrinth arrange-

ment, an additional condition, 27 top and 27 bottom fins, will also be tested.


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The PV/T module studied consists of 12 PV cells arranged in a 3x4 rectangle, with the

flow through the short direction of the rectangle, as shown in Figure 8. The model

orientation is shown in Figure 9, which illustrates a short cross section of the model.

Figure 9: Hybrid Panel Cross Section View

Figure 7: Fin Labyrinth

Figure 8: PV/T Module Landscape View


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Fontenault [9] and Yang et al. [10]. In a typical arrangement, the bottom boundary of a

hybrid solar panel is insulated with materials such as extruded polystyrene, which

reduces convective heat loss to the environment. Including insulation in the model

increases the number of elements that add little value to the studys results. In lieu of

adding insulation to the model, an insulated boundary condition is used for the bottom

surface of the PV/T module. These boundary conditions are illustrated in Figure 10.

Figure 10: Model Boundary Conditions

The model variables in Table 3 are evaluated by the model for each step in the solver,

and are used iteratively to find the steady state solution for the model. An important

variable to note is Q_heat, which is the suns radiation that is not converted to electrical

power by the solar panel, which varies with temperature.

Table 3: Model Variables

Name Expression Units Description

PVEFF PVEFF0*(1-PVdeg*(T-T_Room)) - PV Cell Efficiency Temp. Dependence

Q_Heat Q_Sun*(1-PVEFF) W Suns Energy Converted to Heat

mdot nitf.rho*H_Flow*U_Flow*1[m] kg/s Mass Flow Rate Water (per unit depth)

ThermEFF mdot*nitf.Cp*(T-T_Inlet)/P_in - Thermal Efficiency

EFF_Net PVEFF+ThermEFF - Overall Efficiency


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2.3 Test Arrangements

A 2-D, stationary COMSOL model is used to study the hybrid solar panel. Multiple

avenues of heat transfer within, and in and out of the control volume are explored in this

model. Also, the fins introduced into the flow path will create localized flow separationin the low Reynolds number flow. As a result of the conditions tested, a low Reynolds

number turbulent flow, conjugate heat transfer model is used. The fin test arrangements

are shown below in Table 4.

Table 4: Fin Test Arrangements

Flow Velocity (u) # Top Fins # Bottom Fins Fin Lengths

.002 m/s 0 0 0

002 m/s 9 0 , ,

002 m/s 18 0 , ,

002 m/s 0 9 , ,

002 m/s 0 18 , ,

002 m/s 9 9 , ,

002 m/s 9 9 , ,

002 m/s 18 18 , ,

002 m/s 27 27 , ,

Twenty five fin arrangements are outlined in Table 4. These conditions are expected to

show a useful correlation between the different fin arrangements and the outlet thermal

properties and efficiencies of a PV/T module.

2.4

Model Theory and Relevant Equations

The relevant equations used in this model and for the purpose of determining the panel s

thermal properties overall efficiency are discussed in this section. The thermal, electri-

cal, and overall efficiency equations of the hybrid panel are mentioned above in the

introduction. The relevant equations in the COMSOL conjugate heat transfer model are


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shown below. A simplified computation was used to verify the models relevance for

modeling the conditions, with vector quantities shown in bold.

Steady state heat transfer in solids with no heat generation is described by the conserva-

tion of energy equation

where k is the thermal conductivity of the solid.

Steady state heat transfer in liquids is also described by the conservation of energy

equation, where is the rate of convective heat transfer in the fluid.

The heat flux from solar irradiance into the PV cell is given by

Where is a defined value of the incident heat flux and is the vector normal to theheat transfer surface. This equation is also used to describe a perfectly insulated bounda-

ry. Thermal Insulation in the model means there is no heat transfer across a given

boundary, which essentially means the temperature gradient leading up to and across the

boundary is zero.

Free convection between the atmosphere and the hybrid solar panel is based on the heat

transfer coefficient and the temperature difference between the atmosphere and the

surface of the panel. The convective heat loss from the panel to the atmosphere is given

by the below equation where h is the heat transfer coefficient.


