Mekelle University

EiT-M
Mechanical Engineering Department

Senior project on:

Mathematical modeling and experimental test of heat

pipes for solar thermal application

(For the partial fulfillment of B.SC degree in Mechanical

Engineering)

Submitted by:

Daniel Berhanu

Demis Bisenebit

Advisor: Ashenafi K.(M.SC)

11/10/2004E.C
 Table of Contents

Acknowledgement........................................................................................................................................iv
Abstract......................................................................................................................................................v
Nomenclatures...........................................................................................................................................vi
CHAPTER ONE.............................................................................................................................................1
1. Introduction.................................................................................................................................................1
1.1.Objective of the project........................................................................................................................2
1.1.1. General objective..........................................................................................................................2
1.1.2. Specific objective..........................................................................................................................2
1.2. Methodology........................................................................................................................................2
1.3. Scope of the project.............................................................................................................................2
1.4. Significance of the research.................................................................................................................3
1.5. Literature Review................................................................................................................................3
1.6. Flat Plate Collectors.............................................................................................................................4
1.7. Thermal resistance...............................................................................................................................9
1.7.1 Heat transfer in the evaporator region.........................................................................................10
1.7.2 Liquid–vapor interface temperature drop....................................................................................10
1.7.3 Heat transfer in the condenser.....................................................................................................10
1.7.4 Total temperature drop................................................................................................................11
1.8. Boiling and condensation..................................................................................................................11
1.8.1. Boiling Heat Transfer.................................................................................................................11
1.8.2. Condensation Heat Transfer.......................................................................................................11
1.8.3. Film Condensation inside Horizontal Tubes..............................................................................13
CHAPTER TWO.......................................................................................................................................14
2. Heat pipe theory....................................................................................................................................14
2.2. Heat Pipe Merits................................................................................................................................16
2.4. Applications of heat pipes.................................................................................................................18
CHAPTER THREE....................................................................................................................................19
3.1. Flat plate collector.............................................................................................................................19
3.2. Heat pipe type flat plate collector......................................................................................................19
3.3. Necessary parameters........................................................................................................................20
3.4. Heat Pipes Profile..............................................................................................................................20

ii
 3.5 Mathematical modeling for heat pipe with wick structure..................................................................22
3.6.Thermal analysis.................................................................................................................................27
3.7. Mathematical modeling for wick less heat pipe tube.........................................................................33
3.7.1 Thermal analysis..........................................................................................................................39
CHAPTER FOUR.......................................................................................................................................43
4. Experimental set up and procedure.......................................................................................................44
4.1. Description of prototype................................................................................................................44
4.2. Measurement of Solar Irradiation and Temperature......................................................................45
4.3. Performance of both arrangements................................................................................................45
CHAPTER FIVE........................................................................................................................................46
5. Result and Discussion...........................................................................................................................46
5.1. Experimental result of heat pipe with wick and without wick collectors......................................46
5.2. Results and Discussion on Both Arrangements in the Same Day..................................................48
5.3. Comparison of Numerical and Experimental Results....................................................................52
CHAPTER SIX...........................................................................................................................................53
6.1. Conclusion.........................................................................................................................................53
6.2. Recommendation...............................................................................................................................54
6.3. References..........................................................................................................................................55

iii
 Acknowledgement

We are grateful and would like to express our sincere gratitude to our advisor Mr. Ashenafi
Kebedom (M.SC.) for providing this interesting and exciting topic and then providing his
guidance, assistance and encouragement throughout the duration of the project. We appreciate his
consistent support from the first day of the project to these concluding moments. Sincere thanks
to all staff of the Mechanical Engineering Department who helped us in many ways and
providing equipment and information sources that assisted our studies and projects.

iv
 Abstract

In this project theoretical and experimental study conducted on solar water heater with two kinds
of arrangements. The arrangements were using heat pipe with wick and heat pipe without wick.
In both arrangements, the evaporator section on the solar absorber and the condenser section
inserted in to the storage tank.

Theoretical analysis was made on both types of arrangements employing mathematical models
obtained from literature. The experimental analysis showed that the efficiency of the heat pipe
with wick arrangement is higher than the wick less type arrangement with a maximum difference
of 5%.

Experiments conducted on a prototype with both arrangements indicated that the efficiencies
were close to each other during the morning hours. However, the heat pipe with wick
arrangement showed better performance in the afternoon hours when the solar radiation started to
decrease.

v
Nomenclatures

S The solar irradiation absorbed by a collector per unit area of absorber.

Ul The collector overall heat loss coefficient
hfi The fluid convective heat transfer coefficient between the water and the tube
K Sheet metal thermal conductivity
Cp Specific heat capacity of water
D Outside pipe diameter
Di Inside pipe diameter

δ Sheet metal thickness

M Mass flow rate
Ti Fluid inlet temperature
Ta Ambient temperature
Kb Bond thermal conductivity
B Bond width

vi
 CHAPTER ONE
1. Introduction

Ethiopia is one of the countries endowed with high potential of solar energy. However, the
current use of solar energy is insignificant compared to its potential. Harnessing the solar energy
is possible indifferent ways. The outcome of this project focuses on solar water heating. The main
objective was to study solar water heating system that employs heat pipes. A heat pipe consists of
sealed container (pipe wall and end caps), a wick structure and a small amount of working fluid
inside. Heat applied at one end of the heat pipe is transported to the other end. During this
process, there will be a change of state and there will be a release of latent heat of condensation.
For this reason, heat pipe transport large quantity of heat through a small cross-sectional area.
The project investigated the application of heat pipe as heat pipe as heat exchanging mechanism
in flat plate collectors.

The project will discuss results of theoretical and experimental results made on the prototypes
solar collector with heat pipe without wick arrangement and a heat pipe with wick type
arrangement. The first section will be on literature review conducted on solar energy in general,
flat collectors and heat pipes in particle. The section is on theoretical analysis made in order to
support the hypothesis made with theoretical justification. The remaining sections discuss the
details of the experimental set up, procedure and analysis of results. Finally, on the last section
outlines the main conclusion s as an outcome of the project and recommendation.

1
 1.1.Objective of the project

1.1.1. General objective

The main objective of this project is to make a mathematical model for heat pipe with both type
of arrangement that is heat pipe with wick and without wick structure and also to make
experimental investigation on both type of arrangement and to compare the mathematical model
with the experimental one.

