design and development of double exposure solar cooker
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Thermal Engineering Thesis
2020-05-21
DESIGN AND DEVELOPMENT OF
DOUBLE EXPOSURE SOLAR
COOKER WITH FINNED COOKING VESSEL
Yohannes, Mintesinot
http://hdl.handle.net/123456789/10844
Downloaded from DSpace Repository, DSpace Institution's institutional repository
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BAHIR DAR UNIVERSITY BAHIR DAR INSTITUTE OF TECHNOLOGY
FACULTY OF MECHANICAL AND INDUSTRIAL
ENGINEERING
DESIGN AND DEVELOPMENT OF DOUBLE EXPOSURE SOLAR
COOKER WITH FINNED COOKING VESSEL
BY
Mintesinot Yohannes
Bahir Dar, Ethiopia.
September, 2017
DESIGN AND DEVELOPMENT OF DOUBLE EXPOSURE SOLAR COOKER
WITH FINNED COOKING VESSEL
Mintesinot Yohannes
A thesis submitted to the school of Research and Graduate Studies of Bahir Dar
Institute of Technology, BDU in partial fulfillment of the requirements for the degree
of
Masters of science in Thermal Engineering faculty of Mechanical and Industrial
Engineering
Advisor: Dr. Abdulkadir Aman (PhD)
BahirDar, Ethiopia
September, 2017
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DECLARATION
I, the undersigned, declare that the thesis comprises my own work. In compliance with
internationally accepted practices, I have acknowledged and refereed all materials used in this
work. I understand that non-adherence to the principles of academic honesty and integrity,
misrepresentation/ fabrication of any idea/data/fact/source will constitute sufficient ground for
disciplinary action by the University and can also evoke penal action from the sources which have
not been properly cited or acknowledged.
Name of the student Mintesinot Yohannes Signature _____________
Date of submission: ________________
Bahir Dar
This thesis has been submitted for examination with my approval as a university advisor.
Advisor Name: Dr. Abdulkadir Aman (PhD)
Advisor’s Signature: ______________________________
ii
© 2017
Mintesinot Yohannes
ALL RIGHTS RESERVED
iii
Bahir Dar University
Bahir Dar Institute of Technology
Faculty of Mechanical and Industrial Engineering
THESIS APPROVAL SHEET
Student:
Mintesinot Yohannes
Name Signature Date
The following graduate faculty members certify that this student has successfully presented the
necessary written final thesis and oral presentation for partial fulfillment of the thesis requirements
for the Degree of Master of Science in Thermal Engineering.
Approved by:
Advisor:
Dr. Abdulkadir Aman (PhD)
Name Signature Date
External Examiner:
Dr. Solomon T. (PhD)
Name Signature Date
Internal Examiner:
Prof. (Dr.) V. Siva Ramakrishnan
Name Signature Date
Chair Holder:
Mr. Million Asfaw
Name Signature Date
Faculty Dean:
Mr. Muluken Zegeye
Name Signature Date
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To my family & B.
v
ACKNOWLEDGEMENTS
First I would like thank God for everything. Secondly Special thanks and appreciation to my
supervisor Dr. Abdulkadir Aman (PhD), for his interest, advice, and many suggestions and
constructive support during this thesis work. Thanks to my family for their encouragement and
material support during this study, and also to all my class mates for being beside during
experimental test work.
Bahir-Dar, Ethiopia Mintesinot Yohannes
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ABSTRACT
The solar energy is arguably the most widely available and abundant energy resource. The energy
scarcity, energy cost for cooking purpose, indoor pollution and the time spent in gathering fuel
woods are the main problems that leads us to study and develop the cooker. The purpose of this
study is to design, develop and to investigate the performance of a double exposure solar cooker.
In this study the effects of reflected surface in the box and parabola which is disposed under the
box parts of the cooker were studied in independently under the same climatic condition. During
stagnation test the average temperature and solar isolation of the day (June 10/2017) is 28.70C and
648.3W/m2 respectively that resulted stagnation plate temperature of 152.20C. The “First figure of
merit” of the cooker is 0.127 which represents the cooker marked as grade-A solar cooker. The
test also conducted by removing the parabolic flat reflectors. During these test the “First figure of
merit” is 0.088, which leads the cooker marked as Grade-B solar cooker (according to American
Society of Agricultural Engineers and Bureau of Indian Standards testing standard).
A comparative experimental study of double exposure solar cooker with two different cooking
vessels was conducted, the first one conventional and the second one identical to the first in shape
and volume but its external lateral surface provided with fins. Fins are shown to improve the heat
transfer from the internal hot air of the cooker towards the interior of the vessel where the food to
be cooked is placed. The experimental test results show that under the same climatic condition and
equal cooking time, the temperature of finned cooking vessel reaches 93.6oC while the un-finned
cooking vessel is 88.8oC. The power test also conducted for finned and un-finned cooking vessels.
The coefficient of determination or proportion of variation in cooking power that can be attributed
to the relationship found by regression for finned and un finned cooking vessel is 0.9528 and
0.8952 respectively. The overall efficiency of the cooker also evaluated for both finned and un-
finned cooking vessel under the same climatic condition by limiting the time in 60 min, boiling
efficiency of finned and un-finned cooking is 86% an 69% respectively.
The evaluation of the economic analysis of the system is financially feasible (benefit- cost ratio =
1.37). The capital cost of the system is 4657.18ETB with the yearly maintenance cost of
335.75ETB which can use efficiently for five years and pay back the capital cos in three years.
vii
TABLE OF CONTENTS
DECLARATION ............................................................................................................................. i
ACKNOWLEDGEMENTS ............................................................................................................ v
ABSTRACT ................................................................................................................................... vi
TABLE OF CONTENTS .............................................................................................................. vii
LIST OF ABBREVATIONS ......................................................................................................... xi
LIST OF SYMBOLS .................................................................................................................... xii
LIST OF FIGURES ..................................................................................................................... xiii
LIST OF TABLES ........................................................................................................................ xv
CHAPTER ONE ............................................................................................................................. 1
1. INTRODUCTION .................................................................................................................. 1
1.1. Background ...................................................................................................................... 1
1.2. Statement of problems ...................................................................................................... 4
1.3. Objectives ......................................................................................................................... 4
1.3.1. General objectives ..................................................................................................... 4
1.3.2. Specific objectives .................................................................................................... 5
1.4. Significance of the study .................................................................................................. 5
1.5. Purpose and Scope ........................................................................................................... 5
1.6. Limitation of the study ..................................................................................................... 6
CHAPTER TWO ............................................................................................................................ 7
2. LITERATURE REVIEW ....................................................................................................... 7
2.1. Box-type solar cookers ..................................................................................................... 8
2.2. Classification of Solar Cooker ....................................................................................... 13
2.3. Components of Box Solar Cooker ................................................................................. 14
viii
2.3.1. Booster mirror ......................................................................................................... 16
2.3.2. Insulation................................................................................................................. 17
2.4. Cooking Vessels till Now ............................................................................................... 18
2.5. Conclusion and Gaps ...................................................................................................... 19
CHAPTER THREE ...................................................................................................................... 20
3. METHODOLOGY AND DESIGN PROCEDURES ........................................................... 20
3.1. Energy for cooking ......................................................................................................... 22
3.1.1. Averaged solar data of the site ................................................................................ 22
3.2. Size of the cooker ........................................................................................................... 25
3.3. Thermodynamic assessment of solar cookers ................................................................ 28
3.4. Material selection ........................................................................................................... 29
3.5. Construction of prototype............................................................................................... 30
3.5.1. Stand ....................................................................................................................... 30
3.5.2. The box cooker ....................................................................................................... 31
3.5.3. Booster (Box reflectors) .......................................................................................... 32
3.5.4. Parabolic flat reflectors ........................................................................................... 33
3.6. Measuring instrument ..................................................................................................... 39
3.7. Performance Testing Procedures and Standards ............................................................ 40
3.7.1. The Stagnation Temperature Test ........................................................................... 41
3.7.2. Thermal Load Test, Heat up Condition Test .......................................................... 41
3.8. Cooking Power Estimation............................................................................................. 42
3.8.1. Steps for the Determination of Cooking Power ...................................................... 42
CHAPTER FOUR ......................................................................................................................... 44
4. EXPERMENTAL TEST ANALYSIS .................................................................................. 44
ix
4.1. Performance Testing ...................................................................................................... 44
4.1.1. Stagnation Test........................................................................................................ 44
4.1.2. Stagnation Test with parabolic flat reflectors ......................................................... 45
4.1.3. First Figure of Merit(F1), (with parabolic flat reflectors)....................................... 45
4.1.4. Stagnation test (parabolic flat reflectors off) .......................................................... 46
4.1.5. First Figure of Merit (F1) (Parabolic flat reflectors off). ........................................ 47
4.1.6. Load Test (Water Heating Test) ............................................................................. 47
4.1.7. The second figure of merit(F2) ................................................................................ 49
4.1.8. Water Heating Time ................................................................................................ 50
4.2. Cooking power During Test ........................................................................................... 51
4.3. Efficiency of Finned and Un-Finned Cooking Vessel. .................................................. 51
4.4. Sample of cooking .......................................................................................................... 53
CHAPTER FIVE .......................................................................................................................... 55
5. RESULT AND DISCUSION ............................................................................................... 55
5.1. Stagnation Test Result - Parabolic Reflector ON.......................................................... 55
5.2. Stagnation Test Result- Parabolic Reflector Off ............................................................ 56
5.3. Load Test Result............................................................................................................. 57
5.4. Cooking Power Test Result ............................................................................................ 58
5.5. Overall Result ................................................................................................................. 59
CHAPTER SIX ............................................................................................................................. 61
6. ECONOMIC ANALYSIS OF THE OVERALL SYSTEM ................................................. 61
6.1. Cost of the Double Exposure Solar Cooker ................................................................... 61
6.2. Maintenance Cost ........................................................................................................... 63
6.3. Valuations of Benefit. .................................................................................................... 64
x
6.4. Financial Analysis .......................................................................................................... 66
6.5. Payback period ............................................................................................................... 67
7. CONCLUSIONS AND RECOMMENDATIONS ............................................................... 69
7.1. CONCLUSION .............................................................................................................. 69
7.2. RECOMMENDATIONS ............................................................................................... 70
REFERENCES ............................................................................................................................. 71
APPENDIX ................................................................................................................................... 74
xi
LIST OF ABBREVATIONS
ASAE American Society of Agricultural Engineers.
BCR Benefit Cost Ratio.
BIS Bureau of Indian Standards.
CR Capacity Ratio.
DESC Double-Exposure Solar Cooker.
FAO Food and Agriculture Association.
FPC Flat Plate Collector.
NPV Net Present Value.
PFR Parabolic Flat Reflectors.
SBC Solar Box Cooker.
TIM Transparent Insulating Materials.
xii
LIST OF SYMBOLS
sP Cooking standard power (W)
wM Mass of water (Kg)
iT Initial temperature ( oC )
fT Final temperature ( oC )
t Time in (s)
pC The specific heat capacity of water is (KJ/Kg. K)
θ The temperature difference ( oC )
0 The optical efficiency (%)
I The global solar radiation in (W/m2)
U The thermal loss coefficient in (W/m2K)
𝐴C The collector aperture surface in (m2)
,in outE E Energy entering and leaving the system respectively.
U Wind speed (m/s).
W Material width (m)
L Material Length (m)
K Thermal conductivity of material
Energy efficiency
1F First figure of merit (2Km W )
2F Second figure of merit ( 2Km W )
LU Overall heat loss factor ( 2W m K )
xiii
LIST OF FIGURES
Figure 1-1 The schematic plan of the experimental setup for different 3 positions of reflector (a)
position 1 (b) position 2 (c) Position and (d) overall reflection view. ............................................ 3
Figure 2-1 Solar box cooker used for the experiment, (p.95) by B. Z. Adewole et al [12] ............ 8
Figure 2-2 Thermal performance curve of the solar box cooker under stagnation test condition
(p.97) by B. Z. Adewole et al [12]. ................................................................................................. 9
Figure 2-3 Thermal performance curve of the solar box cooker during sensible heat test of 2.0 kg
of water (p.98) by B. Z. Adewole et al [12]. ................................................................................. 10
Figure 2-4 Variation of water temperature with time for different loads, (p.95) by B. Z. Adewole
et al [12]. ....................................................................................................................................... 11
Figure 2-5 Water boiling test. Comparison between water temperature in the finned cooking pot
and the water temperature in the UN- finned cooking pot............................................................ 11
Figure 2-6 Variation of temperature of the different base of the vessels in summer and winter days
(at Coimbatore) ............................................................................................................................. 12
Figure 2-7 Time variation of temperature of water in different base of the vessels in summer and
winter days (at Coimbatore).......................................................................................................... 13
Figure 2-8 Component of box solar cooker with one reflectors. .................................................. 15
Figure 2-9 The photographic view Booster mirror of box-type solar cooker. .............................. 16
Figure 3-1 Some Energy entering and leaving on glass-1 representation on solid work. ............ 20
Figure 3-2 The solar isolation of the site ( 2 /Whr m day ) ............................................................ 23
Figure 3-3 Closed system heat energy entering and leaving the system. ..................................... 25
Figure 3-4. shows heat energy entering and leaving the system ................................................... 28
Figure 3-5. Schematics and photographic view of Frame (stand) of cooker ................................ 31
Figure 3-6. The photographic view of constructed box soar cooker ............................................ 32
Figure 3-7. (a), Welded rectangular steel frame. (b), Representation on solid work (c) The
photographic view of boosters. ..................................................................................................... 33
xiv
Figure 3-8. Schematic and photographic view of parabolic flat reflector. ................................... 34
Figure 3-9. Schematic diagram of angles used to calculate the arc length ................................... 34
Figure 3-10. Shows the triangle AOB intercepted arc ACB ......................................................... 35
Figure 3-11. Shows the arc length (ACB) .................................................................................... 37
Figure 3-12. The parabolic curve with arc length of S = 110cm. ................................................. 38
Figure 3-13 The full designed, constructed and schematic diagram of the existing double exposure
solar cooker. .................................................................................................................................. 39
Figure 3-14. a) Solar power meter b), thermometer Y-811 c) Thermocouples d) Infrared
thermometer .................................................................................................................................. 40
Figure 4-1. The experimental test result during stagnation test (June 10/2017). .......................... 45
Figure 4-2 Experimental test result during stagnation test condition when parabolic flat reflectors
off (June 13/2017). ........................................................................................................................ 47
Figure 4-3 Finned and un-finned cooking vessel with the same volume. .................................... 48
Figure 4-4. The experimental water temperature test (June 16/2017) .......................................... 48
Figure 4-5 The sample test of cooking by 0.5kg 0f macaroni adding 1.5kg of water. ................. 54
Figure 5-1 Thermal performance curve of the double exposure solar cooker under stagnation test
condition. ...................................................................................................................................... 55
Figure 5-2. Thermal performance curve of the double exposure solar cooker under stagnation test
condition (parabolic flat reflectors off) June 13/2017. ................................................................. 56
Figure 5-3. Thermal performance curve of the double exposure solar cooker under loaded (water
heating) test June 16/2017. ........................................................................................................... 57
Figure 5-4 Standard Cooking power versus Temperature difference graph of un-finned vessel
(Appendix, B-9). ........................................................................................................................... 58
Figure 5-5. Standard Cooking power versus Temperature difference graph of finned cooking vessel
Appendix, (B-10). ......................................................................................................................... 59
xv
LIST OF TABLES
Table 3-1 Monthly average maximum and minimum temperature of Bahir-dar city (Metrology
data)............................................................................................................................................... 23
Table 3-2 Monthly average solar isolation of Bahir-dar city(Metrology data). ........................... 23
Table 3-3 Data and Result of power required. .............................................................................. 25
Table 3-4 Selection standards of materials. .................................................................................. 29
Table 4-1 Shows the instantaneous efficiency of finned cooking vessel ...................................... 52
Table 4-2 The result of instantaneous efficiency of the solar cooker for un-finned cooking vessel
is shown in the table below. .......................................................................................................... 53
Table 5-1 Overall concluded result of the cooker ......................................................................... 60
Table 6-1 Non-linear regression coefficient and other input parameter ( ith component) ........... 61
Table 6-2 linear regression coefficient and other parameter ( jth component) ............................ 62
Table 6-3 The cost of the ith and the jth components are listed in the table below in, by applying
equation 4.8. .................................................................................................................................. 62
Table 6-4 Annual maintenance cost of a family size double Exposure solar cooker. .................. 64
Table 6-5 Cost benefit of the cooker with each type of fuel. ........................................................ 65
Table 6-6 The cost and benefit of the system for next 5 years ..................................................... 66
1
CHAPTER ONE
1. INTRODUCTION
1.1. Background
Ethiopia, a country with thirteen months of sunshine, is blessed with a good amount of solar energy
that can be converted in to heat. The use of this energy has a positive effect on the sustainability
of the economy since it is a renewable energy. And on the global scale, the use of solar energy
reduces environmental degradation. The solar energy is arguably the most widely available and
abundant energy resource. It can be converted in to heat energy through the use of appropriate
solar collector system. Usually water is used as a working fluid as it is the most preferred media
for energy transmission.