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Radiative heat transfer is in included in the model, and is found to be considerable when

the PV/T array is heated several degrees above ambient.

A no slip boundary condition is used at the solid/fluid interface, with the fluid velocity

set as zero along the walls of the flow path. The velocity profile of the fluid is given by:

where is the initial average velocity, which is a defined test condition. TheReynolds number is evaluated at the tip of each fin to evaluate mixing, with the hydrau-

lic diameter, , as twice the flow path. Figure 11 shows a parabolic velocity profile,typical to laminar flow, and the flow path height.

For flow between two parallel plates with the model geometry in Table 2, the Reynolds

number is calculated below.

Figure 11: Hydraulic Diameter


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The flow through the no-fin model has a Reynolds number well below that of turbu-

lent flow, with the transition between laminar and turbulent flow occurring at a Reynolds

number between 2300 and 4000 [15].

The mixing in the model is therefore accounted for by low-Reynolds number turbulent

flow. This behavior is typical of flow through an orifice or diffuser. Diffuser stall,

which is a term typically used in aerofoil aerodynamics, denotes boundary layer separa-

tion and is explained by White: The expanding-area diffuser produces low velocity and

increasing pressure, an adverse gradient. It the diffuser angle is too large, the adverse

gradient is excessive, and the boundary layer will separate at one or both walls, with

backflow, and poor pressure recovery [15]. It is this boundary layer separation or

disruption which is relied upon to increase fluid mixing and therefore heat transfer in the

model. Figure 12, below, shows the rectangular orifice modeled by Tsukahara, Kawase,

and Kawaguchi [16], with the turbulent kinetic energy of a Newtonian fluid shown in

Figure 13. The simulation was carried out with a Reynolds number of 100, and showsthat the reduction in area through the orifice disrupts the normal laminar flow boundary

layers and introduces turbulent kinetic energy in the form of flow mixing.

Figure 12: Rectangular Orifice [16]


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Figure 13: Averaged Streamlines and Contours of Turbulent Kinetic Energy [16]

Figure 12 shows that the flow has increased energy as a result of the expanding area,

causing enhanced mixing, which is the behavior that is expected in this model. Similar

to Tsukahara, Kawase, and Kawaguchi [16], sharp edged bodies, or fins, are used, which

are insensitive to Reynolds number and cause flow separation regardless of the charac-

ter of the boundary layer [15].

2.5

Finite Element Model

The hybrid solar panel model is meshed using the Coarser Physics Controlled Mesh in

COMSOL Multiphysics. COMSOL uses a segregated solver, with two groups that

converge to a single solution, for the low Reynolds number turbulent flow k- . The

segregated solver is computationally complex, and even for a Coarser mesh, approxi-

mately 50,000 elements are created for the more simple models with fewer fins.

Solutions with more fins are more computationally demanding, but the Coarser mesh

was still used to maintain the integrity of the results. An example mesh is shown below

in Figure 14, with the finite element mesh data shown in Table 5.

Figure 14: Coarser Mesh


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Table 5: CoarserMesh Solution Data and PC Specifications

Objects, Domains, Boundaries, Vertices 42 42 199 158

Elements Domain: 64,444 Boundary: 5,989

Degrees of Freedom Solver 1: 27,804 Solver 2: 177,715

Solution Time 6 minutes, 18 seconds

PC Type Lenovo PG101

PC Processor Intel i33220; 3.30 GHz

PC RAM 4 GB

Studies involving 27 fins on the top and bottom of the flow path require the use of, an

Extra Coarse mesh, because the segregated solver runs out of memory during its

Lower/Upper matrix factorization for a Coarser mesh. With the Coarser mesh, the

number of degrees of freedom approached 250,000 for the second solver.