1.1.2. Specific objective

The following listed below are our specific objective in this project
 To fix the solar water collector properly
 To make mathematical analysis for two type of heat pipe arrangement
 To make experimental analysis for two type of heat pipe arrangement
 To compare the mathematical & the experimental analysis
 To put Result & discussion based on the above comparison

1.2.Methodology

 Fixing the worn out parts of the solar collector and storage

 Collecting data from journals, books

 Measuring the solar irradiation and temperature using Pyranometer and thermometer
respectively

 Theoretical and mathematical analysis on both types of arrangements

 Result and discussion

1.3.Scope of the project

 This project does not include part analysis other than copper tube and heat pipe
 Also does not involve measurement of temperatures before 9am and 4pm due to
insufficient intensity of solar irradiation.
 The application area is limited for domestic consumption.

2
 1.4.Significance of the research

As far from the economic and environmental benefits , the mains importance of the project is to
select best efficient pipes for the application of solar thermal system.

1.5.Literature Review
Ethiopia is endowed with very high solar energy resource potential. In order to utilize the
potential various solar energy-harnessing technologies have to be studied and applied. It is
essential to know the availability and intensity of the solar energy on sites where the technology
is planned to be implemented.

There are different theoretical models that can estimate the solar energy intensity (Duffle et al)
introduced a method of calculating solar irradiation based on specific data input is described in
1991. The input data needed include latitude of the site, inclination slope of the collector, the day
of the month, and hours of the day etc, based on the data a series of formulas are used to find the
appropriate angles. The solar radiation is then calculated from the general established beam and
diffuse radiation formula.

Solar and Wind Energy Resource Assessment (SWERA) has produced a report on ’’high
resolution solar radiation assessment for Ethiopia.’’ The report contains very important result of
solar assessment made employing data obtained from Meteosat geo-stationary satellite (schilling
et al, 2004), SWERA uses models to interpret the satellite data into solar irradiation. The out puts
of assessment are presented in the form of solar radiation maps from the whole country. In
addition to the maps, solar irradiation hourly time series data for 17 cities and towns are delivered
in files that can be downloaded from the web site (WWW.unep. Net /SWREA).the report
indicates that the results of the satellite data analysis were not validated using ground
measurement.

Theory and application of heat pipe has been well established Faghiri (1998) and Dunn Reay
(1994) provide both theoretical and applications. The thermal property of heat pipe has been
utilized for many applications. Heat pipe has been used to transport from one side of a component
to another side. By doing these very fast efficient heat transport is obtained that can’t be done in
another way.

There is a limited literature on application of heat pipe for the purpose of solar collectors. Some
reference was made from the report of Brace Research institute regarding heat pipe sizing.
Hilawe (2004) reported experimental analysis of solar collector that employed heat pipes. A
paper on theoretical and experimental result of heat pipe collector (Bong, 1993) will be used for
theoretical analysis.

3
 1.6.Flat Plate Collectors

Where temperature below about 90 oC as they are for space and service water heating flat plate
collectors , which are of the non-concentrating type ,are particularly convenient. They are made
in rectangular panels, from about 1.7 to 2.9 m 2, in area and are relatively simple to construct and
erect. Flat plates can collect and absorb both direct and diffuse solar radiation; they are
consequently effective even on cloudy days when there is no direct radiation. The majority of the
flat plate collectors have five main components as follows

1. a transparent cover (sheet of glass or radiation transmitting plastic

film)
2. Tubes, fins, passage connected to it which carry the fluid.
3. the absorber plate (black)surface
4. insulation at the back and sides
5. The casing or container which encloses the other components and
protects them from the weather.

Solar radiation Absorber

Heat transport fluids

Insulation
Transparent
cover

Figure 1.components of flat plate collector

The front covers are generally glass (may be one or two) that is transparent to incoming solar
radiation and opaque to the infrared re radiation from the absorber. The glass acts as a convective

4
shield to reduce the losses from the absorber plate beneath .thickness of 3 or 4 mm are commonly
used. The advantage of second glass is

losses due to air convection in windy areas is further reduced

Radiation losses in the infrared spectrum are reduced further by 25%.
Advantages of flat plate collectors
 They use both beam and diffused radiation
 Do not require orientation towards the sun
 They require little maintenance
 They are mechanically simpler than concentrating collectors
The performance of solar collectors is described in energy balance that indicates the
distribution of incident solar radiation in to the useful energy gain and various losses .the thermal
losses can be separated into three components

1. Conductive losses

2. Convective losses

3. Radiation losses

Under steady state conditions, the useful heat delivered by solar collector is equal to the energy
absorbed in the metal surface minus the heat losses from the surface directly and indirectly to the
surrounding. This principle can be stated in the relationship.

Qu=AcF'[S-UL (Th-Ta)

Where

Qu Useful energy delivered by collector

Ac Collector area

UL Over all heat loss coefficients

Qtotal , loss
Ul = A ( ΔT )

The heat losses from the surface are the following

(A)Top Loss

This loss occurs through the glass covers taking in to consideration the emitance of plate
and glass, wind convective heat loss. Mathematically can be expressed by

5
 (T T )A (T Ta )A
4 4

pm − σ −
Q top =
a
+
pm

[ ]T
.3 2 N +f −1 1
(T pm− T )
a C
+
1
ε
+
ε (1− ε )
−N
g p +. 05 N p
( N −f )
pm h w

Where

TPM-mean plate temperature

A=Le*W

σ = Stefan Boltzmann constant

hw- wind heat transfer coefficient

hw= 5.7+ 3.8Vw

f= (1-0.04 hw +0.00005 hw2)(1+0.091N)

C= 365.943(0.00883S-0.0001298S2)

To calculate the mea plate temperature, steady state heat conduction from the plate to the fluid is
used, which latter is iterated until similar result is obtained with the correct useful energy.