People uses fuel as energy for cooking. However, many residents at undeveloped countries or rural
area may face difficulties in gaining this source. They may have to walk a long distance to collect
firewood or dung in order to cook. Thus a lot of time would be wasted. The worse is many of them
have to use major incomes for these purpose. Consequently a few decades ago many scientists
have started to develop alternative cooking method that could help to reduce their burden.
Solar energy is the energy from the sun. The sun generates energy in a process called nuclear
fusion. During this process four hydrogen nuclei combine to become helium atom with the release
of energy. This energy is emitted to the space as solar radiation. A small fraction of this energy
reaches the earth. Today solar energy is used in various applications such solar heating, distillation,
drying, cooking etc. To cook food for nourishment is fundamental to any society and these require
the use of energy in some form. The use of solar energy to cook food presents a viable alternative
to the use of fuel wood, kerosene, and other fuels traditionally used in developing countries for the
purpose of preparing food. Increased in the awareness of the global need for alternative energy
source has led to proliferation of research and development in solar cooking. Solar cooking can be
used as an effective mitigation tool with regards to global climate change, deforestation, and
economic debasement of the world’s poorest people. Solar Energy has tremendous advantages in
country like Ethiopia because of it abundance and sustainable source of energy. The use of solar
cookers will have a great potential of reducing the suffering of many people from the shortage and
high cost of fossil and other sources fuels. It will also reduce the tedious task faces by rural women
2
in search of fire wood for cooking. Several factors including access to materials, availability of
traditional cooking fuels, climate, food preferences, and technical capabilities: affect people’s
perception of solar cooking.
One of the alternative have been well developed and widely distributed or promoted for its use is
a solar cooker. Solar cookers are a suitable means of preventing the burning of fossil fuels, forest
resources and protecting the environment. Increasing the capabilities and applications
development of solar cookers are two main areas of this subject, which account for a large number
of experimental and theoretical studies. Solar cooking is a needed process worldwide and finds its
application in areas with good solar radiation intensity. Because of energy supply shortages and
also because the fuel price makes it unaffordable to many people in developing countries, a good
quality and yet affordable cooker is needed.
To date rural women in Ethiopia and other developing countries use labor and waste considerable
time of day in search of firewood to meet their cooking energy requirement. The necessity for the
search for available and affordable alternative source of energy to supplement the use of firewood
for food cooking cannot be over emphasized. Solar energy through solar cooking offers a possible
solution to these problems. Many experimental and theoretical studies have been done to develop
the capabilities of solar cookers, and different methods have been employed to improve the thermal
performance and their efficiency.
Solar box cooker is the simplest type of solar cooker available because it is relatively cheap, low-
tech device [1]. The cooking time depends primarily on the materials being used, the amount of
sunlight at the time of cooking, and the quantity of food that needs to be cooked. Air temperature,
wind, and latitude also affect its performance. The box type solar cookers are becoming more
popular in many countries. Box type solar cookers are slow to heat up but work satisfactory where
there is diffuse radiation, convection heat loss caused by wind, intermittent cloud cover and low
ambient temperature. The box-type solar cooker essentially converts solar energy in to heat energy
which is finally utilized to cook the food stuff kept in the cooker. In general, the box cookers take
long cooking time compare to other cooker like concentrating type to fully cook the food with less
time.
The present investigation is a double exposure solar cooker (DESC) which is a box type solar
cooker with support of parabolic reflector disposed under the cooker desire additional heat input
3
to the cooking vessel, in which the absorber is exposed to the solar radiation from both sides (at
the top of the box from boosters and parabolic flat reflectors placed under the box). A box-part of
DESC is single glazed an at the top as usual to transmit sun radiation and a double-glass at the
bottom allowing the absorber plate to receive maximum solar radiations reflected from parabolic
flat reflector on its lower side.
Figure 1-1 The schematic plan of the experimental setup for different 3 positions of reflector (a)
position 1 (b) position 2 (c) Position and (d) overall reflection view.
A schematic sketch of double exposure solar cooker is shown in Fig. 1.1. The schematic diagram
shows the parabola is reflecting sun radiation from three different positions which should be
4
adjusted properly to distribute the reflected sun radiation in different part of the absorber plate.
Three different positions P1, P2 and P3, during adjusting the parabolic flat reflectors, the three
reflectors in each position should have closer tilt angle in order to reflect same range but different
part of the absorber plate. The heat transfer into the pot in solar cookers of different types was the
subject of a number of experimental and theoretical studies. By developing the prototype in
possible manner, implementing all necessary procedures and input for a given type of solar cooker
it is possible to reduce the cooking time by carrying out modifications on the shape of the cooking
vessel. These modifications can improve heat transfer to the food through the pot walls.
1.2. Statement of problems
The demand of energy for cooking purpose increases with increasing population and consumption
rate. Most of rural area of Ethiopian people goes from one place to another for gathering fuel wood
for cooking purpose and the spent their productive time and energy in searching and collecting
wood, these decreases the productivity of them as well as the country and has led to deforestation,
soil degradation resulting environmental change.
The scarcity of energy, rising of energy cost for cooking purpose and indoor pollution during
cooking which cusses healthy problems are the main problems resulted in financial and health
sector.
The low efficiency and long cooking time in existing box type solar cooker can be aimed to
improve by applying additional reflection element disposed under the box to gain additional heat
input to the box cooker. The heat transfer problems related to cooking vessel and working
temperature range for cooking are the main problems observed in designing and developing these
cooker.
1.3. Objectives
1.3.1. General objectives
The general objective of this study is to design, construct and investigate the performance of a
modified box type solar cooker supported by parabolic reflector disposed under the cooker and
finned cooking vessel aimed to improve the efficiency of box cooker by modified box cooker.
5
1.3.2. Specific objectives
To improve the efficiency of the box solar cookers and to made the first and second figure
of merit above the standard value to make the cooker Grade-A solar cooker.
Determining the cooking energy requirements for an average household based on energy
for cooking a selected food item.
Designing the system based on the solar energy potential for a selected site and size of
cooking vessel used for the setup.
Development of a prototype for the overall system from low cost and locally available
materials.
Developing a finned cooking vessel to increase the effective area for heat transfer
Experimental investigation of the performance of the cooking system with both the finned
and un-finned cooking vessel
Economic analysis of the overall system.
1.4. Significance of the study
The solar cookers if available can offer a partial solution to multitude of cooking problems face by
people of low income. A properly designed and improved cooker if introduce in to the market in
mass scale can supplement the cooking energy requirement of several millions of people and
reduce deforestation and environmental problems associated with the use of fossil fuels Solar
cooker which is safe and simple to operate can satisfactorily be used for cooking in the presence
of sunshine.
1.5. Purpose and Scope
The aim of this study is to develop double exposure solar box cooker with finned cooking vessel
in order to reduce the stresses in cooking by reducing the cooking hour. The cooker has to be easy
to operate with low maintenance cost and should be capable to boil water and cook food.
Study of a double exposure solar cooker is designed based on the weather condition of specific
location of selected site and the test result observed could be based on the location of the location
of the site which may affect the performance of the cooker. The system can be designed to follow
manually tracking mechanism by households depend on the position of the solar radiation.
6
1.6. Limitation of the study
Solar energy is one of the renewable energy which is affected by uncontrolled variable and natural
features in which the cooker is restricted to sunny period. Due to the cost of construction, it is
impossible to try different version of the prototype. The test was conducted with limited number
of instruments and the result may show small deviation from actual and controlled cooking test.
The continuous movement of the solar cooker in every 15 minutes to track maximum solar
radiation, un attended cooking may result in hot spot area and inefficient cooking.
7
CHAPTER TWO
2. LITERATURE REVIEW
Several research works are conducted in different areas of solar cooking ranging from thermal
testing and performance evaluation of different types of solar cooking devices. Such devices
include concentrating solar cookers, Parabolic solar cookers, hot box solar cookers, square and
rectangular box type of solar cookers, Double exposure solar cookers, solar cookers with thermal
storage and many others by various authors with the aim of improving the efficiencies of these
cookers. Ibrahim [2], Conducted an experimental testing of box type solar cooker using the
standard procedure of cooking power. The box type solar cooker was tested to accommodate four
cooking pots in tatna (Egypt) under prevailing weather conditions. The experiment was performed
in July 2002. The cooker was able to cook many kind of food with an overall utilization efficiency
of 26.7%.
The performance of the cooker and the convectional box type solar cooker were investigated.
Hussein [3], Work on the performance of the box type solar cooker with an auxiliary heating. The
performance of the cooker was studied and analyzed. It was done with the help of a built in heating
coil inside the cooker. It was found that the use of auxiliary source allows cooking on cloudiest
days. Nahar [4], work on performance and testing of hot box storage solar cooker. He designed,
fabricated and tested a hot box solar cooker with used engine as storage materials so that cooking
can be performed in late evening. The performance and testing of a solar cooker with storage was
investigated by measuring stagnation temperatures and conducting cooking trials.
The efficiency of the hot box storage solar cooker was found to be 27.5%. (Ngwuoke, 2003) [5],
Designed, constructed and measured performance of plane-reflector augmented box type solar
cooker. The solar cooker consists of aluminum plate absorber painted with black matt and double
glazed lid. They predicted water boiling times using the two figures of merit compared favorably
with the measured values, the performance of the cooker with plane reflector in place was
improved tremendously compare to that without the reflector.
Essan Abdullahiet et al [6], Investigated cylindrical solar cooker with automatic two axes sun
tracking system. He designed, constructed and operated a cylindrical solar cooker with two axes
sun tracking. He carried out series of test during different days in the year 2008 from 8:30am to
8
4:30pm. The test shows that the solar cooker can increase water temperature up to 90oC. (D.Y
Dasin [7], worked out a performance evaluation of parabolic concentrator solar energy cooker in
tropical environment in Abubakar Tafawa Balewa University Bauchi Nigeria their study revealed
that the stagnation temperature of 120oC, 116oC, and 156oc were achieved respectively on three
different days between the month of June and July.
2.1. Box-type solar cookers
A box type cooker is a double walled box container. The space between the two boxes is filled
with insulation. A double- glazed door is incorporated on top of the insulated box. The food is
placed inside the inner box. Reflectors can be added to increase the efficiency of the box cooker
Hot solar box cookers are simple in terms of fabrication, handling, operation, cheap and effective
with minimal attendance required during the cooking process Muthusivagami et al [8].
B. Z. Adewole et al [9] Carried out Thermal Performance of a Reflector Based Solar Box Cooker
Implemented in Ile-Ife, Nigeria. The solar box cooker employed four reflectors, mounted on the
box of the cooker to reflect incidence radiation onto the base of the absorber plate. The inner parts
of the reflectors were constructed with 1 mm aluminum sheet and it’s covered at the outside by
corrugated cardboard of 5 mm thickness. The tilt of the reflectors was fixed at 72.5o from the
horizontal plane of the box cooker. The collector area and cooker surface area were calculated to
be 0.0625 m2 and 0.0719 m2 respectively. The cooker concentration ratio is 1.667. The overall
dimension of the cooker is 255 mm x 255 mm x 465.3 mm and its weight is 1.16 kg.
Figure 2-1 Solar box cooker used for the experiment, (p.95) by B. Z. Adewole et al [12]
9
The use of solar box cooker is not popular among the rural dwellers in Ile-Ife, Nigeria due to some
of the reasons highlighted above. He aimed to test and evaluate the thermal performance of a low
cost, reflector based solar box cooker in Ile-Ife, Nigeria and determine its suitability for cooking
during high and low solar irradiation. The performance of the reflector based solar box cooker
implemented in this study was done based on India standard, (IS 13429: 2000). The standard
highlighted two methods of test: a stagnation test (test without load) and a loaded test. Test on the
cooker was done in the Month of March when the solar irradiation was maximum. The test was
carried out between 11.00 am and 4.00 pm for three consecutive days in order to determine the
maximum plate and water temperature in the cooker at this period.
Maximum absorber plate temperature of 76°C was recorded at 2:20 pm and at an insolation value
of 422 W/m2. Between 11:50 am and 2:50 pm, insolation was high and the plate temperature
increases with increasing insolation even till 4 pm. The result shows that heat loss from absorber
plate of the cooker is minimal and the absorber plate temperature is retained for a long time. This
is desirable for heating water since major mode of heat transfer to the cooking vessels is by
conduction from absorber plate.
Figure 2-2 Thermal performance curve of the solar box cooker under stagnation test condition
(p.97) by B. Z. Adewole et al [12].
10
Figure 2.2, Illustrates the performance test of the cooker under sensible heat test of 2.0 kg of water.