2.6 Expected Results

The expectation is that heat transfer will be maximized when the surface area in contact

with the fluid is maximized with the top fins, the boundary layer and the extent of the

dead flow zones in front and behind the fins is interrupted by the bottom fins, and the

flow path is extended with the labyrinth arrangement. In summary, the expectation is

that the greatest heat transfer will occur with the largest number of large fins on the top

and bottom of the flow path. Altogether, the efficiency of both entities in the panel, the

PV cells and the solar hot water heater, are expected to reach their peak when heat

transfer between the two components of the hybrid solar panel are maximized.

2.7

Model Limitations and Mesh Studies

A general proof of concept calculation, in Appendix A shows that the model, without

heat transfer to the surrounding atmosphere, is about 90% accurate. That is to say that

10% of the heat incident on the module is unaccounted for in the single heat outlet; the

hot water. These limitations are especially noticeable under the low flow, small flow

height conditions, which this model is simulating. Higher flow rates, or larger flow


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heights were not used, because they would not yield the useful temperature delta that is a

design requirement for a hybrid solar panel.

The accuracy of the results is also dependent on the mesh, with a finer mesh yielding

more accurate results. The accuracy and error of the model with no fins, insulated

boundaries, and 375 W of inlet heat transfer is shown below in Table 6 and then plotted

in Figure 15. The inlet heat in the model with insulated boundaries can only be trans-

ferred to the fluid. The added energy is the difference between the outlet fluid energy,

Qfluid Out, and the inlet fluid energy, Qfluid In. The computer used to run the model,

specifications in Table 5, ran out of memory for all meshes finer than the coarse mesh.

More accurate results could be achieved with a computer with more processing power.

Table 6: Mesh Result Heat Balance and Accuracy

Mesh

Chart

Point

Qfluid In

(J)

Qfluid Out

(J)

Delta Q

(J)

Qheat In

(J) % Error % Accuracy

Extremely

Coarse

1

11880 12072 192 375 48.8 51.2

Extra

Coarse

2

11889 12181 292 375 22.1 77.9

Coarser 3 11892 12227 335 375 10.7 89.3

Coarse 4 11895 12240 345 375 8.0 92.0

Figure 15: Mesh Accuracy

0.0

20.0

40.0

60.0

80.0

100.0

1 2 3 4

%Accuracy

Mesh

Mesh Accurary


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3. RESULTS AND DISCUSSION

3.1 PV/T Module Results

The 2-D model is run for the PV/T module with the flow length of three PV Cells for

each of the test arrangements outlined in Table 4. The parameters used in the model are

outlined in Table 2, which represent typical hybrid solar panel dimensions, properties,

and typical test operating conditions. COMSOL Multiphysics iteratively solves the

finite element mesh of the PV/T module using the equations stated in Section 3.4. Outlet

water temperatures and PV cell surface temperatures are averaged by COMSOL for each

test arrangement. COMSOL also uses the equations for the variables shown in Table 3

to calculate the electrical, thermal, and overall efficiency of the PV/T module; , ,and respectively. The electrical and thermal efficiency values are also calculated byhand in Appendixes B and C using the inputs from Table 2 the COMSOL output tem-

peratures. The calculation of the electrical efficiency differed only slightly from the

COMSOL model result; the hand calculation in Appendix B uses the averaged cell

temperature to calculate the efficiency, whereas the model calculates the efficiency at

each element of the cell and then averages, which is a more accurate method. Rounding

error explains the minor difference between the model and Appendix C results of the

thermal efficiency, as both use the averaged outlet water temperature calculated by

COMSOL. The overall efficiency is calculated by addition and is visually verified.

The COMSOL 2-D model result for the velocity distribution for the case with no fins is

shown in Figure 16. This parabolic velocity profile, represents a fully developed,

laminar flow profile, where there are layers of fluid parallel to the flow path, with little

mixing. Flow around fins perpendicular to the flow path, which are added to induce

low Reynolds number turbulent flow, is shown in Figure 17. The no slip boundary

condition is noted along the walls of the flow path, where the velocity is zero at the

walls. The fins introduced into the flow disrupt the developed flow profile exhibited in

between fins. Water is accelerated as the flow path height decreases at the tips of the

fins, and the flow begins to decelerate as the area suddenly increases after each fin. As


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the flow decelerates, the energy kinetic energy is converted to pressure, creating an

adverse gradient, flow separation, and therefore increased convection [15]. The use of

sharp edged fins assures separation despite the low bulk Reynolds number of the fluid.