Qe
Tpm=Tfm+¿
hfi πDi Le n

Where Le=evaporator length Di=internal diameter of heat pipe n=number of heat pipes

B) Bottom (back) loss, Qb

This loss accounts the convective and conductive loss through the insulation.
Mathematically:

6
 A ( T PM −T a )
δ 1
+
Qb= K hb

Where

δ is thickness of insulation

K= insulating material thermal conductivity

hb= convective coefficient between bottom of the insulation and the environment

(Recommended value =12.5 to 25 w/m2- k)

(c) EDGE LOSS ,Qe

This heat dissipation comes from the edge loss to thee environment. It is given by

Qe=heA(Tpm−Ta)

Where

Tpm = Mean plat temperature (°c)

A = perimeter area of edge

Know the total heat loss, Qtotal

Qtotal=Qt +Qb+ Qe

Fin Efficiency, Fe

Fin efficiency of the collector is given by the following relation;

Me(W −Do)
tan( )
2
Me(W −Do )
Fe= 2

7
 ( )
0.5
Ul
K fe δ e
Me=

Qtotal , loss
Ul
= A ( ΔT )

Where

W fin width

Ul over all heat loss coefficient of the collector

K fe thermal conductivity of fin

δ Fin thickness

Fin Efficiency Factor, Fl

[ ]
−1
W UlAe UlAe
+ +
F l=
( W −D o ) Fe+ Do ( UA ) fe ( UA ) he
K fe π Le [ D c + Do ]
Ul ¿ fe
2 ( D c + Do )
( =

[ ]
−1

() ()
ro ri
ln ln
(UA ) ri rv
+
2 πLo K p 2πL o K e,e
he=

Where

Ae evaporator area

Le evaporator length

Ke,ethermal conductivity of fin

(UA) fe evaporator fin conductance

(UA)he = evaporator heat pipe conductance

Lc = condenser length

8
To get the useful energy from the fin

Qu= Fl ¿ (τα )e −Q loss )

Where

Fl = fin efficiency factor

(ατ )ε = absorpitive-transmitive constant

I= solar irradiation Qloss = total heat loss

1.7.Thermal resistance

Heat can both enter and leave the heat pipe by conduction from or to a heat Source/sink by
convection or by thermal radiation. Further temperature drops will occur by thermal conduction
through the heat pipe walls at both the evaporator and condenser regions. The temperature drops
through the wicks arise in several ways. It is found that a thermal resistance exists at the two
vapor–liquid surfaces and also in the vapor column. The processes of evaporation and
condensation are examined in some detail both in order to determine the effective thermal
resistances and also to identify the maximum heat transfer limits in the evaporator and condenser
regions. Finally, the results for thermal resistance and heat transfer limits are summarized.

Figure 2. Thermal Resistance Circuit

9
1.7.1 Heat transfer in the evaporator region

For low values of heat flux, the heat will be transported to the liquid surface partly by conduction
through the wick and liquid and partly by natural convection. Evaporation will be from the liquid
surface. As the heat flux is increased, the liquid in contact with the wall will become
progressively superheated and bubbles will form at nucleation sites. These bubbles will transport
some energy to the surface by latent heat of vaporization and will also greatly increase convective
heat transfer. With further increase of flux, a critical value will be reached, burnout, at which the
wick will dry out and the heat pipe will cease to operate.

1.7.2 Liquid–vapor interface temperature drop

Consider a liquid surface; there will be a continuous flux of molecules leaving the surface by
evaporation. If the liquid is in equilibrium with the vapor above its surface, an equal flux of
molecules will return to the liquid from the vapor and there will be no net loss or gain of mass.
However, when a surface is losing mass by evaporation, clearly the vapor pressure and hence
temperature of the vapor above the surface must be less than the equilibrium value. In the same
way for net condensation to occur the vapors pressure and temperature must be higher than the
equilibrium value.

1.7.3 Heat transfer in the condenser

Vapor will condense on the liquid surface in the condenser, on the mechanism of surface
evaporation and there will be a small temperature drop and hence thermal resistance. Further
temperature drops will occur in the liquid film and in the saturated wick and in the heat pipe
envelope. Condensation can occur in two forms, either by the condensing vapor forming a
continuous liquid surface or by forming a large number of drops. The former, film condensation
occurs in most practical applications, including heat pipes. Condensation is seriously affected by
the presence of a noncondensable gas. However, in the heat pipe, vapor pumping will cause such
gas to be concentrated at the end of the condenser. This part of the condenser will be effectively
shut off and this effect is the basis of the gas-buffered heat pipe. The temperature drop through
the saturated wick may be treated in the same manner as at the evaporator.

10
1.7.4 Total temperature drop
This shows the components of the total temperature drop along a heat pipe and the equivalent
thermal resistances.
• R1 and R9 are the normal heat transfer resistances for heating a solid surface and are calculated
in the usual way.
• R2 and R8 represent the thermal resistance of the heat pipe wall.
• R3 and R7 take account of the thermal resistance of the wick structure and include any
temperature difference between the wall and the liquid together with conduction through the
saturated wick. It is seen that the calculation of R3 is difficult if boiling occurs. R7 is made up
principally from the saturated wick, but if there is appreciable excess liquid then correction must
be added.
• R4 and R6 are the thermal resistances corresponding to the vapor liquid surfaces.
They may be calculated but can usually be neglected.[1]

1.8.Boiling and condensation

1.8.1. Boiling Heat Transfer
Boiling occurs when a liquid is in contact with a surface maintained at a temperature T s
sufficiently above the saturation temperature of the liquid. Boiling is classified as pool boiling or
flow boiling depending on the presence of bulk fluid motion. Boiling is pool boiling in the
absence of fluid motion and flow boiling in its presence. Pool and flow boiling are further
classified as a sub cooled boiling and saturated boiling depending on the bulk fluids temperature.
Four different boiling regimes are observed: natural convection boiling, nucleate boiling,
transition boiling and film boiling. In nucleate boiling, the rate of heat transfer strongly depends
on the nature nucleation (the number of active nucleation sites on the surface, the rate of bubble
formation at each site, etc), which is difficult to predict .the type and the condition of the heated
surface also affect the heat transfer.

1.8.2. Condensation Heat Transfer

Condensation occurs when the temperature of a vapor is reduced to below its saturation
temperature, Tsat. This is usually done by bringing the vapor in to contact with a solid surface
whose temperature Ts is below the saturation temperature Tsat of the vapor. But condensation
can also occur on the free surface of a liquid or even in a gas when the temperature of the liquid
or the gas to which the vapor is exposed is below Tsat in the latter case, the liquid droplets
11
suspended in the gas form a fog. Two distinct forms of condensation are observed: film
condensation and film condensation .in film condensation, the condensate wets the surface and
forms a liquid film on the surface that slides down under the influence of gravity. The thickness
of the liquid film increases in the flow direction as more vapors condense on the film. This is
condensation occurs in practice. In drop wise condensation, the condensed vapor forms droplets
on the surface instead of a continuous film, and the surface is covered by countless droplets of
varying diameter. In film condensation, the surface is blanketed by a liquid film of increasing
thickness, and this liquid wall between solid surface and the vapor serves as resistance to heat
transfer. The heat of vaporization hfg released as the vapor condenses must pass through this
resistance before it can reach the solid surface and be transferred to the medium on the other side.
In drop wise condensation, however, the droplets slide down when they reach a certain size,
clearing the surface and exposing it to vapor. There is no liquid film in this case to resist heat
transfer. As a result, heat transfer rates that are more than 10 times larger than those associated
with film condensation can be achieved with drop wise condensation. Therefore, drop wise
condensation is the preferred mode of condensation in heat transfer applications, and people have
long tried to achieve sustained drop wise condensation by using various vapor additives and
surface coating. These attempts have not been very successful; however, since the drop wise
condensation achieved did not last long and converted to film condensation after some time.
Therefore, it is common practice to be conservative and assume film condensation in the design
of heat transfer equipment.

