This document is a thesis submitted by Ahmad Asyraf Bin Ramli in partial fulfillment of the requirements for a Bachelor of Mechanical Engineering degree from Universiti Malaysia Pahang in 2010. It presents a theoretical analysis of a solar water heating system, developing a mathematical model to analyze how the temperature changes based on factors like the area of the flat plate collector, volume of the insulated storage tank, piping size, and water flow rate. The analysis calculates the efficiency of the collector and storage tank for different sizes and volumes, as well as the solar fraction for different collector and tank sizes under varying temperature and flow conditions. The models provide data to optimize design for high capacity and facilitate future study.

1. THEORETICAL ANALYSIS OF SOLAR WATER HEATING SYSTEM
AHMAD ASYRAF BIN RAMLI
Thesis submitted in partial fulfilment of the requirements
For the award of the degree of
Bachelor of Mechanical Engineering
Faculty of Mechanical Engineering
UNIVERSITI MALAYSIA PAHANG
2010

2. UNIVERSITI MALAYSIA PAHANG
FACULTY OF MECHANICAL ENGINEERING
I certify that the project entitled “THEORETICAL ANALYSIS OF SOLAR WATER
HEATING SYSTEM” is written by AHMAD ASYRAF BIN RAMLI. I have examined
the final copy of this project and in our opinion; it is fully adequate in terms of scope
and quality for the award of the degree of Bachelor of Engineering. I herewith
recommend that it be accepted in partial fulfillment of the requirements for the degree
of Bachelor of Mechanical Engineering.
(Maisara Mohyeldin Gasim Mohamed)
Examiner Signature

3. ii
SUPERVISOR’S DECLARATION
I hereby declare that I have checked this project and in my opinion this project is
adequate in terms of scope and quality for the award of the degree of Bachelor of
Mechanical Engineering.
Signature
Name of Supervisor: AMIR BIN ABDUL RAZAK
Position: Lecturer
Date: 6th
DECEMBER 2010

4. iii
STUDENT’S DECLARATION
I hereby declare that the work in this thesis is my own except for quotations and
summaries which have been duly acknowledged. The project has not been accepted for
any degree and is not concurrently submitted for award of other degree.
Signature
Name: AHMAD ASYRAF BIN RAMLI
ID Number: MA07024
Date: 6th
DECEMBER 2010

5. vi
ACKNOWLEDGEMENT
Assalamualaikum Warahmatullah Wabarakatuh…
First of all, thanks to Allah The Almighty because giving me blessing, health
and ideas to finish my project successfully. Hopefully, Allah always blesses me in the
future. InsyaALLAH..
I am grateful and would like to express my sincere appreciation to my kind
project supervisor, Mr. Amir bin Abdul Razak for his germinal ideas, valuable
guidance, advice and continuous encouragement, constructive criticism and suggestion
throughout this project. Without his continued support and interest, this thesis would not
have been the same as presented here.
My deeply thanks also extends to my dearest family especially to my father
Ramli bin Shamsudin and mother Zaiton bt Ab Kadir which always support and pray
throughout this project. Their blessing gave me high spirit and strength.
Lastly, thanks to all my friends and all people who involve direct and indirect in
provides assistance and co-operations at various occasions. Their view tips are useful
indeed in helping me finish my thesis. Thanks…

6. vii
ABSTRACT
Renewable energy is important for replace the using of electrical energy generated by
petroleum. Energy consumption from petroleum must be reduced because of the limited
petroleum resources and contribute of pollution to the earth. Solar power has become a
source of renewable energy and solar energy applications should be enhanced. Solar
water heating system was a practical application to replace the using of electrical water
heater. More research is needed to increase capability and reduce production costs of
solar water heating system and make the solar water heating system more efficient and
practical. The objective of this project is to do investigation on solar water heating
system in terms of mathematical theory to produce a mathematical model of solar water
heating system. The analysis done by using a mathematical model developed to obtain
data on temperature in the changes of flat plate collector area, storage tank insulation
volume, piping size and mass flow rate of water. Efficiency of flat plate collector and
storage tank insulation is calculated for any changes in size and volume. Solar fraction
is calculated for any changes in the size of a flat plate collector and storage tank
insulation in the consideration of changes in temperature and mass flow rate of water.
Analysis showed the water temperature will increase with increasing area of flat plate
collector, decreased with the increasing volume of insulated storage tank, and decreased
with increasing size of the pipe. an These studies can provide data for the optimum
design with high capacity and the mathematical models will facilitate the future study.