Figure 16: No Fin Velocity Profile

Figure 17: Fin Velocity Disruption


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It should be noted from Figure 17 that the flow quickly re-establishes itself after travel-

ling past a fin. Figure 18 illustrates that, as the fins are moved closer together, the flow

spends less time at a constant velocity, and is instead constantly accelerated across each

fin and decelerated in between the fins. The flow path length is also increased as more

fins are added and the spacing between fins decreases. Flow no longer travels directly

across the panel, but instead crisscrosses between a labyrinth of fins. This arrangement

increases distance the flow travels, without increasing the length of the PV/T module.

Figure 18: Velocity Distribution in a Labyrinth Arrangement

Heat is transferred from the PV cells, through the highly conductive thermal paste and

copper wall, and into the fluid reservoir. The temperature distribution arrangement with

no fins is shown in Figure 19, with lines of constant temperature slowly disappearing

along the flow path. Lines of constant temperature around a fin are illustrated in Figure

20. The lines of constant temperature contour around the fin, illustrating that the fin is a

heat source to the fluid. The fins add surface area to the hot top wall, which increases

the heat transferred to the fluid, raising the water temperature and cooling the PV cells.


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Figure 19: No Fin Temperature Distribution

Figure 20: Temperature Distribution Around a Fin


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Lines of constant temperature are shown in Figure 21 below for a labyrinth fin arrange-

ment. The flow is mixing, causing the fluid temperature to be more evenly distributed.

In Figures 19 and 20, there are many lines of constant temperature that show layers of

water with different temperatures. By contrast, Figure 21 shows a flow with a more

evenly distributed temperature, with fewer lines of constant temperature and the lines

disappearing as the flow mixes and weaves through the labyrinth of fins.

Figure 21: Temperature Contours in a Labyrinth Arrangement

The panel surface temperature has a non-linear distribution as shown in Figure 22. Heat

transfer between the hot solid layers at the top of the PV/T module and the cooling flow

is directly proportional to the driving temperature difference between the two. The

water temperature increases as it travels through the PV/T module, and, with a smaller

temperature difference between the panel and the cooling fluid, there is less heat transfer

to the fluid. The thermal profile in Figure 22 shows that, heat is transferred from the hot

fluid outlet end of the panel through the highly conductive PV, thermal paste, and copper

layers to the cold fluid inlet end. As a result, there is a greater amount of heat transfer


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and therefore a larger temperature rise at the cold fluid inlet end of the panel, and there is

a downward concavity to the curve in Figure 22.

Figure 22: PV Surface Temperature Distribution

The results of each model run are shown in Table 7, related to their fin arrangements

proposed in Table 4. The water inlet temperature for each condition listed below is 25C

(298.15 K), with an average inlet velocity of .002 m/s and flow path height of 5mm. The

other parameters that remain constant are listed in Table 2.


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Table 7: Module Results

Fins Number Fin Length* (K) (K) None 0 0 303.75 302.99 17.84 62.11 79.95

Top

9 303.77 302.97 17.84 62.31 80.15

9 303.80 302.92 17.84 62.68 80.52

9 303.88 302.78 17.85 63.53 81.38

18 303.77 302.96 17.84 62.32 80.16

18 303.83 302.87 17.85 62.96 80.81

18 303.97 302.67 17.86 64.57 82.43

Bottom

9 303.77 302.95 17.84 62.35 80.19

9 303.80 302.86 17.85 62.63 80.48

9 303.85 302.71 17.86 63.24 81.1018 303.78 302.91 17.85 62.37 80.22

18 303.83 302.74 17.86 62.94 80.80

18 303.92 302.49 17.88 63.94 81.82

Labyrinth

(TopandBottom)