The result of the test presents the behavior of pot water temperature and solar box plate temperature
under high fluctuating weather condition namely: solar radiation and ambient temperature. Despite
high weather fluctuation during the period of test, the plate temperature and water temperature
increase significantly reaching maximum temperature of 74°C and 67°C at an insolation of 364
and 416 W/m2, respectively. The plate and water temperature attain temperature suitable for water
heating at 1:20 PM and increase considerably till 4:00 PM. This and other results discussed above
demonstrated the suitability of the designed solar box cooker for heating water even during
fluctuated weather conditions.
Figure 2-3 Thermal performance curve of the solar box cooker during sensible heat test of 2.0 kg
of water (p.98) by B. Z. Adewole et al [12].
11
Figure 2-4 Variation of water temperature with time for different loads, (p.95) by B. Z. Adewole
et al [12].
Ismail Isa Rikoto, [10], Carried out a research on Comparative Analysis on Solar Cooking Using
Box Type Solar Cooker with Finned Cooking Pot. The test was conducted using a box type solar
cooker with two different cooking pots at the testing area of sokoto Energy Research Centre,
Usmanu Danfodiyo University. The two pots are identical in shape and volume with one of the
pots external surface provided with fins.
Figure 2-5 Water boiling test. Comparison between water temperature in the finned cooking pot
and the water temperature in the UN- finned cooking pot.
12
The result of two tests (water heating and boiling test) revealed that 75cl of water was raised to
95oC in 112 and 126 minutes for finned and un-finned cooking pot respectively.
K, Saravanan [11] carried out Energy and Exergy Analysis of Double Exposure Box-Type Solar
Cooker. The temperature of the base of the cooking vessels are 80°C, 75°C, 72°C and 62°C for
copper, aluminum, stainless steel and ceramic pot vessels. It is seen that the copper base vessel has
shown higher temperature compared to the other vessels due to high thermal and low specific heat
capacity of copper. Similarly, in summer, the temperature of the base has been examined after 70
minutes and it is observed that the vessels have reached the temperature of 110°C (copper vessel),
94°C (aluminum vessel), 84°C (silver vessel) and 66°C (ceramic vessel). For all the vessels, the
temperature of the base of the vessels has shown higher than that of winter days due to clear and
sunny weather. This led to the conclusion that, copper vessel has significant impact on convicting
thermal energy to the cooking fluid.
Figure 2-6 Variation of temperature of the different base of the vessels in summer and winter days
(at Coimbatore)
Experiments have been proceeded with load of 1 kg of water in the four vessels and tested. The
boiling point of water has been reached in 70, 80, 90, 100 minutes during summer and 80, 90, 100,
110minutes for copper, aluminum, stainless steel and ceramic pot vessel during winter
13
respectively. The cooker with load confirmed the effectiveness of copper vessel that dominates the
other vessels for cooking.
Figure 2-7 Time variation of temperature of water in different base of the vessels in summer and
winter days (at Coimbatore)
Hence in the proposed DESC, copper base vessels can be used effectively for cooking in short
interval of time and number of times during the working hours of the day in both summer and
winter days.
2.2. Classification of Solar Cooker
The solar cookers are classified in to two parts, solar cooker with storage and without storage. The
double exposure soar cooker can be discussed under the solar cooker without storage which uses
the solar radiation directly (direct cooking type). Under direct solar cooking, box type and the
concentrating type solar cookers are discussed in detail. The classification of solar cookers is
shown below: (p. 157), by Schwarzer & da Silva, Solar Energy 82 (2008).
14
2.3. Components of Box Solar Cooker
A detailed description of solar box cookers is illustrated in Fig.2.8. Each component of the box
cooker has a significant influence on cooking power. Therefore, optimization of these parameters
is vital for obtaining maximum efficiency. Box type cookers are slow to heat up, but work well
even where there is diffuse radiation, convective heat loss caused by wind, intermittent cloud cover
and low ambient temperatures. After the 1980s, researchers especially focused on optimization of
geometry parameters of solar box cookers since they have a dominant effect on performance. In
this context, some researchers analyzed the booster mirror effect on efficiency of box-type solar
cookers [12].
15
Figure 2-8 Component of box solar cooker with one reflectors.
El-Sebaii et al. [13] constructed and tested a box-type solar cooker with multi-step inner reflectors.
A transient mathematical model was proposed for the cooker. The transient performance of the
cooker was determined by computer simulation for typical summer and winter days in Tanta,
Egypt. They observed that the cooker is able to boil 1 kg of water in 24 min when its aperture area
equals 1 m2. Habeebullah et al. [14] introduced an oven type concept to minimize the amount of
heat losses and maximize the concentrated solar energy. They expressed that if the solar box cooker
is augmented with four booster mirrors, heat losses due to wind will reduce since wind will not be
in direct contact with the glazed surface. Results of the mathematical model indicated that oven
type receiving pot has both a higher fluid temperature and overall receiver efficiency compared to
the bare receiver type, working under similar conditions.
El-Sebaii and Aboul-Enein [15] presented a transient mathematical model for a box-type solar
cooker with a one-step outer reflector hinged at the top of the cooker. The model was based on
analytical solution of the energy balance equations using Cramer’s rule for different elements of
the cooker. The boiling and characteristic boiling times of the cooker were decreased by 50% and
30%, respectively, on using the cooker around midday. The analysis was applied to a cooker placed
at Aden, Yemen. They found that the reflector tilt angle and the elevation angle are related by the
relationship 03 2 180R and the cooker which satisfies this condition gives the best
performance.
16
Single pain glass and double pain glass are the most common structures which enable to receive a
higher solar transmission. Optimization of the gap between panes is a significant problem since a
large air gap may encourage convective heat transfer and cause a heat loss. In literature,
recommended air gap depth varies from1 to 2 cm . Absorption of long wave radiation emitted by
collector plates increases the glass temperature and this increment causes heat loss from the cooker
to the surrounding atmosphere. Therefore, transparent insulating materials are suggested in order
to improve the efficiency of solar box cookers [16].
Absorber tray is one of most significant component of a solar box cooker. Solar radiation passes
through the glazing part and absorbed by a surface painted black called absorber tray. An absorber
tray first of all should have a remarkably high absorptivity in order to transfer maximum radiant
energy to food in the cooking pot [17].
2.3.1. Booster mirror
In the field of solar cooking the use of mirror boosters or Side mirror improves the performance
of a SBC by reflecting the extra solar radiation on the aperture area and thus reduces the cooking
time. Supporting mirror boosters depends greatly upon the incidence angle. Mirrors are used to get
the extra solar radiation become less effective when the solar incidence angle increases and more
effective when the mirror angle changes according to the position of sun. The use of side mirrors
in a SBC makes possible cooking of food in low ambient temperature. Various curves were drawn
which proved the mirror boosters in addition has a good enhancement of efficiency of solar
collectors [18].
Figure 2-9 The photographic view Booster mirror of box-type solar cooker.
17
The effect of elongation (ratio of long/width of aperture) of rectangular apertures, provided with a
single mirror booster, on the energy collection was investigated. It was noticed that the rectangular
aperture with booster mirror had higher specific energy collection when compared with similarly
booster square aperture. In the case of horizontal aperture, the rectangular apertures were more
efficient than the equal area of square aperture, when the total energy collected was criterion. The
efficiency was almost a constant for a value of elongation. It was discussed that with an increase
in latitude the energy contribution from the mirrors becomes significant in relation to the
energy intercepted by the aperture directly and mirror became much more effective during
winter solstice ( 0 23.45 ) at higher latitudes [19].
A booster mirror is quite significant for a solar cooker since it allows higher illumination intensity
falling on the transmitting surface of the cooker hence higher working temperatures which enhance
the efficiency. Ibrahim and Elreidy [20] investigated the performance of a solar cooker integrated
with a plane booster mirror reflector under the climatic conditions of Egypt. The experiments
lasted 2 years for various operating conditions. Cooker position and the tilt angle of the booster
mirror were adjusted in order to maximize the sunlight concentration. It was observed that a good
meal for a family of four was cooked in 3 – 4 h. It was also found that better heat transfer occurred
when the cooking pot was covered with an airtight plastic transparent cover rather than using an
ordinary metallic cover. Booster mirrors can be utilized in order to increase the efficiency of solar
collectors since it provides extra solar radiation.
2.3.2. Insulation
Insulation is one of most crucial key points for a box type solar cooker to be able to provide an
efficient cooking. All materials with low thermal conductivity may be used as an insulation
material in solar cookers. However, the main purpose for material selection should be minimizing
heat loss from the solar cooker to the environment with minimal cost. Vandana [21] devised and
constructed a very low cost solar cooker for Indian women who are burdened with household work,
agriculture work and care of animals in addition to all time financial crisis. The proposed fireless
cooker was insulated with strawboard and tested in terms of cooking efficiency.
The results indicated that the fireless cooker of strawboard could both cook as well as keep the
food hot within safe temperatures. Nyahoro et al. [22] presented an explicit finite-difference
method to simulate the thermal performance of short-term thermal storage for a focusing, indoor,
18
institutional, solar cooker. The cooker storage unit consisted of a cylindrical solid block. The block
was enclosed in a uniform layer of insulation except where there were cavities on the top and
bottom surfaces to allow heating of a pot from storage and heating of the storage by solar radiation.
A paraboloid concentrator focused solar radiation through a secondary reflector onto a central
circular zone of the storage block through the cavity in the insulation.
It is essential for the solar thermal applications to store the heat energy maximum for efficiently
working. To prevent the transmission of heat energy from inside the box to the outside the box,
providing insulation is mandatory. Most of the heat loss in a box cooker is through the glass or
plastic in comparison of the walls. This is why insulation is necessary in between the wall of the
frame box and absorber tray as well as in glazing. It affects great, the overall temperature and
cooking power of a SBC. The insulation thickness of 7.5 cm as adequate. This prevents heat from
escaping from inside the SBC. The filling material can be glass wool, paper rolls, hay, straw, etc.
Whatever material is to be used it should be dry and should not be filled too forcefully. The reason
for putting in this material is to prevent the air between the boxes from moving, as still air is a very
good insulator in itself [23].
Pejack [24], has concluded that in order to reduce the heat loss from a SBC, the walls can be made
thicker to increase thermal resistance and then insulated with materials which have low thermal
conductivities. Glass-wool, foam, fiberglass, corkboard, wool felt, cotton, sawdust and paper all
have thermal conductivities similar to that of air,2 00.03– 0.06 W C m and make good insulators
for the walls of a SBC. The cooker can be insulated from the top by using two plates of glass with
a small gap between them. The air between these plates will prevent heat from escaping back
through the glass hence increase the efficiency.
Mishra and Prakash [25], have summarized that the thermal performance of solar cookers with
four different insulations is readily available in rural areas. A comparison of each one of them was
made with the performance of glass wool. Experimental testing was carried out to minimize the
cost of the cooker with a view to enhance its widespread application in the rural environment.
2.4. Cooking Vessels till Now
Using the proper cooking vessel in a solar box cooker (SBC) plays an important role in determining
cooking performance. To date, a number of designs of cooking vessels (for SBC) have been created
19
and tested for quality cooking performance. Khalifa, et al [26], conducted experiments on an Arafa
cooker, which is basically a point-focus concentrator that featured insulated receivers with Pyrex
pots. During testing, manual tracking was carried out every 15–20 minutes. Throughout the
experiments, it was observed that heating of several food items by directly reflected solar radiation
led to reasonable cooking time. Such type of cooking device entails an initial high cost.
Gaur, et al [27], modified the lid of a cooking utensil by changing the usual flat shape into a
concave one. With water as the cooking fluid, the modified lid succeeded in reducing the time of
cooking as compared to a cooking utensil with the normal flat lid. However, the food in the cooking
vessel was noticeably lesser in quantity. Narasimha Rao [28], while testing a cooking vessel on
lugs for solar cooking, showed that if lugs are used, convective heat transfer to the contents in the
vessel might cause reduction in cooking time. However, wind velocity can disturb the incident
beam and lead to re-positioning of heat concentration, there by affecting the time taken to cook.
Another modification was a central annular cavity in the cooking vessel (both in pot and lid).
A cylindrical hole reduces transfer of heat to the cooking fluid in the vessel. The vessel was kept
on lugs inside the SBC. A reduction in cooking time was observed, as compared to using a
conventional vessel. There was a 5.9% improvement in performance of the cooker, which was
2.4% higher than that of a conventional cylindrical vessel Narasimha Rao [29]. However, washing
or cleaning of such cooking vessel posed difficulties. Moreover, the cost is also relatively high
than a conventional cooking vessel.
2.5. Conclusion and Gaps
As some works reviewed in this chapter we can conclude that the heat up condition and the overall
efficiency of box solar cookers are low. The cooking time and the working temperature range
should be improved either by adding other heat up methods of absorber plate and installing fins
on the external surface area of the cooking vessels by satisfying international solar cooking
standards to be accepted work internationally.
20
CHAPTER THREE
3. METHODOLOGY AND DESIGN PROCEDURES
The aim of this thesis work is to design and develop a Double Exposure Solar Cooker (DESC) in
order to reduce the stresses in cooking by reducing the cooking hour as compare to the box cooker.
The cooker has to be easy to operate with low maintenance cost and should be capable to boil
water and cook rice and pasta. The cooker is designed in a way suitable to cook specific types of
food items consumed by Ethiopian households and the system is designed based on the solar
radiation potential of a specific site. Moreover, the cooker is sized based on the cooking energy
requirement for average households.
The transparent cover was used to minimize convection losses from the absorber plate through the
restraint of the stagnant air layer between the absorber plate and the glass. It also enabled reducing
radiation losses from the collector as the glass is transparent to the short wave radiation received
by the sun but it is nearly opaque to long-wave thermal radiation emitted by the absorber plate.
Figure 3-1 Some Energy entering and leaving on glass-1 representation on solid work.
Glazing materials include glass, acrylics, fiberglass, and other materials. Although different
glazing materials have very specific applications and the use of glass has proven the most diverse.
The various types of glass allow the passive solar designer to fine-tune a structure to meet client
needs. The single pane is the simplest of glass types and has a high solar transmission. Single pane
21
glass can be effective when used as storm windows, in warm climate construction for certain solar
collectors and in seasonal greenhouses.
Structures using single pane glass will typically experience large temperature swings, drafts,
increased condensation, and provide a minimal buffer from the outdoors. Perhaps the most
common glass product used today is the double pane unit. Double pane glass is just that: two panes
manufactured into one unit. Isolated glass (thermos pane) incorporates a spacer bar (filled with a
moisture absorbing material called a desiccant) between the panes and is typically sealed with
silicone. The spacer creates a dead air space between the panes. This air space increases the
resistance to heat transfer. In fact, a large air space can actually encourage convective heat transfer
within the unit and produce a heat loss.
Cooking vessel is cylindrical shaped cooking vessels made of aluminum are used for cooking in a
SBC. The outside of vessels is coated black and attached to the center of the absorber plate to
achieve the desired contact between the pots and the absorber plate; in order to increase the rate of
heat transfer by conduction between the absorber plate and the cooking vessels.