7. viii
ABSTRAK
Tenaga boleh diperbaharui amat penting bagi menggantikan penggunaan tenaga elektrik
yang dijanakan oleh petroleum. penggunaan tenaga daripada petroleum perlu
dikurangkan kerana sumber petroleum semakin terhad dan menyumbag kepada
pencemaran yang merosakan bumi. Tenaga suria menjadi salah satu sumber tenaga yang
boleh diperbaharui dan aplikasi tenaga suria perlu dipertingkatkan. Sistem pemanasan
air suria menjadi satu aplikasi yang praktikal untuk digunakan bagi menggantikan
pemanas air menggunakan elektrik. Lebih banyak kajian perlu dilakukan bagi
meningkatkan keupayaan dan mengurangkan kos penghasilan system pemanasan air
suria supaya lebih cekap dan praktikal. Objektif projek ini adalah untuk membuat kajian
terhadap system pemanasan air suria dari segi teori dengan mendapatkan persamaan
matematik dari segi keseluruhan untuk menghasilakan model matematik bagi system
pemanas air suria. Analisis akan dibuat dengan menggunakan model matematik yang
dihasilkan bagi mendapatkan data perubahan suhu terhadap perubahan luas plat
pengumpul datar, perubahan isipadu tangki simpanan berpenebat, perubahan saiz
saluran paip, dan perubahan kadar aliran jisim air. Kecekapan untuk plat pengumpul
datar dan tangki simpanan berpenebat akan dikira untuk setiap perubahan saiz dan
isipadu. Pecahan suria akan dikira untuk setiap perubahan saiz plat pengumpul datar dan
tangki simpanan berpenebat dengan mengambil kira perubahan suhu dan kadar aliran
jisim air. Analisis menunjukan suhu air akan bertambah dengan pertambahan luas plat
pengumpul datar, menurun dengan pertambahan isipadu tangki simpanan berpenebat
dan menurun dengan petambahan saiz paip. Kecekapan akan bertambah dengan
pertambahan luas plat pengumpul datar dan berkurang dengan pertambahan isipadu
tangki simpanan berpenebat. Kajian ini dapat memberi data untuk rekabentuk yang
optimum dengan keupayaan yang tinggi dan model matematik akan memudahkan
kajian pada masa akan datang.

8. xi
TABLE OF CONTENTS
Page
TITLE PAGE i
SUPERVISOR’S DECLARATION iii
STUDENT’S DECLARATION iv
DEDICATION v
ACKNOWLEDGEMENTS vi
ABSTRACT vii
ABSTRAK viii
TABLE OF CONTENTS xi
LIST OF TABLES xiv
LIST OF FIGURES
LIST OF SYMBOL
xv
xvi
LIST OF ABBREVIATIONS xviii
CHAPTER 1 INTRODUCTION 1
1.1 Project Background 1
1.2 Problem statement 2
1.3 Project objective 3
1.4 Project scope 3
CHAPTER 2 LITERATURE REVIEW 4
2.1 Introduction 4
2.2 Solar Water Heating System 5
2.3 Types of Solar Water Heating System 5
2.31 Natural Circulation Systems (thermosyphon
solar system)
5
2.32 Forced-Circulation System 7

9. xii
2.4 Low Flow Pumped System 9
2.5 Auxiliary 10
2.6 Flat Plat Collector 11
2.7 Solar Collector Orientation 12
2.8 Fluid Flow Rates 13
2.9 Specification of Solar Water Heating System 14
2.10 Solar Energy 16
2.10.1 Terminology: 17
2.10.2 Sun Earth Geometry: 22
CHAPTER 3 METHODOLOGY 25
3.1 Introduction 25
3.2 Flow Chart 26
3.3 Component Of Solar Water Heating System. 27
3.4 Designing of the mathematical model 27
3.5 Analysis of mathematical model 28
3.5 Input data 28
CHAPTER 4 RESULTS AND DISCUSSION 29
4.1 Introduction 29
4.2 Mathematical Model 30
4.2.1 Energy Balance for Flat Plate Collector 32
4.2.2 Energy Balance of Insulated Storage Tank 32
4.2.3 Complete Equation of System 33
4.2.4 Estimation of Hourly Radiations 33
4.2.5 Limits in Storage Temperature Profile 35
4.2.6 Efficiency 36
4.2.7 Solar Fraction 36
4.3 Temperature Profile For Different Area of Collector 36
4.4 Temperature Profile for Different Volume of Insulated
Storage Tank
37