9 303.77 302.94 17.84 62.36 80.20

9 303.83 302.81 17.85 62.93 80.78

9 303.94 302.60 17.87 64.24 82.11

18 303.80 302.88 17.85 62.66 80.51

18 303.90 302.67 17.86 63.77 81.63

18 304.06 302.37 17.89 65.52 83.41

27 303.84 302.81 17.85 63.07 80.92

27 303.98 302.54 17.87 64.67 82.54

27 304.25 302.31 17.89 67.67 85.65

The electrical efficiency of the PV cell varied only slightly with each case, with a lowest

efficiency of 17.84% at the no-fin condition and only 17.89% for the most efficient,

many, large fin labyrinth condition. This is behavior is caused by the large driving

temperature difference between the PV Cells and the cooling water as well as the already

low thermal resistance between the two. Adding fins perpendicular to the flow path has

a slightly more dramatic effect on the thermal efficiency of the hybrid solar panel, as the

flow separation does cause the fluid to mix more, and therefore accept more energy from


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to PV cell. The thermal efficiency varies between 62.1% and 67.7%, a 5.6% difference

between the arrangement thermal efficiencies. The thermal efficiency is correlated with

electrical efficiency in Figure 23 below.

Figure 23: PV/T Module Thermal and Electrical Efficiency Correlation

As expected, the electrical and mechanical efficiencies are correlated. As the thermal

efficiency increases, more heat is transferred away from the PV cells, keeping the cells

at a lower operating temperature. Consistent with semiconductor properties, PV cell

efficiency, or hybrid solar panel electrical efficiency, is inversely related to the operating

temperature. Due to the small changes in electrical efficiency, net or overall efficiency

of the PV/T module is largely governed by the thermal efficiency.

Efficiency of the PV/T module is dependent on the fin length for fins both on the top and

the bottom of the flow channel. Longer fins perpendicular to the flow path increase the

efficiency of the hybrid solar panels when compared to small fins. The large fins create

the largest flow disruption, mixing the fluid. The results for the top and bottom fin

arrangements are shown in Figures 24 and 25 respectively.

61.00

62.00

63.00

64.00

65.00

66.00

67.00

68.00

17.83 17.84 17.85 17.86 17.87 17.88 17.89 17.90

The

rmalEfficiency

Electrical Efficiency

PV/T Module Efficiency Correlation


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28

Figure 24: Top Fin Arrangement Efficiency

The top fins are shown to have a more dramatic effect than bottom fins, as the top fins

increase surface area of the hot top wall while still causing separation of boundary

layers in the flow. By contrast, the bottom fins only contribute to flow mixing and

disruption of boundary layers. This is evident when comparing the efficiency graphs of

the top vs. bottom fins; Figures 24 and 25 respectively.

As expected, top and bottom fins together yield the highest efficiencies for the same

number of fins. Flow is mixed due to the addition of top and bottom fins, the surface

area of the hot boundary is increased with the addition of top fins, and the flow path

length is increased as the flow has to crisscross over top and bottom fins as illustrated

in Figure 18. The overall efficiencies of the labyrinth arrangement results are shown in

Figure 26.

79

80

81

82

83

84

85

86

1/4 1/2 3/4

OverallEfficiency

Fin Length

Top Fin Arrangement vs. Overall Efficiency

9 Top Fins

18 Top Fins


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Figure 25: Bottom Fin Arrangement Efficiency

Figure 26: Labyrinth Arrangement Efficiency

79

80

81

82

83

84

85

86

1/4 1/2 3/4

OverallEfficiency

Fin Length

Bottom Fin Arrangement vs. Overall Efficiency

9 Bottom Fins

18 Bottom Fins

79

80

81

82

83

84

85

86

1/4 1/2 3/4

OverallEfficiency

Fin Length

Labyrinth Fin Arrangement vs. Overall Efficiency

9 Labyrinth

18 Labyrinth

27 Labyrinth


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30

The highest overall efficiency is achieved for the arrangement with the largest number of

fins with fins on the top and bottom of the flow path and the largest fin size. This is

evidenced in Figure 26, which shows the case with 27 fins on the top and bottom of the

flow path and fins as long as the flow path height. Figure 27 shows a comparison of

all arrangements together for a full comparison, where the labyrinth flow arrangement

with 27 fins is clearly the most efficient arrangement for a given fin length.