Absorber tray of a box cooker is like a simple flat plate collector (FPC). When solar radiation
passes through a transparent cover (glazing) and impinges on the black painted or coated absorber
surface of high absorptivity, a large portion of this energy is absorbed by the tray and then
transferred to the food to be cooked placed in the cooking vessels inside the cooker.
A double exposure solar cooker in which absorber was exposed to solar radiation from top and
bottom. Some of the likely concepts in absorber design for most types of absorbers Conventional
materials are steel, copper, and aluminum. The absorber should be either painted with a dull black
paint or can be coated with a selective surface to improve performance. In order to maximize the
illumination intensity falling on the absorber tray and enhance the heat transfer from the absorber
tray to the food in cooking vessels, absorber tray is a key item which allows various modifications.
Most of the time test standards are conducted by water heating, during the test the water can be
heated up to optimum temperature to cook foods. In order to design and develop the cooker
methods to go through are listed below.
22
3.1. Energy for cooking
The energy required to cook the selected food item are obtained by taking the temperature range
used to Cook each food item, Folaranmi, J, [30], stated that most food can be fully cooked at the
temperature range of 60-90°C. The values and average temperature of water inside the pot while
the cooker is operated under a set of guidelines given in the standard for tracking procedure,
thermal loading, etc. Temperature measurements made for power test and water heating test
averaged over 10 and 30 minute intervals respectively. Ambient temperature and normal irradiance
(solar energy flux per area) are also measured and recorded, at least as often as load temperature.
Under conditions of high wind, low insolation, or low ambient temperature, tests are not
conducted. So based on such consideration the energy required to boil the water at suitable
temperature to boil rice or pasta is calculated through the following procedure.
For one family which contain four number of people needed to consume 0.75Kg of macaroni, 2
liter of water averaged in a temperature between 60-95oC needed to fully cook the food. 2 liter of
water can be taken as 2 kg of water. The power required to cook the food can be obtained by
equation 3.1.
( )3.1
w pw f iM C T TP
t
Equation 3.1 is divided by 600st to account for the number of seconds in each 10-minute
interval. P is normalized to compare the various cookers in various countries and under various
climates. Funk [31] has shown that the power of radiation is standardize to 700 W/m2. Cooking
standard power Ps during boiling of mass of water ‘m’ from initial temperature Ti to final
temperature Tf during time ‘t’ is calculated from:
7003.2s
b
P PI
3.1.1. Averaged solar data of the site
The Ethiopian metrological service collects the average sunshine hours for some cites of the
country and the solar radiation is calculated from the average sunshine hours. From the minimum
and maximum temperature and solar isolation metrological data from Bahir-Dar city in the table
and figure below respectively.
23
Table 3-1 Monthly average maximum and minimum temperature of Bahir-dar city (Metrology
data).
Month Jan Feb Mar Apr May Jun jul Aug Sep Oct Nov Dec
Daily Min Temp
(oC)
8 9 11 13 13 13 13 13 12 12 10 8
Daily Max Temp
(oC)
29 31 32 32 32 29 26 25 26 27 28 28
Total Rainfall
(mm)
2 2 12 28 80 205 396 375 211 87 12 6
Mean Nọ of
rainy Days
1 1 2 3 10 18 28 28 20 10 3 1
Table 3-2 Monthly average solar isolation of Bahir-dar city(Metrology data).
Month Jan Feb Mar Apr May Jun jul Aug Sep Oct Nov Dec
Average solar
radiation
KWhr/m2 /day
5.67 6.2 6.48 6.6 6.26 5.74 5.02 5 5.67 5.87 6.01 5.67
Figure 3-2 The solar isolation of the site ( 2 /Whr m day )
24
In cooking, the temperature of the water used to cook each food item can be obtained by
considering the following parameters, where wM is the mass of water in kg, pwC is the specific
heat capacity at constant pressure in J/(kg K), T is the temperature difference in K, t is the
duration of the measurement in s.
The initial temperature of the water is 220C, the yearly average ambient temperature of Bahir Dar
is 28.750C and the system is designed to work efficiently in summer season from July to
September, because other left months have suitable solar radiation for cooking. The monthly
average global solar radiation of Bahir-dar for July, August and September is
3 25.28 x10 /sI Whr m day which is equal to 2755.5sI W m The temperature difference
between the initial and final pot content (K) is 0 090 22 68o
f iT T C C C . The power
needed to boil the water at desirable cooking temperature can be calculated as:
Specific Heat capacity of water 4.168KJ/kg.K
thermal conductivity of
aluminum
237 W/m.K
Specific heat capacity of
aluminum
921J/kg.K
The average heating-power of a solar cooker is calculated as,
0 0
3363 295
2 4.168 10 / .5400
104.97 /
w pwM C TP
t
K Kkg J kg k
s
J s
The power of radiation is standardizing to700 w/m2. The standard power is expressed then by:
2
2
( ) 700
700
700 /104.97 /
755.5 /
97.25
pw f i
s
b
b
s
s
MC T TP
t I
PI
W mP J s
W m
P W
25
Table 3-3 Data and Result of power required.
Tf (oC) Ti (
oC) Cpw (KJ/Kg.
K)
Mw(Kg) Measuring
time gap (s)
P(W) Ps(W)
90 22 4168 2 5400s 104.97 97.25
3.2. Size of the cooker
Sizing of the cooker can be determined based on the power obtained for cooking. First law of
thermodynamics for closed system states that Energy can be neither created nor destroyed, it can
only change form and Provides a basis for studying the relationships among the various forms of
energy and exergy interactions.
Figure 3-3 Closed system heat energy entering and leaving the system.
Therefore, every bit of energy should be accounted during a process. A closed system consists of
a fixed amount of mass and no mass may cross the system boundary. The closed system boundary
may move. The net change (increase or decrease) in the total energy of any system during any
process is equal to the difference between the total energy entering and the total energy leaving
the system during that process is,
The total energy energy
energy in the system entering the system leaving the system
In mathematical form
3.3system in outE E E
3.4in loss
d EQ Q
dt
26
0 3.5p c
dMC I U A
dt
Where M is the mass in the pot in kg, pC is the specific heat capacity at constant pressure in J/kg
.K, is the temperature difference between the pot content and the initial temperature in K, 0 is
the optical efficiency, I is the global solar radiation in W/m2, U is the thermal loss coefficient in
W/(m2K), and cA is the collector aperture surface in m2.
The thermal loss coefficient can be evaluated by the formula below, where end startt t is the time
difference taken to boil the water at desirable temperature (s) and start , end are the initial and final
temperature of water respectively.
.ln 3.6
w pw start
end start end
M CU
t t
Where t is in second. It may also be calculated from the optical efficiency and the stagnation
temperature as
.3.7o
stag
IU
T
The optical efficiency may be calculated using the following expression for the typical conditions
of solar irradiance and ambient air temperature for a location.
Nahar [4], proposed the method of calculation of efficiency ( 0 ) of the solar cooker by the
following relation:
0
( )( )100 3.8
w w pot pot wf wi
R abs b
M C M C T T
C A I t
where 0 represents efficiency of the solar cooker; M is mass of water(kg); Mpot is mass of cooking
utensil (kg); Cpot, Specific heat of cooking utensil (J/kg/oC); Tw1, initial temperature of water (0C);
Tw2, Final temperature of water (oC); CR is concentration ratio; Aabs Absorber area (m2); and t is
time interval (s).
27
Concentration Ratio; the principle of solar cooking is that rays of sun are converted to heat and
conducted into the cooking pot. The ability of a solar cooker to collect sun light is directly related
to the projected area of the collector perpendicular to the incident radiation. In this regard, the
geometric concentration ratio is defined as
3.9cR
abs
AC
A
Where 𝐴C is the total collector area (m2) and 𝐴abs is the area of the receiver/absorber surface (m2).
The equation 3.8 can be reduced as equation 3.10 by substituting the concentration ratio CR
(equation 3.9 in to 3.8).
0
( )( )100 3.10
w w pot pot wf wi
c b
M C M C T T
A I t
During sizing of the solar cooker based on the energy required to cook the food can be evaluated
through several steps shown in the above equations (3.5-3.10). The cooking capacity of the solar
cooker are affected due to the uncontrolled climatic condition of the site. The thermal loss
coefficient can be calculated applying equation 3.6 bellows:
.ln
p start
end start end
mcU
t t
3
2
2 4.168 10 22ln
5400 0 90
2.175 /
s s
W m K
The optical effectiveness factor is given by:
0
( )( )100
w w pot pot wf wi
c b
M C M C T T
A I t
3 0 02 4.168 10 0.7 0.921 (90 22 )100
(755.25 5400 )
0.069100%
0.0896
c
c
c
C C
A s
A
A
28
Sizing of the cooker based on the power obtained to cook the selected food item. The net change
(increase or decrease) in the total energy of any system during any process is equal to the difference
between the total energy entering and the total energy leaving the system during that process is,
applying equation (3.5) we can obtain the area of the collector.
0
2
97.25
0.089697.25 755.5 ( 2.175(90 22))
67.6797.25 147.9
97.25 67.67 147.9
0.2
p c
cc
cc
c
dmc W I U A
dt
W AA
W AA
A
A m
The only unknown variable is the area and obtained as 20.2cA m for the aperture area of the
collector.
Figure 3-4. shows heat energy entering and leaving the system
3.3. Thermodynamic assessment of solar cookers
Energy and exergy analysis provide an alternative means of evaluating and comparing solar
cookers. Energy and exergy efficiency for the solar cookers as given in Equation (3.11) and (3.12),
respectively.
29
0[ ( ) /energy output
3.11energy input
w w wf wi
i t sc
m Cp T T tE
E I A
Where is energy efficiency, Mw is water mass, Cpw is specific heat of water, Twf is final
temperature of water, Twi is initial temperature of water, ‘t’ is time, It is total instantaneous solar
radiation and Asc is intercept area of solar cooker.
0
0
[( ) ln ] /exergy output
3.124exergy input
[1 ]3
wf
w w wf wi
X wt
aXit sc
s
TM Cp T T T t
E T
TEI A
T
Where is exergy efficiency, Ta is ambient temperature and Ts is sun temperature. It is necessary
to determine the exergy of incoming solar radiation for conducting second law analysis of solar
cookers. In this an expression for the utilizable part of the solar energy as follows:
41 4
1 3.133 3
a aT T
T T
Where is maximum efficiency ratio, Ta is ambient temperature and T is absolute temperature.
3.4. Material selection
The double exposure solar cooker is one of the cooker uses the renewable energy source that can
be constructed from low cost and locally available materials. The prototype construction materials
are selected based on the property of materials, material cost, construction cost, and overall
advantage and disadvantage of materials used.
Table 3-4 Selection standards of materials.
Material selected to construct Stand
Angle iron
Simple to construct
Simple to disassemble and to transport from one place to
another.
Has less weight compare to other materials
Connected by bolt in simple manner.
30
Easy and comfortable to put the box and parabolic flat
reflector on it.
Selection of Material used for reflecting
Aluminum sheet Has excellent resistance to corrosion on the thin layer of
aluminum oxide than forms on the surface of aluminum
when it exposed to air.
It is a good reflector of radiant energy through the entire
range of wave length.
Has low thermal emissivity.
Selection of Absorber plate
Aluminum alloy Aluminum is an excellent heat conductor.
Is typically less cheap than that of steel.
88% aluminum and 12% magnesium cast.
3.5. Construction of prototype
The construction can be done by locally available material such as wood, transparent glass, sheet
metals, aluminum foil, and other locally materials are selected for the development of prototype.
3.5.1. Stand
The stand is made of iron (locally called angle iron), used to support both the box and parabolic
flat reflectors, it is constructed according to the size of the cooker. The bottom of the stand is
having total dimension of 110cm x 50cm. 100cm x 50cm is for placing the Parabolic flat reflector
and 10cm x 50cm is left for construction of front wheel. The stand can simply have constructed by
connecting the bars together by bolt in the holes prepared for connection.
31
Figure 3-5. Schematics and photographic view of Frame (stand) of cooker
3.5.2. The box cooker
The box can be made from different locally available woods depending on the thermal conductivity
of each woods, on this work the box is made of wood (locally called Australian framed wood) in
order to reduce the heat loss from the cooker. The box is sized based on the absorber area; the
volume of the box is (50 x 40 x 32) cm with the thickness of 2.5cm connected in a rectangular
form by nails.
The top of the box is covered with glass of 50cm x 40 cm fitted with wood frame, the transparent
cover was used to minimize convection losses from the absorber plate through the restraint of the
stagnant air layer between the absorber plate and the glass. It also enabled reducing radiation losses
from the collector as the glass is transparent to the short wave radiation received by the sun but it
is nearly opaque to long-wave thermal radiation emitted by the absorber plate. Mainly it used to
cover the box from external convective air, protect the internal heat from escaping and transmit
the direct and reflected sun radiation to the absorber and cooking vessels.
The bottom of the box is covered by double glass allowing the absorber plate to receive solar
radiations on its lower side with 2.0cm gap between them. The size of bottom internal glass is
46cm x 36cm fitting the internal area of the box.
32
Figure 3-6. The photographic view of constructed box soar cooker
The inner part of the box is covered with flat aluminum sheet which have a thickness of 0.1cm -
0.2cm. it reflects the sun radiation towards to the cooking vessel and absorber plate as secondary
reflector.
3.5.3. Booster (Box reflectors)
There are three rectangular flat reflectors at the top edge of the box, two side edge and one front
rear edge reflector with 40cm x 50cm and 50cm x 60cm area respectively. All reflectors are made
of 2cmx 2cm squared steel (locally called tubollary) connected by arc welding. The roughness on
the frame should be smoothed to rebate the aluminum sheet properly for all side and rear edge
reflector.
The use of boosters or Side Reflectors improves the performance of a SBC by reflecting the extra
solar radiation on the aperture area. The effect of elongation (ratio of length/width of aperture) of
rectangular apertures, provided with a three booster, on the energy collection was investigated. It
was noticed that the rectangular aperture with booster mirror had higher specific energy collection
when compared with similarly booster square aperture. In the case of horizontal aperture, the
rectangular apertures were more efficient than the equal area of square aperture, when the total
energy collected was criterion. The efficiency was almost a constant for a value of elongation [18].
The three rectangular booster are shown below.
33
Figure 3-7. (a), Welded rectangular steel frame. (b), Representation on solid work (c) The
photographic view of boosters.
The booster is constructed from steel frame and aluminum sheet shown on figure (a) and (c)
respectively, the aluminum sheet and rectangular steel frame are connected together by rebate.
The reflectors are connected by hinge helps to move and manually adjust the booster to reflect the
sun radiation to the cooking vessels and absorber plate. The reflector is supported by steel bar used
to adjust the booster by moving forth and back on the pin prepared, to retain at optimum tilt angle
of boosters.
3.5.4. Parabolic flat reflectors
The parabolic flat reflector is used to reflect the sun radiation towards to the box through double
glazed (transparent glass) at the bottom which allow the absorber plate to receive sun radiation.
To construct the parabolic reflector fist we have select materials like aluminum sheet, squared steel
tube (locally called tubollary), rebating material and bolt having 10mm diameter and 50mm length,
preparing all materials in suitable dimension of each part of the parabola. Several steps are
followed to construct the parabolic reflector.