12
 1.8.3. Film Condensation inside Horizontal Tubes
Most condensation processes encountered in refrigeration and air conditioning applications, how
involve condensation on the inner surface of horizontal or vertical tubes. Heat transfer analysis of
condensation inside tubes is complicated by the fact that it is strongly influenced by the vapor
velocity and the rate of liquid accumulation on the walls of the tubes. For low vapor velocities,
Chato recommends the following expression for condensation

[ )]
. 25
gρl ( ρl −ρ v )
h int ernanal =.555
μl ( T sat −T s ) ( 3
hfg + C pl ( T sat −T s )
8

Where hinternal -internal heat transfer coefficient

µl liquid viscosity

ρ l Liquid density

ρ v Vapor density

C pl Specific heat of liquid

13
 CHAPTER TWO
2. Heat pipe theory

A heat pipe is a simple device with no moving parts that can transfer large quantities of heat over
fairly large distances essentially at constant temperature without requiring any power input. A
heat pipe is basically a sealed cylinder tube containing a wick structure lined on the inner surface
and a small amount of fluid such as water at the saturated state as shown in the figure.

Figure 3.Parts of heat pipe showing the working principle

It is composed of three sections :the evaporator section ,where heat is absorbed and fluid is
vaporized ;a condenser section at the other end ,where vapor is condensed and heat is rejected;
and the adiabatic section in between, where vapor and liquid phases of the fluid flowing opposite
directions through the core and the wick, respectively complete the cycle with no significant heat
transfer between surrounding medium.

The type of fluid and the operating pressure inside the heat pipe depend on the operating
temperature of the heat pipe. For example, the critical and the triple point temperature of water
are .01 deg.cent and 374.1 deg.centg. Respectively therefore ware can undergo a liquid- to- vapor
or vapor - to- liquid phase change process in this temperature range only, and thus it will not be
suitable fluid for applications involving temperature beyond this range. furthermore ,water will

undergo a phase –change process at specified temperature only if its pressure equals the
saturation pressure at that temperature .For example, if a heat with water as the working fluid is

14
designed to remove heat at 70 oC ,the pressure inside the heat pipe must be maintained at 31.2
kpa ,which is the boiling pressure of water at this temperature .Note that this value is well below
the atmospheric pressure of 101 kpa ,and thus the heat pipe operates in vacuum environment in
this case. If the pressure inside is maintained at atmospheric pressure instead, heat transfer will
result in an increase in temperature of water instead of evaporation.

2.1.The Operation of a Heat Pipe

The operation of a heat pipe is based on the following physical principles:

 At specified pressure, a liquid will vaporize or vapor will condense at a certain,

called the saturation temperature. Thus fixing the pressure inside fixes a heat
pipe fixes the temperature at which a phase change will take place.
 At specified pressure or temperature the amount of heat absorbed as a unit mass
of liquid vaporizes is equal to the amount of heat rejected as that vapor
condenses.
 The capillary pressure developed in a wick and the hydrostatic pressure will
move a liquid.
 A fluid in channel flows in the direction of decreasing pressure.
Initially, the wick of the heat pipe is saturated with liquid and the core section is filled with
vapor. When the evaporator of the heat pipe is brought into contact with a hot surface, heat will
flow in too the heat pipe. Being at a saturated state the liquid in the evaporator end of the heat
pipe will vaporize as a result of this heat transfer, causing the vapor pressure there to rise .this
resulting pressure difference drives the vapor through core from the evaporator to the condenser.
The condenser is in a cooler environment, and thus its surface is slightly cooler. The vapor that
comes in to contact with this cooler surface condenses, realizing the heat of vaporization, which
is rejected to the surrounding medium. The liquid the returns to the evaporator end through the
wicks a result n\of capillary action in the wick, completing the cycle. As a result, heat is absorbed
at one end of the heat pipe and is rejected at the other end, with the fluid inside serving as
transport medium for heat. The boiling and condensation process associated with extremely high
transfer coefficients and thus it is natural to expect the heat pipe to be an extremely effective heat
transfer device, since its operation is based on alternate boiling and condensation of the working
fluid. Indeed heat pipes have effective conductivities several hundred times that of copper or

15
silver .that is replacing copper bar between two mediums at different temperature by a heat pipe
of equal size can increase the rate heat transfer between those two mediums by several hundred
times .A simple heat pipe with water as working fluid has an effective thermal conductivity of the
order of 10000w/m oC compared with about 400 w/moC for copper.

There e is a small pressure difference between the evaporator and the condenser ends, and thus a
small temperature difference between the two ends of the heat pipe .This temperature difference
is usually between 1 oC and 5oC .

2.2.Heat Pipe Merits

 Large quantities of heat can be moved with a small drop in temperature as the heat
is carried away by evaporation and dissipated in the form of latent heat by
condensation.
 Heat pipes are capable of transporting heat over appreciable distances, thus
permitting separation of heat source and heat sink. The price paid for this
separation in terms of temperature loss is also minimal, usually only a few
degrees.
 The outstanding feature of heat pipe is the ability of the heat pipe to accept heat
non- uniformly .for example, the heat input to the heat pipe from the flame (heat
source) is extremely non-uniform. The heat pipe can accept this non uniformity
since the evaporation rate of working fluid will be high in the area of heat density
and low in less intense heat. This heat distribution allows the isothermal
characteristics of the heat pipe to be preserved so that the heat is delivered to the
thermal load with the same uniformity when the heat input to the heat pipe is more
uniform. Thus the heat pipe has effectively flattened the thermal profile of the heat
 The heat pipe is relatively light in weight since the volume consists essentially of a
vapor.
 It requires no power source to accomplish its function.
 The absence of gravity doesn’t affect the operation of the heat pipe detrimentally.
Liquid flow doesn’t depend on gravity.