10. xiii
4.5 Temperature Profile for Different Configuration of
Water Flow Rates
39
4.6 Efficiency of Insulated Storage Tank and Flat Plate
Collector
40
4.7 Fraction of Insulated Storage Tank and Flat Plate
Collector
42
4.8 Design of SWH From Mathematical Model 44
CHAPTER 5 CONCLUSION 46
5.1 Introduction 46
5.1 Conclusion 46
5.2 Recommendation 47
REFERENCES 48
APPENDICES 50
A1 Gantt chart FYP 1 50
A2 Gantt chart FYP 2 51

11. xiv
LIST OF TABLES
Table No. Page
2.1 Details of solar water heating system (Indian standard 12933) 14
2.2 Details of Collector (Indian standard 12933) 15
2.3 Supply Of Insulated Storage Tanks (Indian standard 12933) 16
2.4
Details Of Stand for Insulated Hot Water Tank (Indian standard
12933)
16
3.2 Input data 28
4.1 Constants for predicting hourly solar radiation with ASHRAE model 34
4.1
Table of temperature profile base on specification of Solar Water
heating system
44

12. xv
LIST OF FIGURES
Figure No. Page
2.1 Natural circulation system (thermosyphon) 6
2.2 Three configurations of forced circulation systems 8
2.3 An example of solar fraction 10
2.4 Schematic of alternative location for auxiliary energy supply 11
2.5 Flat Plate Collector functions 12
2.6 Zenith and solar altitude angles 18
2.7 Slope β Surface azimuth angle γ and solar azimuth angle s
γ 19
2.8 Declination and hour angle 21
3.1 The Flow Diagram of the Project 26
3.2 schematic of solar water heating system 27
4.1 schematic of solar water heating system 30
4.2 Mass and energy balance of Solar Water Heating System 30
4.3 Storage Temperature vs Area of collector 37
4.4 Storage temperature vs Volume of insulated tank 38
4.5 Storage temperature vs Overall piping diameter 39
4.6 Temperature vs Mass flow rates 40
4.7 Efficiency vs volume of storage tank 41
4.8 Efficiency vs area of collector 41
4.9 Fraction Vs Volume of storage tank 42
4.10 Fraction vs Area of collector 43

13. xvi
LIST OF SYMBOLS
Ac
Ast
Cp
FR
F
h/d
Ig
Id
IT
J
K
K
mc
mL
mR
mst
mx
qaux
qL
QL
qLs
qR
qs
qstl
collector area, m2
surface area of the storage tank, m2
specific heat of working fluid, J/kg ˚C
collector heat removal factor
solar fraction over a specified time horizon
height to diameter ratio of storage tank
global solar radiation intensity, W/m2
diffuse radiation intensity, W/m2
solar radiation intensity on tilted surface, W/m2
fraction of net storage heat gain in a time step
fraction of makeup water supplied in a time step
thermal conductivity of storage tank insulation, W/mK
collector mass flow rate, kg/s
desired load mass flow rate, kg/s
storage makeup water mass flow rate, kg/s
mass flow rate from storage to load, kg/s
mass flow rate for mixing, kg/s
auxiliary energy required, W
desired hot water load, W
desired hot water load over a specified time horizon, J
load met by solar energy or energy extracted from the storage, W
energy added to storage through makeup water, W
solar useful heat gain rate, W
rate of storage loss, W