A 2cm x1cm steel (locally called tubolary) having less size and light weight compared to
steel was used to booster frame. Cutting each steel for nine parabolic reflectors at measured
length and width 46 cm x 10 cm respectively then connecting them by arc welding to get
the exact shape and size as shown fig 3.7, c.
Aluminum sheet having equal shape and size (46cm x10 cm) is rebated on rectangular
frame as shown on fig. 3.7, d.
34
Figure 3-8. Schematic and photographic view of parabolic flat reflector.
The purpose of each parabolic reflector is to increase the focus area of sun radiation by adjusting
to different part of the absorber plate. During adjustment the effect of all reflectors can be shown
on the glass at bottom of the box. The arc length of the parabolic curve have a length of 110cm.
Arc of the the reflector can be obtained from mathematical equation below by applaying a number
of mathimatical theroms.
Figure 3-9. Schematic diagram of angles used to calculate the arc length
35
1. Applying pytagores thereom the length AB is calculated .
2 2( ) ( )AB AF BF
2 2100 35 105.95AB cm
2. From trigonometric relation, the angle α can be calculated as:
tanBF
AF
35tan 0.35
100
tan (0.35) 19.29o
3. From triangle property we can have two relationships.
2 180o
, 90 180o oalso
0
19.29 90 180
70.71
o o o
C
4. From circle and line relationship, Angles and arcs determined by lines Intersecting Inside
and on a Circle. Measure of a central angle: tells that the measure of a central angle is the
measure of the arc it intercepts.
Figure 3-10. Shows the triangle AOB intercepted arc ACB
36
𝑚(< 𝐴𝑂𝐵) = 𝑚(𝐴𝐶�̂�) 5. Applying sine law
sin sin
AB r
sin sin
105.95 r
Since the sum of interior angle AOB equals 180oC, we have,
180
902
o
By Substituting β we get
sin(90 )sin 2105.95 r
We know that sin( ) sin cos sin cosA B A B B A
0
sin(90 ) sin90 cos sin cos902 2 2
cos ,sin90 1, cos90 02
o o o
owhere
cossin 2105.95 r
105.95cos2
sinr
6. Applying cosine law
2 2 2 2 cosAB r r r r 2 2 2105.95 2 cosr r r r
211224.97 2 (1 cos )r 2
2
105.95cos (1 cos )25612.5
sin
2
2
11224.98cos ( )(1 cos )25612.5
sin
2
2
cos ( )(1 cos )20.5sin
2 2
2
cos ( )(1 cos ) cos ( )(1 cos )2 20.5
1 cos (1 cos )(1 cos )
2cos ( )20.5
1 cos
7. From half angle formula of triangle we have,
37
2 1cos ( ) (1 cos )
2 2
1 (1 cos )20.5 0.51 cos
The result shows that the triangle AOB is equilateral triangle which is all angles 60o , the
radius of the circle is:
105.95cos 105.95cos302sin sin60
r
105.95 106r cm
Figure 3-11. Shows the arc length (ACB)
The measure of a central angle is the measure of the arc it intercepts. Which the same to the arc
length S is equal to the radius r times the angle θ (in radian).
106 60
180 180o
s r
rs
, 110showsthearclength s cm
38
Figure 3-12. The parabolic curve with arc length of S = 110cm.
The parabolic reflectors are installed on the parabola by means of bolt and nut. Nine holes are
drilled on each side of parabola with 10cm diameter which can rotate the bolt freely in it to adjust
the reflectors towards to the bottom of the box. The bolt is welded on both side of the reflectors
and each reflector are placed 2cm apart as shown on figure 3.7, b.
The double-exposure solar cooker (DESC) that is used in this investigation consists of a box-part
with a double-glass at the bottom allowing the absorber plate to receive solar radiations on its
lower side. The box is equipped with three flat reflectors (one reflector is 50 cm by 60 cm placed
front rear edge of the box frame) and the two side reflectors are 40cm by 50cm, which are installed
upon a wood frame connected with hinges on the upper side of the solar cooker. The walls of solar
box are made of a wooden layer (thickness: 2.5 cm), the inner sides of which are covered with an
aluminum sheet (thickness: 0.1 - 0.2 cm). The height of the back-side and front-side of the box are
equal with 32 cm; the total volume of the box is (50 x 40 x 32 cm). Junction fragments were sealed
properly to prevent escaping air from system. At the top of the box part, a glass plate of 4 mm
thickness was fixed in position with wooden frame to avoid breakage due to expansion and also to
make the cooking space airtight.
The parabolic part of system is composed of 9 flat reflectors, 10cm x 46 cm, which are mounted
on a parabolic curve and are set manually. Exposing reflectors to the sun radiation are manually
set for the sunlight be concentrated on the absorber plate. The absorber plate is a black steel sheet
of (0.1 - 0.2) cm thickness. The absorber plate is mounted horizontally and receives solar radiation
from two sides (from box reflector and parabolic flat reflectors).
39
Figure 3-13 The full designed, constructed and schematic diagram of the existing double exposure
solar cooker.
The fig. 3.13 shows the developed double exposure solar cooker which is prepared for conducting
the experimental test. During cooking, mostly noon time the shadow of the box interrupts the
reflection of some part of the parabolic flat reflectors. During such kind of shadow, the parabola
is designed and constructed to move back and forth (translation movement) to get the full reflection
of sun radiation.
A two commercial cooking vessel, of 20 cm in diameter and 10 cm in depth, was placed in the
center of the box part. One of the cooking vessels is finned with equal shape and size with the
conventional cooking vessel. The cooking vessel is made of an aluminum sheet of 0.2 cm thickness
and the outer surfaces of the cooking vessel are painted black.
3.6. Measuring instrument
During operation of the test, the measuring instruments are prepared dual in number to have precise
value. Solar irradiation was measured by solar power meter, TENMARS TM-207. Temperatures
were measured by Y-811 thermometer, thermocouple and infrared thermometer. The detail
features of the measuring instruments are shown in Appendix D
40
TM-207 Solar Power meter is ideal for the measurement of the solar radiation that is emitted by
the sun from a nuclear fusion reaction that creates electromagnetic energy. The spectrum of solar
radiation is close to that of a black body with a temperature of about 5800 K. About half of the
radiation is in the visible short-wave part of the electromagnetic spectrum. The other half is mostly
in the near-infrared part, with some in the ultraviolet part of the spectrum.
YC-811 Thermometer are available in single, dual or multiple inputs. We also provide a wide
selection of k-types probes data logging futures across the range. A k-type thermocouple accepts
a various type if thermocouple. A thermocouple is a temperature measuring device consisting of
two dissimilar metals. The metals are welded at the tip to form what is commonly known as the
thermos couple junction.
The infrared thermometer uses for measuring the surface temperature but the temperature was
very widely varied on the surfaces of the concentrator.
Figure 3-14. a) Solar power meter b), thermometer Y-811 c) Thermocouples d) Infrared
thermometer
3.7. Performance Testing Procedures and Standards
A procedure for testing the solar cookers was developed based on existing international testing
standards. They include three major testing standards for solar cookers that are commonly
employed in different parts of the world. These are the American Society of Agricultural Engineers
Standard, Bureau of Indian Standards Testing Method, and European Committee on Solar Cooking
Research Testing Standard and others [32,33]. Based on the existing international testing standards
tests were performed on the solar cooker, these are
The stagnation temperature Test
41
Thermal load test, heat up condition test
Cooking power estimation.
Instantaneous and cumulative efficiency of the cooker.
Effect of finned and un-finned cooking vessel.
3.7.1. The Stagnation Temperature Test
The stagnation temperature test was conducted for the evaluation of first figure of merit (F1) of
solar cooker. The quasi-steady state, the final steady cooker absorber temperature, is achieved
when the stagnation temperature is attained. The procedure for determining stagnation temperature
is stated as follows.
The solar cooker was placed in the open sun without load.
Calibrated thermocouples were connected to the solar cooker to measure both the cooker
tray and ambient temperatures simultaneously at a given interval till the stagnation
condition was reached. These measurements were recorded.
Intensity of total solar radiation on horizontal surface and wind speed at the level of
aperture of the cooker were monitored, measured, and recorded at regular interval using
solar power meter, digital radiation pyranometer and digital anemometer, respectively.
The data of the stagnation test is recorded in table Form.
3.7.2. Thermal Load Test, Heat up Condition Test
The thermal load or water boiling test was conducted to determine the second figure of merit F2
and it was evaluated under full-load condition. The solar box cooker was loaded with 2 kg of water
in an aluminum cooking vessel painted black; the water temperature was initially above the
ambient temperature. Solar radiation, ambient air temperature, water temperature, and time were
recorded at a regular interval till the water temperature exceeded the boiling temperature of the
site. In summary the following measurements were made during the test:
The water temperature at a regular time interval until the water temperature exceed boiling
temperature of the site.
Time duration between initial and final water temperatures was recorded;
The average ambient temperature and average solar radiation intensity between initial and
final time were calculated. The other data of the full load test is recorded in table form.
42
In order to minimize error in the results obtained the following precautionary steps were taken.
The test was conducted in clear weather, and it was ensured that the solar radiation during
the test exceeded 600 W/m2.
Water and ambient temperatures were measured with thermocouples. Each thermocouple
junction was immersed in the water in the cooking vessel and secured 10 mm above the
bottom, at center.
Thermocouples leads were made to pass through the cooking vessel lid inside a thermally
nonconductive sleeve to protect the thermocouple wires from bending and temperature
extremes.
3.8. Cooking Power Estimation
The cooking power is inversely proportional to the temperature difference and the solar isolation.
Several steps are going through to estimate the power needed to cook the food these are:
3.8.1. Steps for the Determination of Cooking Power
1. The solar box cooker was loaded with 2 kg of water in an aluminum cooking vessel painted
black. The average water temperature in the cooking vessel was recorded at intervals of ten
minutes. Solar insolation, and ambient temperature were also recorded at least as
frequently.
2. The change in water temperature for each ten-minute interval was multiplied by the mass
and specific heat capacity of the water contained in the cooking vessel. This product was
divided by the 600 seconds contained in a ten-minute interval to determine cooking power
of the cooker.
3. In order to determine the standardizing cooking power, cooking power (P) for each interval
was corrected to a standard insolation of 700 W/m2, by multiplying the interval observed
cooking power by 700 W/m2 and dividing by the interval average insolation recorded
during the test.
4. Cooking power (P), and standardized cooking power (Ps), were calculated by step (2) and
(3). The Standardized cooking power, (Ps), was plotted against the temperature difference
(Td), for each time interval. Temperature difference (Td), was calculated by equation (4.7).
A linear regression of the plotted points was used to find the relationship between cooking
43
power and temperature difference in terms of intercept, W, and slope, W/°C. The thermal
performance of solar cooker was evaluated according to the international standards of
American Society of Agricultural Engineers (ASAE), and in this standard it is
recommended to use linear fit. The coefficient of determination, (R2) or proportion of
variation in cooking power that can be attributed to the relationship found by regression
should be better than 0.75 according to Funk and Larson.
44
CHAPTER FOUR
4. EXPERMENTAL TEST ANALYSIS
Thermal performance testing of the solar cooker was conducted in Bahir-Dar, Ethiopia. Bahir-Dar
is located at 11.59 latitude and 37.39 longitude and it is situated at elevation 1799 meters above
sea level. During each test, both cooking vessels were placed side by side on the absorber of the
solar cooker and loaded with the same mass of water at the same temperature. The temperatures
of the water in each vessel, of the absorber, of the air in the cooker as well as ambient temperature
and horizontal irradiation were recorded at 30 min intervals. Solar irradiation was measured by
solar power meter, TENMARS TM-207. Temperatures were measured by Y-811 thermometer and
infrared thermometer. The thermocouple used for the temperature measurement of water inside
the vessel is introduced by opening the lid and the door of the vessel, but this kind of measuring
will lead convection loss from absorber and water to the ambient convective air. Once both the
vessels filled with water were placed in the cooker, the door was closed until test starts. During
tests, the cooker was manually oriented according to azimuth at an interval of 15 min in order to
collect a maximum of solar radiation.
4.1. Performance Testing
The standard highlighted two methods of test: a stagnation test (test without load) and a load test
(water heating test). Test on the cooker was done in the Month of June 11–20 when the solar
irradiation was low and varies with cloudy condition, if the test taken on month March and April
it will be better experimental result. The test was carried out between 9:00 am and 4:00 pm for
nine consecutive days in order to determine the maximum plate and water temperature in the
cooker at this period.
4.1.1. Stagnation Test
A number of tests without load were conducted on the cooker to determine its stagnation
temperature and also to check the rise in temperature inside the cooker. The stagnation
temperature, ambient temperature (Ta) and absorber plate temperature (Tp) were measured for
different time of the day between 3:00 am and 4:00 pm during cooker operation.
45
4.1.2. Stagnation Test with parabolic flat reflectors
The test was conducted for three series days from June 10-12/2017. The result of stagnation
temperature under no load condition is shown in Figure 4.1. The average ambient temperature for
the test day was 28.7°C. Maximum absorber plate temperature was recorded at 12:30 pm and at
an insolation value of 950 W/m2 and the ambient temperature 31.90C Between 11:30 am and 1:30
pm, insolation was high but vary with cloudy condition that will matter decreasing the absorber
temperature, the plate temperature increases with increasing insolation.
Figure 4-1. The experimental test result during stagnation test (June 10/2017).
4.1.3. First Figure of Merit(F1), (with parabolic flat reflectors)
The first figure of merit (𝐹1) is defined as the ratio of optical efficiency, 0( ) , and the overall heat
loss coefficient, ( )LU . A quasi-steady state (stagnation test condition) is achieved when the
stagnation temperature is attained. High optical efficiency and low heat loss are desirable for
efficient cooker performance. Thus the ratio 0 LU which is a unique cooker parameter can serve
as a performance criterion. Higher values of 𝐹1 would indicate better cooker performance. This
46
test was performed in order to determine the performance of the double exposure solar cooker by
obtaining the first figure of merit of the cooker and compare it with the standard.
01
( )4.1
p a
L s
T TF
U I
Where 𝐹1 is first figure of merit ( 2Km W ), 0( ) is optical efficiency (%), ( )LU is overall heat loss
factor 2W m K , 𝑇𝑝 is absorber plate stagnation temperature (oC), 𝑇a is ambient temperature at
stagnation (oC), and 𝐼𝑠 is insolation on a horizontal surface at stagnation 2( )W m .
Results are shown in Appendix. (B-1). From table the following values were obtained in order to
compute the first figure of merit. 𝐹1: 0 0 231.9 C, 152.2 C, 950 a p sT T I W m .
0 2
1
( ) (152.2 31.9)0.127
950
p a
s
T TF Cm W
I
Equation (4.1) was used to compute 𝐹1. The obtained value of 𝐹1 is ( 0 20.127 /Cm W ) where the
allowed standard 𝐹1 test states that if the value of 𝐹1 is greater than 0.12, the cooker is marked as
A-Grade and if 𝐹1 is less than 0.12 the cooker is marked as a B-Grade solar cooker [34]. The test
showed that the constructed double exposure solar cooker is marked as an A-Grade solar cooker.