16
  It is an ideal device for removing heat from a concentrated heat source or from
low temperature heat source .this feature is very much useful for space
applications.
 The heat pipe transmits heat from the heat source to the heat sink essentially
isothermally. Other means of transmitting heat results in temperature drop s that
requires correspondingly larger radiation to dissipate equivalent quantities of heat
at lower temperatures.
 Since the vapor is used for transporting latent heat of vaporization between the
heat source and sink, quite small vapor flow rates can produce large heat
fluxes .the vapor pressure gradient and therefore the temperature gradient, need to
produce these fluxes is very small.
 The weight of heat pipe is considerably smaller compared with any other heat
transfer equipment .it is hardly.

2.3.Limitations of Heat Pipes

Like any other device the heat pipe also has limitations as listed below


Undesired increase in the point to point temperature differential along the heat
pipe can lead to damage to the evaporator section

The heat pipe is normally rated in terms of the thermal power that can be
transferred at the given temperature .if this is exceeded, an increase in the
temperature difference along the heat pipe is exhibited .its further effect occurs
quite abruptly as the pumping capacity of the wick is exceeded which causes
starvation of fluid-flowing the extreme of the evaporator and its temperature
rises rapidly.

The cost of a given heat pipe tend to reach a minimum in the 70 oC to 120 oC
temperature range.

17
 2.4.Applications of heat pipes

Heat pipes are extensively used in many modern computer systems, where increased power
requirements and subsequent increases in heat emission have resulted greater demands on cooling
systems. Heat pipes are typically used to move heat away from components such as CPUs and
GPUs to heat sinks where thermal energy may be dissipated into the environment.

Heat pipes are also being widely used in solar thermal water heating applications in combination
with evacuated tube solar collector arrays. In these applications, distilled water is commonly used
as the heat transfer fluid inside a sealed length of copper tubing that is located within an
evacuated glass tube and orientated towards the Sun.

In solar thermal water heating applications, an evacuated tube collector can deliver up to 40%
more efficiency compared to more traditional "flat plate" solar water heaters. Evacuated tube
collectors eliminate the need for anti-freeze additives to be added as the vacuum helps prevent
heat loss - these types of solar thermal water heaters are frost protected down to more than -35
degrees C and are being used in Antarctica to heat water.

Heat pipes have been used for many applications:

 Remote heat rejection from a concentrated source (e.g. computer chip)

 Obtain uniform temperature
 Efficient heat exchangers

18
 CHAPTER THREE
3. Theoretical analysis

3.1. Flat plate collector

A solar collector is a simple heat exchanger that converts solar radiation in to useful heat. A flat
plate collector consists of a rectangular box, flat bottom with insulation, sheet metal as a
collector, water, glass cover and a hot water storage tank.

The sheet metal is the main solar energy absorbing surface. The surface is often painted black to
improve the energy absorption. The glass cover transmits the solar radiation and at the same time
reduces convection and radiation losses to the surrounding. The energy absorbed on the is
transferred to heat water through conduction and convection. The bottom insulation reduces any
heat loss from the collector

3.2. Heat pipe type flat plate collector

A heat pipe consists of a sealed tube under vacuum (a wick structure or may also be wickless)
and a small amount of working fluid inside. Heat applied at one end of the pipe is transported to
the other end. During this process there will be a change of state and there will, be a release of
latent heat condensation.

In solar collector application the evaporator part of the heat pipe will be on the surface of the
solar absorber and the condenser part exchanges the heat to the circulating water. What makes
wick heat pipe different from wickless heat pipe?

The purpose of a wick

 The necessary flow passage for the return of the condensed liquid
 Surface pores at the liquid vapor interface for the development of the required capillary
pumping pressure, and
 A heat flow path between the inner wall of the container and the container and the liquid vapor
interface

19
 3.3.Necessary parameters

Geographically Mekelle is situated in 14o latitude. Thus the tilt angle of the solar collector is
taken to be 15o to attain maximum solar radiation intensity. The temperature the water fed to the
tanker measured by thermometer is found to be 22 oC and the average ambient temperature from
the metrological data of Mekelle University is 23oC.

Since wind speed is significant in Mekelle, the design takes into account the convective heat loss
due to wind .From the data of the metrology the average wind speed is 3.4m/sec. But for design
purpose the wind speed is taken to be 5m/sec. Mekelle is found in the northern hemisphere .this
makes the facing of the solar collector to be towards south as the apparent movement of the sun is
slightly inclined towards the southern hemisphere.

3.4.Heat Pipes Profile

 Working of the heat pipe fluid ,Tv=60oC=333.15K

 Condenser length is 15o above the evaporator

For a pipe operating temperature of 333.15K water suitable working fluid due to the following
advantages

 Better liquid transport capability

 Higher thermal conductivity
 Low cost availability

Hence water is the working fluid.

Properties of water at Ta=23oC

Density = 996.86 kg/m3

Viscosity =9.392e-4 kg/m-s

Specific heat of vaporization=4179J/kg-k

The heat pipe material is copper has superior conductance at 333.15 K, in addition to its
availability and low cost. The configuration of a heat pipe is round as this is the most efficient
configuration from stress point of view. In addition round tubes and pipes of many materials are
readily available. The wick is Wrapped screen since it is simple and satisfies the performance
specification.

20
Properties of water at the saturation temperature Tv=333.15K

Liquid density, ρ =983.15 kg/m

l 3

Liquid viscosity μ =.467e-3 kg/m-s

l

Surface tension, σ =6.63e-2N/m

Heat of vaporization, λ =2.358e6 J/kg-k

Vapor viscosity, μ v =1.093e-5 kg/m-s

ν

Vapor density ρ v =.13 kg/m3

Vapor specific heat ratio,Υ v =1.33

Liquid thermal conductivity=.654w/m2-k

Specific heat of a liquid =4185J/kg-k

21
3.5.Mathematical modeling for heat pipe with wick structure
Heat pipe with wick specifications and Assumptions

Outer diameter of heat pipe ,Do=12 mm

Inner diameter of heat pipe, Di=10 mm

Vapor core diameter Dv= 8 mm

Screen wick thickness tw =1.5mm

length of condenser ,L c=250mm

length of adiabatic section, La=50mm

total length of heat pipe, Lt = 700mm

the amount of energy transformed from the evaporator, Qe=100w

sheet metal thermal conductivity, k=205w/m²c°

specific heat capacity of water, Cp = 4200J/Kg.c°

22
Analysis

Calculation of Losses

(a)Top loss, Qt

(T Ta )A
4 4

Q (T pm − T )A a σ pm −
top = +

[ ]T
.3 2 N +f −1 1
(T pm− T)a C
+
1
ε
+
ε (1− ε )
−N
g p +. 05 N p
( N −f )
pm h w

