ABSTRACT
This work investigated the variation of top loss heat transfer coefficient
with the emittance of the absorber plate, the collector tilt angle and air
gap spacing between the absorber plate and the cover plate. The effects of
the emittance of the absorber plate, the collector tilt angle and air gap
spacing between the plate and the cover on the collector performance
were also considered. Data collected from the thermosyphon solar water
heater constructed by the National Centre for Energy Research and
Development (NCERD), UNN was used in the analysis. Evaluations of
thermal losses by radiative and convective heat transfer coefficient were
performed. It was observed that increase in the emittance of the absorber
plate resulted in dissipation of more heat to the atmosphere and
consequent increase in top loss heat transfer coefficient which led to
reduced system performance. The collector tilt angle had little effect on
the top loss heat transfer coefficient and consequently had insignificant
effect on the performance of the collector. Increase in the air gap spacing
between the absorber plate and the cover plate resulted in decrease in the
top loss heat transfer coefficient. It was also observed that passive flatplate
solar collector had a better performance at a low mean absorber
plate temperature. In addition, a correlation that relates the efficiency of
the collector with the absorber plate emittance, collector tilt angle and the
air gap spacing between the absorber plate and the cover plate was
developed for the NCERD thermosyphon water heater.
vi
TABLE OF CONTENTS
Title Page i
Approval ii
Dedication iii
Acknowledgement iv
Abstract v
Table of content vi
List of Table ix
List of Figure x
Nomenclature xi
CHAPTER ONE
INTRODUCTION
1.1 Need for Solar Energy 1
1.2 The Structure of the Sun 1
1.3 The Energy of the Sum 2
1.4 Solar Energy Utilization 3
1.4.1 Photochemcial Processes 3
1.4.2 Photovoltaic Processes 3
1.4.3 Photothermal Processes 4
1.5 Need for Solar Plate Collector 4
1.6 Solution Method 4
1.7 The Objective of the Thesis 5
CHAPTER TWO
LITERATURE REVIEW
2.1 Flat Plate Collector 6
2.2 Consideration of Some Flat Plate Collector Models 6
2.3 Conclusion 12
CHAPTER THREE
THEORETICAL CONSIDERATION
3.1 The Solar Constant 13
vii
3.2 Electromagnetic Spectrum 14
3.3 Thermal Radiation 14
3.4 Solar Radiation at Earth’s Surface 14
3.5 Radiation Heat Transfer for Solar Energy Utilization 15
3.6 General Description of Flat-Plate Collector 16
3.7 The Principle of Flat-Plate Collectors 17
3.8 Energy Absorbed by the Flat-Plate Collector 18
3.9 Thermal Losses in Flat-Plate Collector 18
3.10 Radiation Transmission through Covers 19
3.11 Collector Overall Heat Transfer Coefficient 20
3.12 Evaluation of Top-loss Coefficient 22
3.13 Thermal Losses and Efficiency of Flat-Plate Collector 23
3.14 Heat Transfer Analysis of the Solar Collector 24
3.15 Collector Efficiency Factor 25
3.16 Temperature Distribution in Flow Direction 26
3.17 Collector Heat Removal Factor 27
3.18 Collector Efficiency 27
3.19 Multiple Linear Regressions 29
3.20 LU Decomposition 30
CHAPTER FOUR
ANALYSIS OF RESULTS AND DISCUSSION
4.1 Source of Data 31
4.2 Determination of Heat Transfer Coefficients 33
4.3 Determination of Cover Plate Temperature, g T 34
4.4 Determination of the Mean Plate Temperature, T 35
4.5 Determination of the Collector Efficiency, 36
4.6 Evaluation of Parameters for Day 1 to Day 5 36
4.7 Summary of the computed results 37
4.8 Variation of top loss coefficient and efficiency
with plate emittance 43
viii
4.9 Variation of top loss coefficient and
efficiency with collector tilt angle 46
4.10 Variation of top loss coefficient and efficiency with air gap
spacing between the absorber plate and the cover plate 48
4.11 Correlation of the collector efficiency with the absorber
plate emittance, collector tilt angle and the air gap spacing 49
4.12 Coefficient of Determination 51
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION 53
REFERENCES 54
Appendix I Computed Values for the Parameters 57
Appendix I1: Visual Basic Solution Source Codes 122
Appendix III: Some Important parameters of the
Solar Plate Collector 137
Appendix IV: Some Important Physical Constant 138
Appendix V: Metallic Properties for Absorber Plates 139
Appendix VI: Thermal insulating Properties for Solar
Collectors 140
Appendix VII: Thermal and Optical Properties of
Cover Plate Material 141
Appendix VIII: Variation of Some Properties of
Air with Temperature at atmospheric
Pressure 142
Appendix IX: Latitude and Longitude of some
Cities in Nigeria 143
ix
LIST OF TABLES
Table 4.1: Data of 19th December, 2002 (Day 1) 32
Table 4.2: Data of 19th January, 2003 (Day 2) 32
Table 4.3: Data of 4th February, 2003 (Day 3) 32
Table 4.4: Data of 15th July, 2003 (Day 4) 32
Table 4.5: Data of 23rd July, 2003 (Day 5) 33