14. xvii
R
Rb
Ta
TL
TR
Tsat
Tst
Tsti
Tstf
t
tins
tt
Ust
UL
Vst
Vsti
Vstib
VL
VR
Β
Φ
ρ
ρg
ρt
(τα)
maximum auxiliary heater power, W
tilt factor
ambient temperature, ˚C
desired load (hot water) temperature, ˚C
makeup water temperature, ˚C
saturation temperature, ˚C
storage temperature at any instant of time, ˚C
storage temperature at the beginning of a time step,
storage temperature at the end of a time step, ˚C
time step in the analysis, s
storage tank insulation thickness, m
storage tank wall thickness, m
storage heat loss coefficient, W/m2
˚C
collector overall heat loss coefficient, W/m2
˚C
storage volume at any instant of time, m3
initial storage volume in a time step, m3
initial Storage volume at the beginning of the day, m3
volume of water withdrawn by load in a time step, m3
volume of water replenished to the storage tank in time step, m3
collector tilt, rad
latitude of location, rad
density of working fluid, kg/m3
ground reflectance
density of storage tank material, kg/m3
average transmittance absorptance product

15. xviii
LIST OF ABBREVIATIONS
ISO
LPD
SWH
international organization for standardization
liters per day
Solar water heating

16. CHAPTER 1
INTRODUCTION
1.1 PROJECT BACKGROUND
The solar energy is the most capable of the alternative energy sources. Despite
this hopeful evaluation of the potential of solar energy, considerable technical and
economic problems must be solved before utilization of solar energy can occur. The
solar power development will depend on how we deal with a number of serious
constraint, including scientific and technological problem, marketing and financial
limitations, and political. In addition, the education of engineers will have to changes its
focus from non-renewable fossil-fuel technology to renewable power source. There has
been a general agreement that the most significant of the renewable energy sources is
solar radiation.
Thermal conversion is a technological scheme that utilizes a solar radiation.
When a dark surface is placed in sunshine, it absorbs solar energy and heats up. Solar
energy collector working with sun facing surfaces will transfer energy to the water that
flow through it. To reduce heat loses to atmosphere and to improve it efficiency, one or
two sheet of glass are usually placed over the absorbed surface. This type of thermal
collector suffers from heat losses due to radiation and convection. Such losses increase
rapidly as the temperature of the working fluid increases. Improvement such as the use
of selective surfaces, evacuation of the collector to reduce heat losses, and the special
glass is use to increase the efficiency of the absorber.
Solar water heating (SWH) is a proven and famous renewable energy
technology and has been used in many countries of the world. The SWH system

17. 2
investigated consists of mainly three parts, namely a flat plate solar collector, a heat
exchanger (storage tank) and a circulating pump. Solar water heating system have been
the famous application that using solar radiation as an energy sources that using thermal
conversions.
This project will analyze the Solar Water Heating System based on the
theoretical analysis from the mathematical model. The mathematical model will be
consider all the part of the solar water heating system to find the solar water heating
system temperature when the size and the behavior of solar water heating is changing.
1.2 PROBLEM STATEMENT
In today’s modern world, where new technologies are introduced every day,
electrical energy use is increasing quickly Fossil fuel particularly petroleum fuel is the
major contributor to electrical production. Quickly depleting reserve of petroleum and
decreasing air quality raise question about the future. Solar can be use as a clean
alternative energy to reduce electrical production and is promising in the effect to
establish environmentally friendly for electrical system. So far, many extensive studies
investigated solar water heating system and become the famous application for home
and building.
The using of solar water heating system not familiar in Malaysia and the people in
Malaysia still not realize about the practical of using solar water heating systems. It’s
important to study about the power produce to heat the water using solar water heating
system and proving about energy saving of solar water heating system.
1.3 PROJECT OBJECTIVE
The objectives of this analysis are to:
i. Find the mathematical model of solar water heating system.
ii. Find the change in water temperature from variable behavior of all part in solar
water heating system.
iii. Find the efficiency and fraction of design using mathematical model.