Where

TPM-mean plate temperature

A=Le*W=0.21m2

hw- wind heat transfer coefficient

w
2
hw= 5.7+ 3.8Vw =24.7 m − K

f= (1-0.04 hw +0.00005 hw2)(1+0.091N)

= 0.375

C= 365.943(0.00883S-0.0001298S2)

= 37.3

Surface temperature of the collector

When heat loss by convection and conduction equal solar energy absorbed by the plate , the combined
convection and radiation heat loss can be assumed to be 12w/m2.k

I =h(Ts−Ta)

900* 0.09 =12(Ts-296)

23
 Ts =91°c

To determine Tpm using steady state heat conduction from the plate to the fluid the following
formula is used;

Qe
Tpm=Tfm + hfi πDi Le n

Where

Le=evaporator length

n=number of heat pipes

Di=internal diameter of heat pipe

W
2
hfi= 300 w/m2 k m − K

Qe= 100W

Tfm= 333.15K

Substituting all these values;

Tpm= 348.15K

Again substituting all these values;

Qt = 68.6 W

(b) BOTTOM LOSS ,Qb

A ( T PM −T a )
δ 1
+
Qb= K hb

Where

24
δ is thickness of insulation δ=80 mm

K= insulating material thermal conductivity

mW
=18 m 2−k

hb= convective coefficient between bottom of the insulation and the environment

(Recommended value =12.5 to 25)

Qb= 2.35W

(c) Edge loss , Qe

Qe=heA(T pm−Ta)

Where

Tpm = 348.15K

W
2
he= 0.5 m

A = 0.285m2

Substituting these values to the above equation

Qe= 5.24W

Total loss Qtotal=Qt +Qb + Qe

= 68.6w+2.35w+5.24w

=76.29w

Qtotal
UL=
A (∆T )

=6.966

25
 m ( w−D )
tan ⁡( )
2
F=
m ( w−D )
2

=0.918

Ul
m=√ =6.15
K∗α

' 1/Ul
F=
w¿¿

Substituting all the above values

'
F =0.54

Finally the collector heat removal factor will be

MCp ¿ ¿

Substituting all the above value, FR= 0.49

Here the useful energy gain will be

Qu= AcFR[S−UL(Ti−Ta)]

Ac=0.21 Ti=60c° FR=0.49 Ta=23c°

S=
(ατ )ε I
*

= 0.9* 900

o
= 810w/mc

Qu=56.827w

After this point we will find the absorber efficiency

26
 Qu
η=
A c∗I

56.827 w
¿
0.21∗900

= 30.06%

This is the performance of the absorber to convert the solar irradiation into the useful energy

After this we can calculate the outlet water temperature

¿=Tiexp (−Nw)+Th ¿

Where
o o
To = outlet water temperature S = 900 w/mc *0.9 Ta = 23c

Ti = inlet water temperature Ul = 6.966

Nh= factor on condenser section Nw = factor on condenser section

Nh= ( F ´MCp
AcUL
)∧Nw=( AhwUhw
MCp )

Nh= 0.347 (factor on condenser section) Nw = 9.74 (factor on condenser section)

The area Ahwand the condensation heat transfer coefficient Uhw are calculated from the
condenser section.

Th=
[ S
UL
+Ta+Ti [
1−exp (−Nw )
Nh
/ 1+ ]] [
1−exp (−Nw )
Nh ]
Substituting the above values, To = 52°c

3.6.Thermal analysis

27
The useful energy gained by a single heat pipe is the difference between solar energy absorbed
and the heat loss to the ambient over the length of the absorber. The rate of useful energy
collected may be modeled.

Rp=Rw , c + Rw , e+ Rp , c+ Rp , e + Rv+ ℜ ,i+ Rc , i

Where

Rp = is the summation of the total resistance

Rw , c = is the resistance occurred by the wick structure on the condenser section

Rw , e = is the resistance occurred by the wick structure on the evaporator section

Rp , c = is the resistance occurred by the pipe on the condenser section

Rp , e= is the resistance occurred by the pipe on the evaporator section

Rv = is the temperature associated with the temperature drop in the vapor flow

ℜ, i∧Rc , i are the resistance which occur due to the phase change of the working fluid at liquid
–vapor interface

2
twro
Rw , c =
2 LcriKe , e

Where

Ke,e– is the effective thermal conductivity

K 1 [K 1+kW −( 1−€ ) ( Kl−Kw ) ]

Ke,e =
[ ( K 1+ Kw ) + ( 1−€ ) ( Kl−Kw ) ]

= 1.6 w/m.k

Substituting the above values

Rw , c = 9*10−3 m².K/w

Rw , e = R w , c * Lc
¿

0.25
= 0.009 *
0.7

28
 = 3.214*10−3 m².K/w

rotp
Rp , c =
2 LcKp

= 3.166* x 10−5 m².K/w

Rp , e= Rp , c * Lc
¿

0.25
= 0.00003166 *
0.7

=1.36* x 10−5 m².K/w

Rv =is the temperature associated with the temperature drop in the vapor flow

1 1
πro ² Fv [ LC+la+ Lc ]
Rv = 6 6
ρvλJ

Where

(fvRev) μv
Fv =
2 Avr ² h , vρvρ

= 0.0155

Here

Rv=.655*10−9 m².K/w

Properties of water at 100°c

Vapor viscosity μv = 1.28*10−5 Kg/m.sec

Drag coefficient fv Rev =16

Vapor density ρv= 0.58Kg/m³

Latent heat of vaporization hfg= 2.254J/Kg

Vapor hydraulics radius rh,v= 0.01005m

29
 2
ℜ, i =
h eΠdiLe

k1
Where he =
tw

1.56
he = = 1560
0.001

Substituting the above values

Ri,e = 0.0544 m².K/w

1
Ri,c =
h cΠdiLc

Where hc = 0.728 gρl ¿ ¿

hc = 1421.016

Substituting the above values

Rc , i = 0.0898 m².K/w

Now

1
UHP =
Rw , c + Rw , e+ Rp , c + R p ,e + Rv+ Rc ,i+ ℜ, i

UHP = 38085 m².K/w

Here the temperature drop across the evaporator & condenser section will be given as