Figure 27: All Fin Arrangements

3.2

PV/T Array Results

With the PV/T module results evaluated, the most efficient module case is repeated in an

array. From section 4.2, the most efficient module was the case with many, large fins in

a labyrinth arrangement. This is compared to an array with no fins for an overall com-

parison to the outlet water temperature and efficiency. The array is shown in Figure 28,

which consists of three modules, Figure 8, linked together. The boundary between each

module is assumed to be perfectly insulated, with only the outlet water temperature

carried from one module to the next. A perfectly insulated boundary assumption allows

79

80

81

82

83

84

85

86

1/4 1/2 3/4

OverallEfficiency

Fin Length

All Fin Arrangements vs. Overall Efficiency

27 Labyrinth

18 Labyrinth

18 Top Fins

9 Labyrinth

18 Bottom Fins

9 Bottom Fins

9 Top Fins


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31

for each module to be run as a separate entity, removing concerns of conduction from

the outlet, hot end of the array affecting the results already calculated at the cold, inlet

end. Also, the insulated boundary condition better reflects the use of a gasket material

between modules to prevent leaks in the flow path.

Figure 28: PV/T Array [6]

The array results are displayed in Table 8, with the same inlet and boundary conditions

as the PV/T module, including the inlet water temperature of 298.15 K. As an array, the

hybrid solar panel with a labyrinth fin arrangement delivers , calculated inAppendix D, of water that has been heated by 16.5 degrees Celsius. Without fins, the

model array heats the water to a temperature of 15.06 degrees, 1.4 degrees less than the

arrangement with fins. The energy transferred to the water has also cooled the PV cells,

maintaining, in both cases a similar cell operating efficiency. There is more heat trans-

ferred to the water in the case with the labyrinth fin arrangement, creating a higher

thermal efficiency; however, as the water temperature rises, the PV cell temperature

increases, decreasing the PV cell efficiency towards the end of the array. As a result of

this, the average electrical efficiency of the arrays, with and without fins, is about equal

at 17.5%, despite the higher electrical of the first module with the labyrinth fin arrange-

ment.


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Table 8: Array Results

Fins Number Fin Length* (K) (K)

None 0 0 313.21 307.88 17.47 55.68 73.15Labyrinth 27 314.66 307.79 17.48 60.93 78.02

The difference in overall efficiency is therefore controlled by the thermal efficiency, as

noted in Table 8. The amount of energy recouped from the environment is calculated in

the Appendix E, is a total of 440 W, for the conditions listed in Table 2.

As designed, the water and cell temperature of the hybrid solar panel continually rise as

flow travels along the flow path, so the heat transfer due to convection and radiation

increase. There is a greater amount of heat lost to the atmosphere and, as result, the

thermal efficiency of the PV/T array is lower than the module efficiency for both the

arrangement with no fins and the labyrinth. The convective and radiative heat losses to

the atmosphere for the array are calculated in Appendixes F and G respectively. The

values are and , showing the heat losses are consid-erable as the array reaches high temperatures.

3.3

Other Considerations

Because of this models 2-D nature, heat exchange structures such as pins were not

explored. An arrangement of many, small, cylindrical pins are expected to have a

positive effect on heat transfer between the fluid and the PV Cell. For a very space or

weight limited application, where cost doesnt have as much of an impact, a porous

media heat exchange process might also be explored.


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4. CONCLUSIONS

The greatest overall PV/T module efficiency of 85.7% occurs with the labyrinth ar-

rangement or the arrangement with 27 top and 27 bottom fins that are the height of the

flow path. This is an approximate 5.7% increase in efficiency over the arrangement withno fins. Sharp edged fins are used to cause flow separation, which mixes the fluid

despite the low Reynolds number and regardless of the boundary layer formation. Not

only is the flow mixing increased, but the flow path has been extended, as the flow

crisscrosses around the fins at the top and the bottom of the flow path. This increases

surface area between the working fluid and the hot, upper heat transfer boundary,

without increasing the length of the hybrid solar panel. The thermal efficiency has the

greatest variation, with the PV cell efficiency kept relatively constant due to the small

temperature differences of the PV cell temperature between each arrangement.