18. 3
1.4 PROJECT SCOPE
The project scope is to:
i. study on solar water heating system
ii. Design a mathematical model of solar water heating system
iii. Simulate the behavior of the Solar Water Heating System using the mathematical
model

19. CHAPTER 2
LITERATURE REVIEW
2.1. INTRODUCTION
A solar water heating system (SWH) is the device that uses solar energy for hot
water production. Solar water heating system (SWH) is renewable energy technology
and has been used in many countries of the world. This natural energy is absolutely free
and the supply is unlimited in the day whenever there is sunlight. The usage of this
energy does not produce any pollutant and therefore is most Environment Friendly. In
residential countries, energy consumption in the building sector need of high energy
budget. Most energy is needed production of hot water and space heating. Hot water is
important for bathing and for washing, utensils and other domestic purpose in urban as
well as in country areas. Heating water is usually burning by firewood in the country
areas and by fossil fuel energy such as kerosene oil, petroleum gas (LPG), coal and
electricity in metropolitan areas. In this consider, consumption of solar energy through
solar water heating (SWH) systems can be replace to reducing energy amount required.
(Staff, D., and Campbell, S., 1978)
SWH is approve and readily available technology use renewable energy for
conventional water heating. A lot of types of SWH are available and can be used in
much application. Domestic hot water usually uses small system applications while
larger systems are used in industrial applications. There are two types of water heating
systems based on the type of the circulation: natural circulation and forced circulation.
Natural circulation solar water heaters are simple in design and low cost. Forced
circulation water heaters are used in freezing climates and for commercial and industrial
process heat. (Staff, D., and Campbell, S., 1978)

20. 5
Suitable design of solar water heating system is will give maximum benefit to
the user, mainly for a large system. Designing solar hot water system need suitable
sizing of different components and must considering on solar insulations and hot water
demand. In this review, the effect of sizing of part on the system is studied and a novel
strategy for the system part is proposed to improve the design and performance of solar
water heating systems.
2.2 SOLAR WATER HEATING SYSTEM
Energy application from the sun to heat water is nothing new. Solar water
heaters have been use since the 1800s. What's difference is configuration is most
modern solar water heaters are placing in the roof with resembles to sky. Solar water
heaters are an environmentally and to reduce energy bills. (Staff, D., and Campbell, S.,
1978)
Solar water heaters come in differences of configurations in the design, cost,
performance, and level of system. Most systems have auxiliary such as electricity or
gas. A solar water heating system has a part of a insulated water storage tank, a solar
collector, a back-up energy source, and a pump and controls. (Staff, D., and Campbell,
S., 1978)
2.3 TYPES OF SOLAR WATER HEATING SYSTEM
There are basically two types of solar water heating system(D. Yogi Goswami, Jan F.
Kreider, 1999):
2.3.1 Natural Circulation Systems (thermosyphon solar system)
The natural tendency of a less dense fluid to rise above a denser fluid can be
used in a simple solar water heater to cause fluid motion through a collector. The
density difference is created within the solar collector where heat is added to the liquid.
In the system shown in Figure 2.1 as water gets heated in collector, it rises to the tank
and the cooler water from the tank moves to the bottom of the collector, setting up a

21. 6
natural circulation loop. It also called a thermosyphon loop. Since these water heaters
not use a pump, it is a passive water heater. For the thermosyphon to work, the storage
tank must be located higher than the collector. (D. Yogi Goswami, Jan F. Kreider, 1999)
Figure 2.1: Natural circulation system (thermosyphon)
Source : D. Yogi Goswami, Jan F. Kreider, 1999
Since the driving force in a thermosyphon system is only a small density
difference and not a pump, larger-than-normal plumbing fixtures must be used to reduce
pipe friction losses. In general, one pipe size larger than normal would be uses with a
pump system are satisfactory.
Since the hot-water system load vary little during a year, the angle of tilt is that
equal to the latitude, that is, . The temperature difference between the collector
inlet water and collector outlet water is usually 8-11˚C during the middle of a sunny
day. After sunset, a thermosyphon system can reverse its flow direction and lose heat to
the environments during the night. To avoid reverse flow, the top header of the absorber
should be at least 30cm below the cold leg fitting on the storage tank, as shown;
otherwise a check valve would be needed. . (D. Yogi Goswami, Jan F. Kreider, 1999)
Several features inherent in thermosyphon design unit utility. If it’s to be
operated in a freezing climate, a nonfreezing fluid must be used, which in turn requires
a heat exchanges between collector and portable water storage. (If portable water is not
required, the collector can be drained during cold period instead). Heat exchanger of
either the shell-and-tube type or the immersion-coil type required higher flow rates for
efficient operation than a thermosyphon can provide. Therefore, the thermosyphon is