The low value of first figure of merit may be an indication that here were higher convection and
radiation losses from the side walls made of wooden box or side insulator is not thick enough.
4.1.4. Stagnation test (parabolic flat reflectors off)
These kind of test can be observed on other works done before on box solar cookers, basically to
observe the effect of parabolic flat reflectors on the absorber plate temperature at specific location.
The stagnation test was conducted for three consecutive days from June 13-15/2017. Maximum
absorber plate temperature was recorded at 12:00 pm and at an insolation value of 996 W/m2. The
maximum insolation of 996 W/m2 at 12:00 PM and minimum of 232 W/m2 at 9:00AM were
recorded. The average solar radiation and ambient temperature observed during the period of test
were 663.7 W/m2 and 27.25°respectively.
47
Figure 4-2 Experimental test result during stagnation test condition when parabolic flat reflectors
off (June 13/2017).
4.1.5. First Figure of Merit (F1) (Parabolic flat reflectors off).
The test also done by removing the parabolic flat reflectors in order to observe the effect of
parabolic flat reflectors on the cooker, also the first figure of merit can be calculated as bellow.
From Appendix. (B-4) the following values were obtained in order to compute 𝐹1, for the system
when parabolic flat reflectors off. 0 0 232.3 C, 120.2 C, 996 a p sT T I W m .
0 2
1
( ) (120.2 32.3)0.088
996
p a
s
T TF Cm W
I
The result of First figure of merit (F1= 0.088) shows that for the system, according to the ASAE
International Test procedure and Bureau of Indian Standards (BIS) for testing the thermal
performance of solar cooker. Removing the parabolic flat reflector will make the cooker is marked
as grade B, because the result of 0 2
1F 0.088 Cm W is less than the standard 0 20.12 Cm W .
4.1.6. Load Test (Water Heating Test)
During the test both finned and un-finned cooking vessels were placed on the absorber plate of the
solar cooker and loaded with the same mass of water having equal temperature. On the figure
below test was done by placing a 2kg of water-filled cylindrical pot covered by a lid, in the cooker.
48
The test was conducted for two series days from June 16 &17/2017. The test was carried out on
sunny day between 3:00 AM and 12:30PM daily until we get the max temperature observed and
comparatively the good solar insolation is taken for test result bellow. The absorber plate
temperature (Tab), Ambient temperature (Ta), Water temperature (Tw), and Solar radiation (Hs)
were measured using the instrumentation described in section 3.6.
The test was conducted using two cooking vessel namely finned and un-finned vessel as shown on
the figure 4.5. the fins are welded on the thin steel plate and tied all over the external surface of
the vessel which can use for all vessel having the same diameter.
Figure 4-3 Finned and un-finned cooking vessel with the same volume.
Variation in solar radiation, ambient temperature, plate temperature and water temperature
during water heating test of 2.0 kg (2 liter) of water are shown in figure 4.7. Periodic overcast of
weather caused fluctuation in the solar radiation.
Figure 4-4. The experimental water temperature test (June 16/2017)
49
The most food can be fully cooked at the temperature range of 60-90°C. for both un-finned and
finned cooking vessels the water temperature during the period of test reached temperature values
between 60-88.8°C (93.60C) respectively at insolation values from 436 W/m2 to 968 W/m2
between the hour of 10:00 AM and 12:30 PM, the figure 4.7 shows the temperature and solar
isolation variation with time on June/17/2007 from morning 9:00AM - 12:30PM.
4.1.7. The second figure of merit(F2)
The second figure of merit, 𝐹2, of double exposure solar cooker is evaluated under full-load
condition and can be defined as the product of the heat exchanger efficiency factor (𝐹’) and optical
efficiency (𝜂𝑜 =𝛼𝜏). F2, takes into account the heat exchange efficiency of cookers and is obtained
through the sensible heating of load of water. It can be expressed as
' 1 1 12 0
2 1 1 2
( ) 1 (1 )(( ) / )ln 4.3
( ) 1 (1 )(( ) / )w w a s
w a s
F MC F T T IF F
A t t F T T I
Where 𝐹1 is first figure of merit (Km2/w), 𝑀 is mass of water (kg), 𝐶w is specific heat capacity of
water (J/Kg∘C), 𝐴 is aperture area of the solar cooker (m2), 𝑡1 and 𝑡2 are initial time and final time
(s) respectively, 𝑇𝑤1 is initial water temperature (∘C), 𝑇𝑤2 is final water temperature (∘C), 𝐼𝑠 is
average insolation (W/m2), and 𝑇𝑎 is average ambient temperature (∘C).
To estimate the first figure of merit (F1) and second figure of merit (F2), it is required to measure
the intensity of solar radiation falling at the surface of the cooker, ambient temperature, wind
speed, initial water temperature, final water temperature etc. It is recommended that experiment
should be done within 1:30 h of the solar noon with the intensity of solar radiation above or
equal to 600 W/m2. Initial temperature of water should be higher than the ambient temperature and
the final temperature of water should be lower than the boiling point. It may be 90 or 930C to avoid
error in reading from the experimental curve as the curve flattens at higher temperature i.e. around
the boiling temperature of the water for the given location [34].
F2 increases, with increase in number of pots, if load is kept constant and equally distributed. This
is attributed to an improvement in the heat exchange efficiency factor (F’) with number of pots.
Also F2 increases with increase in load, if number of pot is kept constant and the load is equally
distributed. This is because of an improvement in heat capacity ratio CR, as mass of water in the
pots increases.
50
The average ambient temperature and average solar radiation intensity between initial and final
time were calculated. The data of the full load test is given in Appendix. (B-7). 0 2
1 0.127 /F Cm w
, 2wM kg , 4168 /wC J KgK , 030.13 CaT 0
1 63.3 CwT , 0
2 93.6 CwT , and 2786 sI W m
20.1656A m , 2 1 9000t t s .
2
0.127(2 4168) 1 (1 0.127)((63.3 30.13) / 786)ln
0.1656(9000) 1 (1 0.127)((93.6 30.13) / 786)
0.431
F
The criteria for F2 value by Indian standard is that F2 should be greater than 0.42. The F2 value of
0.431 obtained from this study compare favorably with the standard.
4.1.8. Water Heating Time
The equation (below) is the standard time to boil gives as the accurate time to reach the optimum
temperature by considering the temperature of the absorber plate and the ambient temperature at
particular time. The time (t), for sensible heating from initial ambient temperature Tamb to a
temperature Tw2 can be obtained from:
1 2
2 1
( )ln 1 4.4w w w ambFM C T T
tF A FG
The time needed to boil the water is the main feature to observe the efficiency of the cooker, the
time that the temperature of the water reaches at 93.60C, considering all tested values F1 =
0.1270Cm2/W, F2 = 0.431, A=0.1656m2, Ta=28.40C, Cp=4.168KJ/Kg.K, Mw= 2kg, and Is =
968W/m2, base tested value above the time takes to boil can be obtained as:
30.127 2 4.168 10 (93.6 33.4)ln 1
0.431 0.2 0.127 968
8261.8 2: 29min
t
s
During the test, the temperature of the water can be measured in every 30min gap, to reach the
water from initial temperature (20.5oC) to Final temperature of water (93.60C) the final
temperature is measured at 9000s but the water reached the temperature of 93.60C at 8261.82s,
which is before 738.2s (9000-8261.8 = 738.2s).
51
This is a simplification of Eq. (4.3) dividing the equation by 60 to obtain the time in minutes. The
time for sensible heating is:
1 2
2 1
( )ln 1 4.5
60w w w ambFM C T T
tF A FG
8261.8137min
60t
Note: the above time (137min) does not show the cooking time or boiling time of the cooker.
During such test the cooker should wait until he/she get the maximum water temperature, so it may
take long testing hour.
4.2. Cooking power During Test
Cooking power experiment was conducted based on international standard procedure on June 18
& 19/2017. Experiment was conducted for the load of 2.0 kg of water. Solar cooker was exposed
to the sun from 10:00 AM to 2.00 PM, and the following values were recorded at 10-minute
interval: initial temperature of water, final temperature of water, ambient temperature, and solar
insolation for both un- finned and finned cooking vessel as shown in Appendix B-9 and B-10
respectively.
2 1( ) 7004.6
w pw w w
s
s
M C T TP
t I
2 4.7d w aT T T
4.3. Efficiency of Finned and Un-Finned Cooking Vessel.
4.3.1. Instantaneous Efficiency of Finned and Un-Finned Cooking Vessel.
The instantaneous efficiency of the solar cooker is the ratio of the energy output to energy input in
each measurement intervals. Where is energy efficiency, Mw is water mass, Cpw is specific heat
of water, Twf is final temperature of water, Twi is initial temperature of water, t is time, It is total
instantaneous solar radiation and Asc is intercept area of solar cooker. The instantaneous efficiency
can be calculating as:
52
0[ ( ) /energy output
energy input
w w wf wi
i t sc
m Cp T T tE
E I A
. 2 2
00.
[2 4168 / . (46.4 22.5) /1800
470 / 0.2
0.67
fin ist
fin ins
kg J Kg K s
W m m
Table 4-1 Shows the instantaneous efficiency of finned cooking vessel
Constants
Mass of water 2kg
Cp of water 4168J/kg.K
Time t 1800s
Ac 0.2m2
Time interval (min)
Water Temperature
of finned cooking
vessel(°C)
Instantaneous
Solar Isolation
(W/m2)
Instantaneous
efficiency of the
cooker with finned C.
Vessel (%)
9:00AM 22.5 310 1.17
9:30AM 46.4 470 0.67
10:00AM 63.3 580 0.4
10:30AM 76.4 746 0.2
Note: The result shows the instantaneous efficiency of the cooker, at the beginning of test the
temperature is low (22.50C), However the temperature of the water increases fastly until it reaches
high temperature. We can understand that the temperature change decrease when the temperature
of the water goes to maximum.
53
Table 4-2 The result of instantaneous efficiency of the solar cooker for un-finned cooking vessel
is shown in the table below.
Time interval
(min)
Water
Temperature of
un-finned cooking
vessel (°C)
Solar Isolation
(W/m2)
Instantaneous
efficiency of the cooker
with
un-finned C. Vessel (%)
9:00AM 22.5 310 1.37
9:30AM 50.3 470 0.72
10:00AM 68.4 580 0.15
10:30AM 73.3 746 0.18
4.3.2. Overall Efficiency of the cooker
The overall efficiency of the cooker is calculated based on the suitable cooking temperature range,
final water temperatures were chosen between 65°C and 95°C, respectively [14]. The test
computed dependently for both finned and un-finned cooking vessel placed side by side to observe
the boiling capacity of both cooker in t = 60min, the initial and the final temperature of the finned
cooking vessel is 20.5oC and 78.2oC respectively in 60 min. The initial and final temperature of
un-finned cooking vessel is 20.5oC and 66.7 respectively in 60min with average solar isolation of
768W/m2. The simple cooking efficiency of finned and un-finned cooking vessel in 60min is,
0[ ( ) /energy output
energy input
w w wf wi
i t sc
m Cp T T tE
E I A
. 2 2
[2 4168 / . (78.2 20.5) / 3600 ]0.86%
768 / 0.2fin
kg J Kg K s
W m m
002 2
[2 4168 / . (66.7 20.5) / 3600 ]0.69
768 / 0.2un fin
kg J Kg K s
W m m
4.4. Sample of cooking
The figure bellow shows the sample test of the cooking capacity of the cooker (DESC) on the final
day of the test June 20/ 2017. The test on the final day, 0.5kg of macaroni is cooked in 1.5 liter
(1.5kg) of water in the solar isolation range between 710W/m2 to 920W/m2 and at average ambient
54
temperature of 280C. The initial temperature of the water used to cook the macaroni is 23.40C. The
cooker fully cooked within 47min suitable to eat as shown in the figure below:
Figure 4-5 The sample test of cooking by 0.5kg 0f macaroni adding 1.5kg of water.
55
CHAPTER FIVE
5. RESULT AND DISCUSION
5.1. Stagnation Test Result - Parabolic Reflector ON
The graph indicates the variation in the solar radiation and ambient temperature and their effects
on the stagnation temperature observed in the absorber plate of the double exposure solar cooker.
The average ambient temperature for the test day was 28.7°C. Maximum absorber plate
temperature of 152.2°C was recorded at 12:30 pm and at an insolation value of 950 W/m2 and the
ambient temperature 31.90C.
The Fig. 5.1 and 5.2 shows, the temperature curve is increasing gradually but the solar isolation
curve is fluctuating up and down, these shows either the heat maintaining capacity of the absorber
plate and cooking vessel is high or the absolute measuring time shows repeated fluctuation while
collecting measured data at a time of test (which means the isolation is decreasing during
measuring minutes).
`
Figure 5-1 Thermal performance curve of the double exposure solar cooker under stagnation test
condition.
24.3 25.2 25.9 27 29.3 31.4 33.4 31.923.4
46.3
58.9
97.8
110.1
131
144.3152.2
278
508
648
793 790820 840
950
0
100
200
300
400
500
600
700
800
900
1000
0
20
40
60
80
100
120
140
160
EM
PE
RA
TU
RE
(0C
)
TIME
STAGNATION TESTAmbient Temperature(°C) Absorber plate Temp.(°C)
Solar Isolation ( W/me2 )
56
The maximum insolation of 950 W/m2 at 12:30 PM and minimum of 278 W/m2 at 9:00 AM were
recorded. The average solar radiation and ambient temperature observed during the period of test
were 648.3 W/m2 and 28.7° respectively. The result shows that heat loss from absorber plate of
the cooker is minimal and the absorber plate temperature is retained for a long time while the door
of the cooker is closed. This is desirable for heating water since major mode of heat transfer to the
cooking vessels is by conduction from absorber plate.
5.2. Stagnation Test Result- Parabolic Reflector Off
Maximum absorber plate temperature of 120.2°C was recorded at 12:00 pm and at an insolation
value of 996 W/m2. The average solar radiation and ambient temperature observed during the
period of test were 663.7 W/m2 and 27.25°respectively.
Figure 5-2. Thermal performance curve of the double exposure solar cooker under stagnation test
condition (parabolic flat reflectors off) June 13/2017.
24 25.9 24.3 25.4 26.7 28.932.3 31.3
24.8
39.3
62.4
84.3
100.3
112.6120.2 119.8
232
448
569
708640
779
996 968
0
200
400
600
800
1000
1200
0
20
40
60
80
100
120
140
Sola
r Is
ola
tion (
W/m
2)
Tem
per
ature
(oC
)
Time
Stagnation Test (parabolic Ref. Off)
Ambient Temperature (°C) Absorber Plate Temperature (°C)
solar Isolation (W/me2)
57
The result shows the presence of the flat reflectors mounted on parabola will increase temperature
of the absorber plate up by 31.90C in which 21% of absorber temperature obtained from the
parabolic flat reflectors.