Table 4.6: Values of plate emittance, top loss
coefficient and efficiency of the collector 37
Table 4.7 Values of collector tilt angle, top loss
coefficient and efficiency of the collector 39
Table 4.8: Values of air gap spacing, top loss
coefficient and efficiency of the colletor 41
Table 4.9: Values of efficiency, absorber plate
emittance, and collector tilt angle and air gap
spacing 50
Table 4.10: Computation of R2 52
x
LIST FIGURES
Figure 3.1 Schematic of sun-earth relation 13
Figure 3.2 Basic flat plate solar collector cross section 16
Figure 3.3 Features of radiation transmission 19
Figure 3.4 Energy balance on fluid element 26
Figure 4.1 A plot of the variation of the top loss heat
transfer coefficient with absorber plate emittance 43
Figure 4.2 A plot of the variation of the efficiency of the
collector with absorber plate emittance 44
Figure 4.3 A plot of the variation of the top loss heat
transfer coefficient with the collector tilt angle 46
Figure 4.4 A plot of the variation of the efficiency of the
collector with collector tilt angle 46
Figure 4.5 A plot of the variation of the top loss heat
transfer coefficient with the air gap spacing
between absorber plate land cover plate 48
Figure 4.6 A plot of the variation of the collector efficiency
with the air gap spacing between absorber plate
and cover plate 48
xi
NOMENCLATURE
A area, m2
Au astronomical unit
C conductance, W/m0K
c velocity, m/s
C1 Planck’s first radiation constant, Wm2
C2 Planck’s second radiation constant, m0K
Cp specific heat capacity at constant pressure, kJ/kg0K
D diameter, m
Do Outside diameter, m
Di Inside diameter, m
E energy, J
e emissive power, W/m2
F collector efficiency factor
FR collector heat removal factor
H hydrogen
h heat transfer coefficient,W/m2oK
He helium
hcp convective heat transfer coefficient between the
absorber plate and the cover,W/m2oK
hrg radiative heat transfer coefficient between the absorber
plate and the cover,W/m2oK
hrs radiative heat transfer coefficient between the cover
and the sky,W/m2oK
hw wind loss coefficient,W/m2oK
I radiation intensity, W/m2oK
Isc Solar constant, W/m2oK
K length extinction coefficient,cm-1
k thermal conductivity, W/mK
L length, m; loss
m mass, kg
m mass flow rate, kg/s
n index of refraction
xii
N number of covers
Nu Nusselt Number
NCERD National Centre for Energy Research and
Development.
Q energy per unit time, W
q energy per unit time per unit area, W/m2
R ratio of total radiation on tilted surface to that on plane of
measurement
Ra Rayleigh Number
T temperature,0K
UB bottom loss heat transfer coefficient, W/m2oK
UE edge loss heat transfer coefficient ,W/m2oK
UL overall loss heat transfer coefficient, W/m2oK
UT top loss heat transfer coefficient, W/m2oK
W distance between tube centers, m
absorptance
collector tilt angle, degree; coefficients of the least square
estimators
thickness, m
emittance
angle between surface normal and bean radiation, degree
wavelength, m
reflectance
Stefan Boltzmanns constant,W/m2oK4
dynamic viscosity, kg/ms
transmittance
hour angle, degree
i incident
Subscript
a ambient
i inlet
o outlet
xiii
u useful
B bottom
e effective
c collector
p plate
f fluid
z zenith
1
CHAPTER 1
INTRODUCTION
1.1 Need for Solar Energy
Conventional energy resources are not only limited in supply but are
exhaustive in nature. In the near future, the present energy conversion
systems will change drastically, due to lack of conventional fuels. Thus,
there is a need for alternative energy resources, since energy remains central
to the existence and survival of mankind. Many studies of world energy
supply and demand and of projected national and regional energy
requirements suggest that there will be an increasing strain on conventional
petroleum and natural gas supplies to the point where substitution for these
fuels on a large scale will become necessary towards the end of the century,
if not before[1]. The two most significant permanent sources of energy are
nuclear and solar energy.
Nuclear energy is associated with changes in the structure and composition
of the nucleus of matter. Nuclear energy requires advanced technology and
costly means for its safe and reliable utilization and may have undesirable
side effects [2]. On the other hand, although, the engineering design and
analysis of solar processes present unique problems, the utilization of solar
energy shows promise of becoming a dependable energy source. Solar energy
in its manifold forms is potentially the most important energy source that is
renewable indefinitely (that is as long as the Sun shines) and, in the very
long term when fossil and fission fuels are exhausted, the Sun is the only
alternative to those nuclear fusion and fission reactors which might be
constructed on Earth [1].
1.2 The Structure of the Sun
The Sun is the source of solar energy. It is a sphere of hot gaseous matter.