Qu
Tp , e−Tp , c =
ApUHP

ΠDo ²
Where Ap=Π Tp,e= 75.15°c Qu = 62.9w
4

Ap= 1.13.10−4 UHP = 38085

Substituting the above values

62.29 w
75.15-Tp,e = −4
1.13 .10 ∧38085

Tp,c = 63°c

30
Now the temperature drop across the evaporator-condenser section will be

ΔT = Tp,e-Tpc

= 75.15 – 63

= 12.15°c

After this the overall efficiency of the solar collector can be calculated as

Qout
η=
Qin

Where

Qout= mc∆ T

= ρVC∆ T

= 996.2kg/m³ * 0.0058m³ *(52-22)°c ¿4200J/Kg.c°

722198.7 w
Qout =
8∗3600 sec

= 25.4w

Qout 25.4
Now η = = =45%
Qin 56.827

Table, 1Final mathematical parameters for heat pipe with wick structure

Inlet water temperature 22°c

outlet water temperature 52°c

surface temperature 91°c

evaporator temperature 75.15°c

condenser temperature 63°c

Temperature drop across evaporator-condenser 12.5°c

Absorber efficiency
30.06%
Overall solar collector efficiency 45%

31
Table, 2 The useful energy, outlet water temperature and efficiency for different irradiation
values

Irradiation Qu, useful energy outlet energy(w) Outlet water Efficiency

(w/m²) (w) Temperature(°c) (%)

900 56.82735 25.4 52 45

800 52.33 22.66 48.9 43.3

700 49.57 19.88 45.6 40.1

600 46.27 17.12 42.3 37

500 42.91 14.16 38.8 33

400 38.5 11.55 35.7 30

300 33.76 8.779 32.4 26

Theoretical Results of Heat Pipe With Wick

outlet water temprature(°c)
1000 60
solar irradiation(w/m²)

900
50
800
700
40 Irradiation (w/m²)
600
Outlet water
500 30 Temperature(°c)
400
20
300
200
10
100
0 0
1 2 3 4 5 6 7

Figure, Theoretical result of heat pipe with wick, solar irradiation vs. outlet water temperature

32
 Theoretical Resulet of Heat Pipe With Wick
1000 50
900 45
solar irradiation(w/m²)

800 40

Efficiency(%)
700 35
600 30 Efficiency (%)
Irradiation (w/m²)
500 25
400 20
300 15
200 10
100 5
0 0
1 2 3 4 5 6 7

Figure, Theoretical result of heat pipe with wick, solar irradiation vs. efficiency

The numerical results of heat pipe with wick which shows the decrement of outlet water
temperature and efficiency as solar irradiation decreases from 900w/m 2 to 300w/m2. This due
decrement of useful (outlet) in the condenser.

3.7.Mathematical modeling for wick less heat pipe tube

Heat pipe without wick structure specifications and assumptions

Outer diameter of heat pipe ,Do=12 mm

Inner diameter of heat pipe, Di=10 mm

length of condenser ,L c=400mm

length of adiabatic section, La=50mm

total length of heat pipe, Lt = 1150mm

the amount of energy transformed from the evaporator, Qe=100w

sheet metal thermal conductivity, k=205w/m²c°

specific heat capacity of water, Cp=4200J/Kg.c°

33
Analysis

Calculation of Losses

(a) Top loss, Qt

(T T )A (T Ta )A
4 4

pm − σ pm −
Q top =
a
+

[ ]T
.3 2 N +f −1 1
(T pm− T )
a C
+
1
ε
+
ε (1− ε )
−N
g p +. 05 N p
( N −f )
pm h w

Where

34
TPM-mean plate temperature

A=Le*W=0.287m2

hw- wind heat transfer coefficient

w
2
hw= 5.7+ 3.8Vw =24.7 m − K

f= (1-0.04 hw +0.00005 hw2)(1+0.091N)

= 0.375

C= 365.943(0.00883S-0.0001298S2)

= 37.3 Surface temperature of the collector

when heat loss by convection and conduction equal solar energy absorbed by the plate , the combined
convection and radiation heat loss can be assumed to be 12w/m2.k

I =h(Ts−Ta)

900* 0.09 =12(Ts-296)

Ts =91°c

To determine Tpm using steady state heat conduction from the plate to the fluid the following
formula is used;

Qe
Tpm=Tfm + hfi πDi Le n

Where

Le=evaporator length

n=number of heat pipes

Di=internal diameter of heat pipe

W
2
hfi= 300 w/m2 k m − K

35
 Qe= 100W

Tfm= 333.15 K

Substituting all these values;

Tpm= 348.15K

Again substituting all these values;

Qt =72.4W

(b) Bottom Loss, Qb

A ( T PM −T a )
δ 1
+
Qb= K hb

Where

δ is thickness of insulation δ=80 mm

K= insulating material thermal conductivity

mW
=18 2−k
m

hb= convective coefficient between bottom of the insulation and the environment

(Recommended value =12.5 to 25)

Qb= 2.439W

(c) Edge Loss, Qe

Qe=heA (Tpm-Ta)

Where

Tpm = 348.15K

36
 W
2
he= 0.5 m

A = 0.285m2

Substituting these values to the above equation

Qe= 5.47W

Total loss Qtotal = Qt+Qb +Qe

=80.30W

Fin Efficiency, Fe

Fin efficiency of the collector is given by the following relation;

Me ( W −Do)
tan( )
2
Me ( W −Do )
Fe= 2

( )
0.5
Ul
K fe δ e
Where Me=

Qtotal , loss
Ul = A ( ΔT )

Substituting these values

W
2
Ul=7.33 m −k

Me=6.68

Fe=0.917

Now to find the collector efficiency

37
 ' 1/Ul
F=
w¿¿

Substituting all the above value

F'=0.521

Finally the collector heat removal factor will be

MCp ¿ ¿

Substituting all the above value, FR= 0.47

Here the useful energy gain will be

Qu= AcFR[S−UL (Ti−Ta)]

Where

Ac=0.287m² Ti=60c° Ul=7.33

FR=0.47 Ta=23c°

S=
(ατ )ε I
*

= 0.9* 900

o
=810w/mc

Qu=52.9w

After this point, we will find the absorber efficiency

Qu
η=
Ac∗I

72.67
=
0.285∗900

38
= 28.13%

This is the performance of the absorber to convert the solar irradiation into the useful energy

After this we can calculate the outlet water temperature

¿=T i exp(−Nw )+ Th¿

Where
o o
To = outlet water temperature S = 900 w/mc *0.9 Ta = 23c

Ti = inlet water temperature Ul = 7.33

Nh= factor on condenser section Nw = factor on condenser section

Nh= ( F ´MCp
AcUL
)∧Nw=( AhwUhw
MCp )

Nh = 0.347 (factor on condenser section) Nw = 9.74 (factor on condenser section)

The area Ahwand the condensation heat transfer coefficient Uhw are calculated from the
condenser section.