When connected as an array, three modules linked in a head to tail arrangement, heat the

water by 16.5 degrees Celsius, collecting 440 W from the environment in the form of

usable electrical and thermal energy. The fins in the array provide a 4.8% increase in the

overall efficiency over the array without fins, 78.0% vs. 73.2% respectively. Despite the

model limitations, fins perpendicular to the hybrid solar panel flow path are shown in

this model to increase the heat transfer between the PV cells and the cooling water,

increasing the amount of energy collected from the suns light.

As predicted, the efficiency of a hybrid solar panel can be increased with fins perpendic-

ular to the flow path. The efficiency increase is dependent on the number, size, and

arrangement of the fins, with the ideal arrangement consisting of many, large fins,

alternating between the top and bottom of the flow path in the direction of flow. Meth-

ods such as the labyrinth flow arrangement in a hybrid solar panel can be used to

optimize the energy conversion efficiency from solar energy, to a useful alternative to

fossil fuels.


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REFERENCES

1. NASA Goodard Space Flight Center. X-ray Spectroscopy and the Chemistry of

Supernova Remnants. March 25, 2010. Retrieved from http://imagine.gsfc.nasa.gov/docs/teachers/lessons/xray_spectra/spectra_unit.html. October 16, 2013.

2. Wagner, Doris J. Rensselaer Polytechnic Institute. Glossary for Semiconductors.

2004. Retrieved from http://www.rpi.edu/dept/phys/ScIT/Information Pro-

cessing/ semicond/sc_ glossary/scglossary.htm. October 12, 2013.

3. Chow, T. T. A review on photovoltaic/thermal hybrid solar technology; Applied

Energy, Volume 87, Issue 2010, Pages 365-379.

4. Skoplaki, E. and Palyvos, J.A. On the temperature dependence of photovoltaic

module electrical performance. Solar Energy, Volume 83, Issue 2009, Pages

614-624.

5. Armstrong, S. and Hurly, W.G. A thermal model for photovoltaic panels under

varying atmospheric conditions. Applied Thermal Engineering, Volume 30, Is-

sue 2010, Pages 1488-1495.

6. SMS075-090W Monocrystalline Photovoltaic Module. Iwiss Solar. http://iwiss-

solar.com/Solar-Module/SMS075-090W-Monocrystalline-Photovoltaic-Module/

November 22, 2013.

7. National Renewable Energy Laboratory. Solar Water Heating. March 1996.

Retrieved from http://www.nrel.gov/ docs/legosti/fy96/17459.pdf. September

29, 2013.

8. Green Air Incorporated. Efficient Solar Energy. November 29, 2012. Re-

trieved from http://www.getgreenair.com/solar. October 21, 2013.


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9. Fontenault, Bradley. Active Forced Convection Photovoltaic/Thermal Panel

Efficiency Optimization Analysis April 2012.

10.D. J. Yang, Z. F. Yuan, P. H. Lee, and H. M. Yin, Simulation and experimental

validation of heat transfer in a novel hybrid solar panel, International Journal of

Heat and Mass Transfer. Volume 55, Issue 2012, pages 1076-1082.

11.B. Sopori et al., Calculation of emissivity of Si wafers, Journal of Electronic Ma-

terials. Volume 28, Issue 1999, pages 13851389.

12.Brand TC-5026 Thermally Conductive Compound. Dow Corning. 2010. Form

No. 11-1689A-01. Retrieved From http://www.dowcorning.com/content/

publishedlit /11-1689a-01.pdf . October 27, 2013.

13.Suniva. ARTisun Select Monocrystalline Photovoltaic Cells. February 9, 2012.