The Sun generates its energy by fusion reactions. It has a mass of about
1.99 x 1030kg with an estimated diameter of 1.39 x 106km. The density of
the sun is estimated at 1410kg/m3. The solar interior constitutes the main
2
mass of the Sun and has gases at pressure of a billion atmospheres and
temperature of 8.0 x 106 to 4.0 x 107oK [2].
[3] reported that the center to 0.23R (where R = radius of the Sun), which
contains 40% of the mass of the Sun is estimated to generate 90% of the
interior energy of the Sun. The energy generated in this core part of the Sun
is radiated in the form of gamma rays up to a distance of about 0.7R from
the centre, where the temperature has dropped to about 130,000oK.
The zone from 0.7R to 1.0R is known as the convective zone. It contains fluid
in which energy transfer is mainly by convection. The temperature at the
outer surface of the convective zone is about 6,000oK. This outer layer of the
convective zone is called the photosphere. It is essentially opaque, as the
gases which it is composed are strongly ionized and are able to absorb and
emit continuous spectrum of radiation. The photosphere is the source of
most solar radiation.
Above the photosphere is a layer of cooler gases called the reversing layer.
Outside of the reversing layer is the chromosphere. The chromosphere is at
about 106oK. The light emitted by the chromosphere is of short wave length
because of the high temperature. Still further out is the corona. The corona
is made of highly ionized gases of very low density. Its temperature is about
106oK.
1.3 The Energy of the Sun
The fusion reactions which have been suggested to supply the energy
radiated by the Sun have been several reactions; the one considered the
most important is a process in which hydrogen combines to form helium [3].
The equation of the reaction is:
41H12He4+26.7MeV (1.1)
In the reaction, four protons having a total uncombined mass of 4.0304amu
formed helium of mass 4.0027amu. The difference in mass of the reactant
and the product is 0.0277atomic mass unit of matter. This mass is
converted to energy in accordance with the Einstein relationship (E= mc2).
3
Several of these chain reactions taking place in the interior region of the Sun
generate most of the energy of the Sun.
1.4 Solar Energy Utilization
The direct and indirect uses of solar energy by mankind have been in
existence for centuries. Man had used solar energy for drying purposes,
warming purposes and so on. The various uses of the solar energy can be
categorized into three broad classes; viz; photochemical processes,
photovoltaic processes and photothermal processes.
1.4.1 Photochemical Processes
Photochemical processes have been defined as those in which the absorption
of solar photons in a molecule produces excited states, or alternatively in a
semi-conductor raises electrons from the valence band to the conduction
band. As a result of the chemical reactions which may then occur, some of
the excited energy may be stored as chemical energy or a useful chemical
reaction may be catalyzed. Photochemical is a technology to synthesize
valuable chemical materials or fuels by the use of solar energy.
1.4.2 Photovoltaic Processes
Photovoltaic solar system is the process of converting light energy from the
Sun into electricity in the absence of mechanical generators. The
photovoltaic effect generates electromotive force as a result of the absorption
of ionizing radiation. When photons from the Sun are absorbed by some
semi-conductors, they create free electrons with higher energies than the
electrons which provide the bonding in the base crystal. Once these free
electrons are created, there must be an electric field to induce these higher
energy electrons to flow out of the semi-conductors to do useful work.
Photovoltaic solar systems generate direct current. Inverters are required to
convert the direct current into alternating current. When the electricity
generated is to be used in a later time, a deep cycle motive battery is
required to store the electrical energy. Power from photovoltaic solar systems
can be used for powering alarm systems, navigational aids, electric bulbs,
home appliancies, water pumps, and for grid connection.
4
1.4.3 Photothermal Processes
Photothermal processes involve the use of solar plate collectors. Solar plate
collectors intercept solar radiation and convert the radiation into heat. Solar
plate collectors are either focusing (concentrating) type or flat plate type.
Focusing collectors usually have concave reflectors to concentrate the
radiation falling on the total area of the reflector onto a heat exchanger of
smaller surface area, thereby increasing the energy flux. Focusing collectors
use optical system in the form of reflectors. In flat-plate collectors, the area
intercepting solar radiation is the same as the area absorbing solar
radiation.
1.5 Need for Solar Plate Collector
Solar plate collectors convert solar radiation to heat energy. This heat energy
can be utilized in various applications. In Nigeria today, Power Holding
Company of Nigeria Plc, a body saddled with supplying power to, and
operating, the national grid has failed. Nigerians therefore need an efficient
and cost effective means of meeting their energy needs. It is in this respect
that the need for solar plate collector systems becomes imperative
1.6 The Objectives of the Thesis
The objectives of this work are
a. To consider the theoretical analysis of a passive flat plate solar
collector.
b. To investigate the effects of collector tilt angle, absorber plate
emittance and the air spacing between the absorber plate and the
cover plate on the top loss coefficient and consequently on the
performance of the collector.
c. To develop a correlation that relates the efficiency of the passive flat
plate solar collector to the collector tilt angle, absorber plate
emittance and the air spacing between the absorber plate and the
cover plate.
5
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