5.3. Load Test Result
The maximum insolation of 968 W/m2at 12:30 pm and minimum of 310 W/m2 at 9:00 am morning
was recorded. The average solar radiation and ambient temperature observed during the period of
test were 683 W/m2 and 28.5° respectively. The maximum water temperature measured inside the
un-finned cooking is 88.8°C, and better result obtained finned cooking vessel which is 93.60C was
observed at 12:30 pm.
Figure 5-3. Thermal performance curve of the double exposure solar cooker under loaded (water
heating) test June 16/2017.
24.5 24.1 26.2 2731 32 31.2 33.4
20.5
46.4
63.3
76.483.4 86.8 89.3
93.6
20.5
50.3
68.473.3
79.6 81.285.8 88.8
36.4
65.4
78.1
89.1
106.3
116.2
128.3136.4
420470
580
746792
820 810
968
0
200
400
600
800
1000
1200
0
20
40
60
80
100
120
140
160
9:00AM 9:30AM 10:00AM 10:30AM 11:00AM 11:30AM 12:00PM 12:30PMSo
lar
Isola
tion(W
/m2)
Tem
per
ature
(0C
)
Time
Water Heating Test
Ambient Temperature(°C)
Water Temperature of finnd cooking vessel(°C)
Water Temperature of un-finned cooking vessel(°C)
Absorber plate Temperature(°C)
Solar Isolation (W/me2)
58
The result shows that ones the temperature of the water inside the finned cooking vessel increased,
it maintains the heat for long time, while the un-finned cooking vessel loses the heat in the same
condition with the finned cooking vessel with deceasing solar isolation.
5.4. Cooking Power Test Result
From the data recorded were used to calculate 𝑃, 𝑃𝑠, and 𝑇𝑑 for each interval. Standard cooking
power (𝑃𝑠) is plotted against the difference between water temperature and ambient temperature
(𝑇𝑑) as shown in Figure 5.4 and 5.5. A linear regression was used to examine the relationship
between standard cooking power and temperature difference.
Figure 5-4 Standard Cooking power versus Temperature difference graph of un-finned vessel (Appendix, B-9).
The Figure 5.4 is plotted using the values calculated by standard power and temperature difference
equation 4.6 and 4.7 respectively by using the tested data on Appendix (B-9).
Figure 5.4, shows that the cooking regression equation of power test for un-finned cooking vessel
is 𝑃𝑠 = 127.43 − 1.767𝑇𝑑. The value of the coefficient of determination (𝑅2) or proportion of
variation in cooking power that can be attributed to the relationship found by regression should be
better than 0.75 according to Funk and Larson. For this test the coefficient of determination is
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60
Sta
ndar
d p
ow
er(W
)
Temperature diffrence(oC)
Cooking power of the test Vs temprerature diffrence
𝑃𝑠 = 127.43 − 1.767𝑇𝑑𝑅2=0.8952
59
0.8952 > 0.75 (recommended standard value). The cooking power at 50∘C temperature difference
was calculated using the regression equation 𝑃50= 39.08W.
Figure 5-5. Standard Cooking power versus Temperature difference graph of finned cooking vessel
Appendix, (B-10).
The power test for finned cooking vessel shows that the cooking regression equation is 𝑃𝑠 = 148.31
− 1.968𝑇𝑑. For this test the coefficient of determination is 0.9528 > 0.75 which is mathematically
the square of correlation value of the power versus the temperature difference. The cooking power
at 50∘C temperature difference was calculated using the regression equation 𝑃50= 49.91W. The
figure 5.5 shows that as temperature difference increases, the standard cooking power decreases.
5.5. Overall Result
The overall result of double exposure solar cooker is tabulated below in table 5.1 which includes
the stagnation test as well as the first and second figure of merit for both systems with parabolic
and without parabolic reflectors, the water heating test considering both finned and un-finned
cooking vessel, estimation of cooking power for finned and un-finned cooking vessel and finally
the overall efficiency of the solar cooker.
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70
Sta
ndar
d p
ow
er(W
)
Temperature diffrence, 𝑇𝑑 (oC)
Cooking power of the Test Vs Temprerature diffrence
𝑃𝑠 = -1.968𝑇𝑑 + 148.31,
𝑅2 = 0.9528
60
Table 5-1 Overall concluded result of the cooker
Test Type Test Condition Result and
standard value
The stagnation temperature when the
parabolic reflector ON
Stagnation test condition 152.2oC
the first figure of merit when the
parabolic reflector ON
Stagnation test condition 0.127 > 0.12
The stagnation temperature when the
parabolic reflector off
Stagnation test condition 120oC
the first figure of merit when the
parabolic reflector off
Stagnation test condition 0.088 < 0.12
Water heating test for finned cooking
vessel
Water heating test 93.6oC
Water heating test for un-finned
cooking vessel
Water heating test 88.8oC
The value of the coefficient of
determination Finned cooking vessel
Power test 0.9528 > 0.75
The value of the coefficient of
determination un-Finned cooking
vessel
Power test 0.8952 > 0.75
Efficiency of Finned cooking vessel 86%
Efficiency of un-Finned cooking
vessel
69%
61
CHAPTER SIX
6. ECONOMIC ANALYSIS OF THE OVERALL SYSTEM
A double exposure solar cooker consist of rectangular enclosure which usually constructed from
woods to reduce the heat loss due to its low thermal conductivity. A rectangular aluminum try is
housed in the enclosure which absorbs solar radiation. The inner glass is usually toughened to
avoid cracking during cooking by avoiding internal shock. A transparent glass enhances input
radiation. Blackened aluminum pot are used for cooking.
6.1. Cost of the Double Exposure Solar Cooker
According to cooking requirement, solar cooker of different size may be used the family size, on
this system, depending on the market price and size the cost of each equipment’s used to construct
the double exposure solar cooker. The materials and price of each component are listed bellow
Table 6-1 Non-linear regression coefficient and other input parameter ( ith component)
Component Market size
of material
(m2)
Rate/
m2
(Birr)
Thickness
(m)
Regression
coefficient
( i )
Manufactur
ing
size(m2)
Number
of item
( in )
Enclosure (wood) (0.3x10) = 3 450 0.2 0.33 0.75 1
Reflector Booster (1 x 2) =2 420 0.001-0.002 0.5 0.3 3
Parabolic
reflector
(1 x 2) = 2 420 0.001-0.002 0.5 0.05 9
Absorber tray 0.5 110 0.002-0.004 2 0.182 1
Top and Bottom
glassing
(1 x 2) =2 410 0.004 0.5 0.2 2
Inner glass
(Transparent
glass)
(1 x 2) =2 380 0.003 0.46 0.182 1
Secondary
reflector (inside
the box)
(1 x 2) =2 400 0.001-0.002 0.5 0.2 4
(Aperture area A= 0.2m2) solar cooker standardized by the MENS is reported to suitable for
cooking meals for 4-5 persons [35]. The standard design for sizes, solar cooker designed with the
aperture area of 0.25- 1m2 were envisaged. From size and mass of components and market prices,
the fallowing relation of main cost Cmain has been developed.
62
7 6
. ,1 1
( ) 6.1main i i i m i i m ji j
C n A p n p
Where 1...7i refers, respectively, to enclosure, booster, parabolic reflector, absorber tray, top and
bottom glazing, inner glazing, and secondary reflector, i is regression coefficient. and 1...5j
refers to angle iron, coaster wheel, steel (locally tubollary) and glass wool, respectively.
Table 6-2 linear regression coefficient and other parameter ( jth component)
Component Rate (birr)
,m jP
thickness Manufacturi
ng amount
Number of
item ( jn )
Cost of stand (angle
iron)
115 0.002m ___ 3
Coaster Wheel 15 0.05m ___ 4
Steel (locally called
Tubollary)
250 0.002m-0.004m ___ 4
Glass wool 130 ---- 1.2kg 1
Painting ink 100 ---- 1liter 1
Labor cost 2000 ---- ----- 1
Table 6-3 The cost of the ith and the jth components are listed in the table below in, by applying
equation 4.8.
No( in ) Component ( ith ) Cost of each material (Birr)
1 Enclosure 112.5birr
2 Booster (Box Reflector) 189birr
3 Parabolic Reflector 94.5birr
4 Absorber tray 54.6 birr
5 Top and Bottom Glass 82birr
6 Inner Glass 34.58birr
7 secondary Reflector (inner reflector 160birr
63
Total cost 727.18birr
No ( jn ) Components ( jth ) Cost of each material
1 Cost of stand (angle iron) 345birr
2 Coaster wheel 60birr
3 Steel(tubolar) 1000birr
4 Glass wool 130birr
5 Painting ink 100birr
6 Labor cost 100birr
Total cost 3635birr
The total capital cost of the project is the summation of the main cost ith component, jth component
and labor and miscellaneous costs.
7 6
. ,1 1
( 1) ( ) 6.2c i i i m i j m ji j
C n A p n p
is a fraction and represents the proportion of total cost which includes miscellaneous items such
as pots, frame, hinges, rivets, nails etc. The fraction is 0.0676. The value of regression
coefficients and other input parameters corresponding to the seven main components are given in
the Table 6.1. The capital cost of the project is;
(0.0676 1) 727.18 3635
4657.18
c
c
C birr birr
C birr
6.2. Maintenance Cost
The routine maintenance of the double exposure solar cooker includes coating of absorber tray and
cooking vessels with black paint at least ones a year, replacement of coaster wheel, tray, utensil,
glass and reflector. Table 6.4 shows detail of annual cost incurred on maintenance. The
maintenance cost is expressed as a fraction ( ) of Cc , i.e.
64
Table 6-4 Annual maintenance cost of a family size double Exposure solar cooker.
Components Repair
Required
Frequency of
repair/Replacement
Estimated
cost(birr)
Annual
Cost
(Birr)
Utensil and Tray Repainting Ones in 6 month 50 100
Coaster Wheel Replacement Ones in 4 years 60 15
Tray and Utensil
(finned & Un-finned)
Replacement Ones in 2 years 194.4 97.2
Booster and parabolic
Reflector
Replacement Ones in 3 years 283.5 94.4
Glass Replacement Ones in 3 Years 116.5 29.12
Total cost per
year
335.75birr
6.3m cC C
The capital cost for family size double exposure solar cooker (Table 4.5) is 4657.18birr. The annual
maintenance cost is 7.2% of the capital cost, i.e. 0.072 .
6.3. Valuations of Benefit.
Benefit accrued to the users of the solar cookers may be valued in terms of the number of the
number of meals cooked per annum and fuel saved per meal. If ,m aN represents the number of
meals cooked annually and mp is the money value of fuel saved per meal. Then the annual saving
(birr) for the users are:
, 6.4a m a mB N p
The monetary worth of the fuel saved per meal depends on the unit market prices ( mp ), calorific
value ( kQ ) and utilization efficiency ( k )of fuel, as well as the useful energy ( mU ) requires to
cook a single meal, i.e.:
( ) 6.5m m k k kp U p Q
65
The useful energy required to cook a single meal is a function of a type and amount of meal. An
approximate procedure for estimating the value Um for representative meal is given as:
2
, ,1
( ) 6.6m l l b a n ch n w el
U m c T T m E m L
Where 1...2l refers to rice, and water respectively. L is the latent heat of vaporization
2264.7KJ/Kg and ,w em is the mass of water being evaporated is assumed to be 0.075Kg. The
specific energies required for chemical change (kJ/Kg) in food item ,ch nE have been taken as 252
KJ/Kg [34] and the value of C1 were set equal to 1.84 [37] for rice. The representative meal consists
of 0.7kg of rice. The water requirement is 1.5 times their respective masses. The additional amount
of water to compensate for evaporative losses in a conventional cooking were calculated as
0.075kg, 0.15kg and 0.075kg for rice, pulse and potatoes respectively.
2
, ,1
( )
0.7 1.84(94 28.75) 2 4.168(94 28.75) 0.075 252 0.075 2264.67
84.04 543.92 18.9 169.85
816.7
0.8
m l l b a n ch n w el
m
U m c T T m E m L
U
KJ
MJ
In cooking 0.8MJ energy is consumed per day per meal and 1.6MJ per day per two meals.
Table 6-5 Cost benefit of the cooker with each type of fuel.
Type of Fuel Cost Of Fuel /meal
(Pm)
Number of
Meal/annum (Nm,a)
Benefit
/annum(Ba)
Fire Wood 1.1birr 670 737birr
Caw Dung 1.25birr 337 421.25birr
Charcoal 1.37birr 242 331.54birr
Kerosene 1.34birr 1048 1404.32brr
LPG 0.98birr 670 656.6birr
66
6.4. Financial Analysis
The present value of the cost of the overall system and the total benefit of the system can be
evaluated based on the interest rate of commercial bank of Ethiopia. The system is aimed to have
10 years’ life span, for better efficiency we can safely assume that the system works for five years.
The total cost of the system is Cc = 4657.18 ETB, the maintenance cost of the system per year is
Cm =335.75ETB and the benefit of the system for households which uses kerosene for cooking is
1404.32ETB.
Table 6-6 The cost and benefit of the system for next 5 years
Cost (Birr) Year Benefit (birr)
4657.18 1 1404.32
335.75 2 1404.32
335.75 3 1404.32
335.75 4 1404.32
335.75 5 1404.32
Salvage Vale 1000
Let’s take a 5% interest rate which is an interest rate similar to that which is used by the commercial
bank of Ethiopia when it lends money.
( )6.7
( 1)n
M nN
i
Equation used to calculate the present value of future money is
Where;
N - is the present value of future money.
( )M n - is the value of a money after n years.
n - is the number of years.
i - is the interest rate.
Using the above equation 6.7, the present value of the cost of the system N is
67
5
4(335.75) 4657.18
(0.05 1)
4701.3
N
ETB
The present value of the benefit of the system is calculated as:
5
5(1404.32) 1000
(0.05 1)
6285.13
N
ETB
Net present value. The net present value (NPV) shows the economic gain that can be expected
from the system in currency units of the base year. It is calculated by subtracting the economic
costs of the system from the economic benefits.
NPV present worthof benefit present worthof cost
6285.13 4701.3
1583.83
NPV
ETB
The benefit-cost ratio is equal to the present worth of benefit divided by the present worth of the
cost of the system.
cos
present worthof benefitBCR
present worthof t
6285.131.37
4701.3BCR
The ratio of the benefit to cost of the system indicates that double exposure solar cooker is
financially feasible.
6.5. Payback period
The payback period (also termed the break-even point) is the period of time after which the benefits
from system equal the total cost of system. It defines the point in time at which an intervention
starts to produce net economic benefits.
Theunit cost of thecookerpayback period
Amount of saved
68
4657.183
1404.32payback period
The payback period of the benefit of the system per one fuel type is 3 years, after 3 years the
household can gain the benefit of system by maintaining the cooker with estimated cost of
maintenance per annum.