Retrieved from http://www.suniva.com/products/ARTisun-Select-02-09-12. No-

vember 12, 2013

14.United States Environmental Protection Agency. Average Temperature of Shal-

low Groundwater. January 10, 2013. Retrieved from

http://www.epa.gov/athens/learn2model/part-two/onsite/ex/jne_henrys_

map.html. October 7th

, 2013.

15.White, Frank M. Fluid Mechanics 6th

Ed. McGraw-Hill series in mechanical

engineering. 1221 Avenue of the Americas, New York, NY. Copyright 2008.

16.Tsukahara, Takahiro, Kawase, Tomohiro, and Kawaguchi, Yasuo. DNS of Vis-

coelastic Turbulent Channel Flow with Rectangular Orifice at Low Reynolds

Number. International Journal of Heat and Fluid Flow Volume 32, Issue 2011,

Pages 529-538.


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APPENDIX A: CONSERVATION OF ENERGY CALCULATION

For a control volume, using the conservation of energy, the first law of thermodynamics

with no heat generation is

The inlet energy is the energy incident from the sun, taken for a unit length to relate to

the temperature rise in the 2-D model

The outlet energy is the energy absorbed by the fluid

Per unit width, the mass flow rate is the flow is

The temperature difference is then solved by setting the energy inlet equal to the energy

added to the flow.


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APPENDIX B: ELECTRICAL EFFICIENCY VERIFICATION

The equation for the electrical efficiency of a hybrid solar panel is dependent on the PV

cell temperature. The COMSOL model evaluates the efficiency at each element of the

PV cell layer in the model and then determines an average efficiency. The simplecalculation to verify the electrical efficiency is accomplished using only the average cell

temperature of the labyrinth arrangement with 27 top and bottom fins of flow path

height and the below equation [3].

The values of the room temperature efficiency,

, the temperature coefficient of

mono-crystalline silicon cells, , and the room temperature, are taken fromTable 2, with the value for the average cell temperature in Table 4.

The a temperature difference is the same in Celsius as Kelvin, with the temperature

values left in Kelvin for convenience. This is the same value calculated by the

COMSOL model for each cell element and then averaged. Using the average tempera-

ture of the PV cells is a very good estimate for the small temperature differences and

relatively linear temperature profile of the model results


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APPENDIX C: THERMAL EFFICIENCY VERIFICATION

The thermal efficiency of the labyrinth arrangement with 27 top and bottom fins of

flow path height is calculated using the below equation [3].

The output water temperature value from the PV/T module and inputs for the mass flow

rate, , and the suns inlet radiative power in, , previously calculated inSection 7.1, and , or the suns power into the panel, is are used tocalculate the efficiency. The specific heat value is taken at the outlet water temperature

of approximately 15C.

This value closely matches the 67.67% calculated by the model, and can be explained by

rounding error in this hand calculation.


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APPENDIX D: VOLUME FLOW RATE

The cross sectional area of the flow path is the height of the flow path multiplied by the

panel, or array width.

The volume flow rate is then calculated by multiplying the flow path cross sectional area

by the average flow velocity.

To make the units more intuitive, the volume flow rate is converted to liters per minute


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APPENDIX E: TOTAL ENERGY COLLECTED

For a PV/T cell, the Overall efficiency for a condition can be used to obtain the energy

collected from the environment.

The inlet energy is the energy incident from the sun using the dimensions of the PV/T

cell array is calculated below

The outlet energy of the cell is then taken using the efficiency of the PV/T cell with

many, large fins, in a labyrinth arrangement.


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APPENDIX F: CONVECTIVE HEAT LOSS

Convective heat loss for the hybrid solar panel array is given by the below equation.

The heat transfer coefficient of 10.52

and an ambient temperature of 298.15K are

taken from Table 2. The average PV/T array surface temperature for the labyrinth

arrangement is from Table 7. The collector area is


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APPENDIX G: RADIATIVE HEAT LOSS

Heat loss to the environment through radiation is described by the Stephan Bolzam

equation.

The average cell surface temperature

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