22. 7
usually limited to nonfreezing climates. For mild freeze climates, a heat exchanger coil
welded to the outer surface of the tank and filled with antifreeze may work well. . (D.
Yogi Goswami, Jan F. Kreider, 1999)
2.3.2 Forced-Circulation System
If a thermosyphon system cannot be used for climatic, structural, or architectural
reason, a forced- circulation system is required.
In order to accommodate the thermal expansion of water from heating, a small
(about 2 gallon capacity) expansion tank and a pressure relief valve are provided in the
solar loop. Because water always stays in the collector of this system, antifreeze
(propylene glycol or ethylene glycol) is required for location where freezing condition
can occur. During stagnation condition (in summer), the temperature in the collector can
become very high, causing the pressure in the loop to increase. This can cause leak in
the loop unless some fluid is allowed to escape through a pressure-release valve.
Whether the result of leaks or of draining, air enters the loop causing the pumps to run
dry. This disadvantage can be overcome in a closed loop drain back system which is not
pressurized. In this system, when the pump shut off, the water in the collector drains
back into a small holding tank while the air in the holding tank goes up to fill the
collector. The holding tank can be located where freezing does not occur, but still at a
high level to reduce pumping power. In all three configuration differential controller
measures the temperature differential between the solar collector and the storage, and
turns the circulation pump on when the differential goes below a set limit (usually 2˚C).
Alternatively, a photovoltaic (PV) panel and d DC pump may be used. The PV panel
turns on the pump only when the solar radiation is above a minimum level. Therefore,
the differential controller and the temperature sensors may be eliminated. . (D. Yogi
Goswami, Jan F. Kreider, 1999)

23. 8
(1)
(2)
(3)
Figure 2.2: Three configurations of forced circulation systems: (1) open loop, (2) closed
loop, and (3) closed loop with drain back.
Source: D. Yogi Goswami, Jan F. Kreider, 1999
Figure 2.2 show in an open loop system the solar loop is at atmospheric
pressure, therefore, the collectors are empty when they are not providing useful heat. A
disadvantage of the system is the high pumping power required to pump the water to the
collector every time the collectors become hot. This disadvantage is overcome in the
pressurized closed loop system since the pump has to overcome only the resistance of
the pipes. In this system, the solar loop remains filled with water under pressure. (D.
Yogi Goswami, Jan F. Kreider, 1999)

24. 9
2.4 LOW FLOW PUMPED SYSTEM
The collector flow rates in the range of 0.01 to 0.02kg/m2
s, lead to high values
of collector heat removal factor, FR. However in direct system (without a collector heat
exchanger) they also lead to relatively high fluid velocities in piping and subsequent
mixing (or partial mixing) in tanks. Van koppen et al. (1979) suggested the advantages
of low flow and stratified tanks, and recent work has confirmed that it can be
advantageous to use reduced fluid flow rates in the collectors loops, accept a lower FR
and gain the advantages of increase stratification with resulting reduced collector inlet
temperature. The result can be a net improvement in system performance. Lower flow
rates result in greater temperature rise across collectors, and if tanks are perfect
stratified, the temperature difference from top to bottom will increase as the flow rates
decreases. As pointed out by Hollands an Lightstone (1989) in very useful review, the
use of lower flow rates can have the additional advantages of reduction in both the first
cost and operating cost of the system through use of smaller pipes and pumps and
reduction of operating cost for pumps operation. Flow rates used in Swedish flat-plates
collector have typically been in range of 0.002 to 0.007kg/m2
s. (Dalenback, 1990).
Figure 2.3 from simulation studies by wuestling et al. (1985), illustrates for a
specific example the effect of collector flow rates per unit area of system performance
(expressed as solar fraction, F) for a fully mixed tank and for a highly stratified tank.
The potential advantages of the low-flow system are evident; the maximum
performance for the stratified tank (F = 0.66) is a third grater than that for the fully
mixed tank (F =0.48). This level of improvement is not realized in practice, as real
tanks are in general neither fully mixed nor fully stratified. As Holland and Lightstone
(1989) point out, the degree of improvement depend in part on load patterns, as loads
that draw the tanks down completely by the beginning of collection in the morning will
result in less improvement in performance that if the tanks is hot in the morning.
However, the gains that have been reported in experiment are significant.