69
7. CONCLUSIONS AND RECOMMENDATIONS
7.1. CONCLUSION
The double exposure solar cooker is the best alternative way to improve the performance of the
box solar cooker by adding parabolic flat reflector with minimum production cost with better
additional heat input to the absorber plate.
On the basis of comparative experimental study of double exposure solar cooker, the presence of
parabolic flat reflector and without parabolic reflector which has been tested under the same
climatic condition shows that the presence of parabolic flat reflector results absorber plate
temperature of 1520C, which is additional temperature of 31.90C compare to the cooker without
parabolic reflector. The purpose of each PFR is to increase the focus area by adjusting each
reflectors towards to different part of the absorber plate. The stagnation test shows the first and the
second figure of merit holds the cooker can be marked as grade “A” solar cooker according to the
test standard of ASAE and BIS.
The overall efficiency of the cooker also evaluated for both finned and un-finned cooking vessel
under the same climatic condition by limiting the time in 60 min, boiling efficiency of finned and
un-finned cooking is 86% an 69% respectively.
A comparative experimental study of a DESC with two different cooking vessels was conducted,
the first one finned and the second one is un-finned cooking vessel with the same volume. The
experiment shows the finned cooking vessel results only 4.8oC additional temperature compare to
that of un-finned cooking vessel, these shows providing fin on the external surface has small
improvement. Finally, the overall financial analysis of the system shows the benefit/cost ratio =
1.37 indicate cooker is economically feasible and the system can pay back the overall capital cost
in three years.
70
7.2. RECOMMENDATIONS
During cooking and accessing the pot from font door the man/women may cover full
reflection of sun radiation and the door of DESC should be provided at the back side of the
box to simply access the food.
Hot air has tendency to move upward due to its lower density, the cooker should carefully
observe the losses at the top or side door and other construction imperfection.
A spherical reflective ball should be placed at center of the box to know the exact position
of the sun in order to rotate the cooker to track maximum solar radiation.
71
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74
APPENDIX
Appendix. A
The calorific value of fuels in MJ/Kg and the cost of each fuel are shown in the graph below.
The calorific value of fuel.
The cos of various fuel in birr per kilogram (from Nitin Saxena, 2014).
17
8
28
38
45.5
0
5
10
15
20
25
30
35
40
45
50
Fire wood Cow dung Charcoal Kerosene LPG
Chalorific Value in MJ/Kg
27.1
25
15
2.5
7
0 5 10 15 20 25 30
LPG
kerosene
Charcoal
Cow dung
Fire wood
Cost of Various in Birr. per kg
75
Appendix. (B-1)
The stagnation test was conducted for three consecutive days from June 10-12/2017. Thermal
performance table of the double exposure solar cooker under stagnation test condition when the
parabolic flat reflector is on (June 10/2017).
Time Ambient
Temperature(°C)
Absorber plate
Temp.(°C)
Solar Isolation
(W/m2)
9:00AM 24.3 23.4 278
9:30AM 25.2 46.3 508
10:00AM 25.9 58.9 648
10:30AM 27 97.8 793
11:00AM 29.3 110.1 790
11:30AM 31.4 131 820
12:00PM 33.4 144.3 840
12:30PM 31.9 152.2 950
1:00PM 32.1 146.3 915
1:30:PM 28 138 704
2:00PM 29.7 126.1 611
2:30PM 30.3 122 536
3:00PM 29 112.4 501
3:30PM 27.3 90.2 420
4:00PM 25.9 87 411
Appendix. (B-2)
Thermal performance table of the double exposure solar cooker under stagnation test condition
when the parabolic flat reflector is on (June 11/2017).
Time Ambient
Temperature(°C)
Absorber plate
Temp.(°C)
Solar Isolation
(W/m2)
9:00AM 22 21 370
9:30AM 24.6 36 426
10:00AM 25.3 48.7 503
10:30AM 27.8 59.2 733
11:00AM 28.7 88.3 786
11:30AM 28 102.4 827
12:00PM 32.3 126.1 840
12:30PM 29.9 142.2 910
1:00PM 31.2 141.3 908
1:30:PM 30.3 136 880
76
2:00PM 33 140 766
2:30PM 29 134.7 674
3:00PM 28 131 563
3:30PM 27 127 520
4:00PM 26 126.3 654
Appendix. (B-3)
Thermal performance table of the double exposure solar cooker under stagnation test condition
when the parabolic flat reflector is on (June 12/2017).
Time Ambient
Temperature(°C)
Absorber plate
Temp.(°C)
Solar
Isolation
(W/m2)
9:00AM 20 21 452
9:30AM 24 42 516
10:00AM 25.3 53.4 560
10:30AM 25.6 72.9 706
11:00AM 27.7 98.6 795
11:30AM 27 110 835
12:00PM 28.9 123.3 881
12:30PM 31 134 850
1:00PM 31.4 141.4 905
1:30:PM 32.1 144.5 930
2:00PM 30.3 139 980
2:30PM 29 135 824
3:00PM 27.4 131.3 750
3:30PM 27.3 130 711
4:00PM 26 128 498
Appendix. (B-4)
The stagnation test by making the parabolic flat reflector off was conducted from June 13-15/2017.
Thermal performance Table of the solar cooker when parabolic flat reflectors off, at stagnation test
condition (June13/2017).
Time interval
(min)
Ambient
Temperature
(°C)
Absorber plate
Temperature
(°C)
Solar Isolation
(W/m2)
9:00AM 24 24.8 232
9:30AM 25.9 39.3 448
77
10:00AM 24.3 62.4 569
10:30AM 25.4 84.3 708
11:00AM 26.7 100.3 640
11:30AM 28.9 112.6 779
12:00PM 32.3 120.2 996
12:30PM 31.3 119.8 968
1:00PM 29.4 116.3 823
1:30:PM 27.3 94.3 796
2:00PM 28.4 96.1 766
2:30PM 27.1 92.3 674
3:00PM 26.4 86 563
3:30PM 26.5 71.2 520
4:00PM 24.9 70.4 474
Appendix. (B-5)
Thermal performance Table of the solar cooker when parabolic flat reflectors off, at stagnation test
condition (June14/2017).
Time Ambient Temperature(°C) Absorber plate
Temp.(°C)
Solar
Isolation
(W/m2) 9:00AM 23 21.4 359
9:30AM 25.3 52 516
10:00AM 26.3 63 567
10:30AM 27.4 77.3 711
11:00AM 29 88.1 789
11:30AM 28.9 103 835
12:00PM 29.2 109.3 850
12:30PM 31.4 116 871
1:00PM 31.8 115.3 909
1:30:PM 29.3 107.4 930
2:00PM 27.2 102 980
2:30PM 28.6 97 867
3:00PM 27.4 95 750
3:30PM 26 89.3 673
4:00PM 25.2 86.1 498
78
Appendix. (B-6)
Thermal performance Table of the solar cooker when parabolic flat reflectors off, at stagnation test
condition (June15/2017)
Time Ambient Temperature(°C) Absorber plate
Temp.(°C)
Solar
Isolation
(W/m2) 9:00AM 24 26 406
9:30AM 23.4 39 520
10:00AM 26.3 63 680
10:30AM 27.1 72.4 712
11:00AM 27.8 89.3 745
11:30AM 28.9 103.4 796
12:00PM 27.2 118 808
12:30PM 28 119.6 932
1:00PM 30 113.4 884
1:30:PM 29 108 802
2:00PM 26 102 792
2:30PM 27.8 107 843
3:00PM 29 98.3 765
3:30PM 30.1 100.4 754
4:00PM 27 86.1 542
Appendix. (B-7)
Thermal performance table of the double exposure solar cooker under water heating test condition
for finned and un- finned cooking vessel (June 16/2017).
Time Ambient
Temperature(°C)
Water
Temperature
of finned
cooking
vessel(°C)
Water
Temperature
of un-finned
cooking
vessel(°C)
Absorber plate
Temperature(°C)
Solar
Isolation
(W/m2)
9:00AM 24.5 20.5 20.5 36.4 420
9:30AM 24.1 46.4 50.3 65.4 470
10:00AM 26.2 63.3 68.4 78.1 580
10:30AM 27 76.4 73.3 89.1 746
79
Appendix. (B-8)
Thermal performance table of the double exposure solar cooker under water heating test condition
for finned and un- finned cooking vessel (June 17/2017).
Time Ambient
Temperature(°C)
Water
Temperature
of finned
cooking
vessel(°C)
Water
Temperature of
un-finned
cooking
vessel(o C)
Absorber plate
Temperature(°C)
Solar
Isolation
(W/m2)
9:00AM 23 20.8 20.8 24 324
9:30AM 23.8 42.3 52.3 60.4 460
10:00AM 26 67 72.1 79.3 682
10:30AM 26.3 78.3 78.6 82.4 719
11:00AM 26.8 82.1 84.1 90.3 745
11:30AM 27.4 86.3 87.3 110.8 781
12:00PM 28 87.2 86.1 127.3 807
12:30PM 30.2 90.6 86.4 130.2 926
1:00PM 32.6 91.2 88.3 132 932
1:30:PM 29.8 89.7 82 128 910
2:00PM 31 90 77.6 110.4 820
2:30PM 29.4 86 74 108.3 812
3:00PM 27 83.8 75 99.8 737
3:30PM 26 82 71 96.4 643
4:00PM 26.6 79.3 72.1 97.2 720
11:00AM 31 83.4 79.6 106.3 792
11:30AM 32 86.8 81.2 116.2 820
12:00PM 31.2 89.3 85.8 128.3 810
12:30PM 33.4 93.6 88.8 136.4 968
1:00PM 28.3 93.4 87.4 130.3 880
1:30:PM 34 92.5 83.8 127.1 896
2:00PM 29.7 91.2 78 120 747
2:30PM 29 86.4 73.2 118.4 640
3:00PM 27.3 84.9 70 106 621
3:30PM 26.8 83 68 98.9 528
4:00PM 24.2 80.1 63 94.3 436
80
Appendix. (B-9)
Power estimation of double exposure solar cooker thermal performance checking values for heat
up condition of un- finned cooking vessel (June 1/2017).
Constants
Mw 2kg
Cw 4186J/kg.K
Ʈ 600s
Time
Interval
(Min.)
T1(0C) T2(0C) P(W) Is
(W/m2) Ta (0C)
Tw
(0C) Td (0C) Ps (W)
10.10 22.5 26.9 61.395 320.00 22.6 26.9 4.3 134.301
10.20 26.9 31.4 62.790 386.00 24.1 31.4 7.3 113.868
10.30 31.4 36.8 75.348 452.00 26.2 36.8 10.6 116.689
10.40 36.8 41.1 59.999 516.00 27 41.1 14.1 81.394
10.50 41.1 46.7 78.139 560.00 28.1 46.7 18.6 97.673
11.00 46.7 52.0 73.953 580.00 28.9 52.0 23.1 89.253
11.10 52.0 56.8 66.976 623.00 29.2 56.8 27.6 75.254
11.20 56.8 61.0 58.604 666.00 29.6 61.0 31.4 61.596
11.30 61.0 65.8 66.976 709.00 30.4 65.8 35.4 66.126
11.40 65.8 69.3 48.837 752.00 30.8 69.3 38.5 45.460
11.50 69.3 74.1 66.976 795.00 31.2 74.1 42.9 58.973
12.00 74.1 78.9 66.976 838.00 31.7 78.9 47.2 55.947
12.10 78.9 81.5 36.279 881.00 32 81.5 49.5 28.825
12.20 81.5 86 62.790 924.00 34.4 86 51.6 47.568
12.30 86.0 88.8 39.069 968.00 32.2 88.8 56.6 28.253
81
Appendix. (B-10)
Power estimation of double exposure solar cooker thermal performance checking values for heat
up condition of finned cooking vessel.
Time Interval
(Min.)
T1(0C) T2(0C) P(W) Is
(W/m2)
Ta (0C) Tw (0C) Td (0C) Ps (W)
10.10 22.5 27.2 65.581 320.00 22.6 27.2 4.6 143.458
10.20 27.2 33.0 80.929 386.00 24.1 33.0 8.9 146.763
10.30 33.0 38.7 79.534 452.00 26.2 38.7 12.5 123.172
10.40 38.7 44.0 73.953 516.00 27 44.0 17.0 100.323
10.50 44.0 49.6 78.139 560.00 28.1 49.6 21.5 97.673
11.00 49.6 55.0 75.348 580.00 28.9 55.0 26.1 90.937
11.10 55.0 60.3 73.953 623.00 29.2 60.3 31.1 83.093
11.20 60.3 65.4 71.162 666.00 29.6 65.4 35.8 74.795
11.30 65.4 70.8 75.348 709.00 30.4 70.8 40.4 74.392
11.40 70.8 76.2 75.348 752.00 30.8 76.2 45.4 70.138
11.50 76.2 80.3 57.209 795.00 31.2 80.3 49.1 50.372
12.00 80.3 84.3 55.813 838.00 31.7 84.3 52.6 46.622
12.10 84.3 88.1 53.023 881.00 32 88.1 56.1 42.129
12.20 88.1 92 54.418 924.00 34.4 92 57.6 41.226
12.30 92.0 93.6 22.325 968.00 32.2 93.6 61.4 16.144
Where:- P = Interval Cooking Power (Watt)
w pwM C TP
t
Ps = Standard Cooking Power (Watt)
700s
b
P PI
Td = Temperature Difference (oC)
2d w aT T T
Ta = Ambient Temperature (oC)
Tw = Water Temperature (oC)
82
T1 = Initial Water Temp. (oC)
T2 = Final Water Temp. (oC)
Cw = Specific Heat Capacity (4186J/kgK)
Mw = Mass of Water (kg)
Is = Average Solar Isolation (W/m2)
I = Solar Radiation (W/m2)
Appendix. C
TM-207 Solar Power meter: The units of measure are Watts per square meter or BTU, the typical
test and measuring applications are:
Meteorology applications
Agriculture applications
Physics and optical laboratories
Solar radiation measurement.
Solar transmission measurement
Solar power research
Identify high performance windows
Light Intensity Measurement for the car windows
Model No: TM-207
Product Description
- 3½ digits LCD display with maximum reading of 2000.
- External sensor.
- Measuring the Solar radiation emitted by the sun.
- Display units: W/m2 (Watts per square meter) or BTU.
- Data Hold/ MAX/MIN functions
YC-811 Thermometer: The most common thermocouple junction is the type K as it is providing
the widest operating temperature range.
YC-8xxN Series Thermometer K/J /T/E Types.
83
Appendix-E
The construction phase of double exposure solar cooker including the vessel provided with fin and
conventional cooking vessel are shown below.
84
Note:
Internal air-1 - is the hot air gap between the top glass and the absorber plate.
Internal air- 2 – is the hot air inside the cooking vessel when the pot is closed.
Internal air-3 – is the hot air gap between the absorber plate and glass-2 located under the absorber
plate.
Internal air-4- is the hot air gap between the bottom glass-3 and the inner glass 2.
85
Appendix. F
the part and orthographic view of the double exposure solar cooker are shown on A3 tracing paper
bellow.
86