¿=
[ S
UL
+ Ta+Ti[1−exp (−Nw )
Nh
/ 1+]] [
1−exp (−Nw )
Nh ]
Substituting the above values, To = 50.7c°

3.7.1Thermal analysis
The useful energy gained by a single heat pipe is the difference between solar energy absorbed
and the heat loss to the ambient over the length of the absorber. The rate of useful energy
collected may be modeled.

Rp=Rp , c + Rp ,e + Rv+ ℜ ,i+ Rc , i

39
Where

Rp = is the summation of the total resistance

Rp , c = is the resistance occurred by the pipe on the condenser section

Rp , e = is the resistance occurred by the pipe on the evaporator section

Rv = is the temperature associated with the temperature drop in the vapor flow

ℜ, iAnd Rc , i = are the resistance which occur due to the phase change of the working fluid at
liquid –vapor interface

rotp
Rp , c =
2 LcKp

= 3.166* x 10−5 m².K/w

Rp , e = Rp , c * Lc
¿

0.25
= 3.166* x 10−5 m².K/w *
0.7

=1.36* x 10−5 m².K/w

= is the temperature associated with the temperature drop in the vapor flow

1 1
πro ² Fv [ LC+la+ Lc ]
Rv = 6 6
ρvλJ

Where

(fvRev) μv
Fv =
2 Avr ² h , vρvρ

= 0.0155

Here

40
Rv =4.655*10−9 m².K/w

Properties of water at 100°c

Vapor viscosity μv = 1.28*10−5 Kg/m.sec

Drag coefficient fv Rev =16

Vapor density ρv = 0.58Kg/m³

Latent heat of vaporization hfg= 2.254J/Kg

Vapor hydraulics radius rh,v= 0.01005m

2
ℜ, i =
h eΠdiLe

k1
Where he =
tw

1.56
he = = 1560
0.001

Substituting the above values

Ri,e = 0.0544 m².K/w

1
Ri,c =
h cΠdiLc

gρl (ρ 1−ρv ( K 3 h fg ) )
Where hc = 0.728¿
diNΔT

hc= 1421.016

Substituting the above values

Ri,c = 0.0898 m².K/w

Now

1
UHP =
Rp , c + Rp , e+ Rv + Rc , i+ ℜ ,i

UHP = 38012 m².K/w

41
Here the temperature drop across the evaporator & condenser section will be given as

Qu
Tp , e−Tp , c =
ApUHP

ΠDo ²
Where Ap=Π Tp,e = 75.15°c Qu=52.9w
4

Ap = 1.13.10−4 UHP = 38012

Substituting the above values

52.9 w
75.15-Tp,c = −4
1.13 .10 ∧38085

Tp,c= 61.42°c

Now the temperature drop across the evaporator-condenser section will be

ΔT = Tp,e-Tpc

= 75.15 – 61.42

= 13.73°c

Now the overall efficiency of the solar collector will be given as

Qout
η=
Qin

Where Qout = mc∆ T

= ρVC∆ T

= 996.2kg/m³ * 0.015m*4200J/kg. °c *(50.7-22) °c

= 1801229w

1801229 w
Qout=
8∗3600 sec

= 30.2w

Now

Qout 30.3 w
η= = = 42%
Qin 72.9 w

Table, 3 Final mathematical parameters for heat pipe without wick

42
Inlet water temperature 22°c

outlet water temperature 51°c

surface temperature 91°c

evaporator temperature 75.15°c

condenser temperature 61.42°c

Temperature drop across evaporator-condenser 13.73°c

Absorber efficiency
28.13%
Overall collector efficiency 42.%

Table, 4 The useful energy, outlet water temperature and efficiency for different irradiation
values

Irradiation (w/m²) Qu, useful energy outlet Out let water temperature Efficiency (%)
(w) energy(w (°c)
)

900 72.67 30.2 51 42

800 69.09 27.5 47.6 39.8

700 66.44 24.19 44.6 36.27

600 63.84 21.8 41.3 32.89

500 61.56 19.16 38.2 31.12

400 55.40 15.38 35 27.76

43
 Theoretical Results of Wickless Heat Pipe

outlet water temprature (°c)

1000 60
900
solar irradiation(w/m²)

50
800
700
40
600 Outlet water temperature (°c)
500 30 Irradiation (w/m²)
400
20
300
200
10
100
0 0
1 2 3 4 5 6

Figure, theoretical result of wickless heat pipe , solar irradiation vs. outlet water temperature

Theoretical Results of Wickless Heat Pipe

1000 45

outlet water temprature(°c)

solar irradiation(w/m²)

900 40
800 35
700
30
600 Efficiency (%)
25
500 Irradiation (w/m²)
20
400
15
300
200 10

100 5
0 0
1 2 3 4 5 6

Figure, theoretical result of wickless heat pipe, solar irradiation vs. outlet water temperature

As it is seen from the table and graph, the heat pipe type arrangement has better performance. In
addition, the efficiency of both arrangements decreases as solar irradiation intensity decreases.
The numerical results of heat pipe without wick, which shows the decrement of outlet water
temperature, and efficiency as solar irradiation decreases from 900w/m 2 to 300w/m2. This due
decrement of useful (outlet) in the condenser.

44
 CHAPTER FOUR

4. Experimental set up and procedure

4.1. Description of prototype

A prototype solar collector was manufactured to conduct experiments of both wickless heat pipe
and heat pipe wick type arrangements. A picture of the first prototype is shown in figure; the
overall dimensions of the collector box are 1000mm long, 300mm wide and 70mm depth. The
absorber effective area is 0.21 m2 (i.e. 250 wide and 700 mm long). The collector surface was
inclined at 150 facing south. The hot water tank has a capacity of 5.8 liters and the tank was fully
insulated.

Glass
Storag
e

Thermo Collector
couple box

Fram

Figure 4. Picture showing the heat pipe with wick prototype with description of parts

A picture of the second prototype is shown in figure; the overall dimensions of the collector box
are 1600mm long, 250mm wide and 50mm depth. The absorber effective is 0.285 m 2 (i.e. 220
wide and 950 mm long). The collector surface was inclined at 15 0 facing south. The hot water
tank has a capacity of 12 liters and the tank was fully insulated.

45
 Pyranometer
Glass

Storage

Collect
Fram or box

Figure 5. Picture showing the heat pipe without wick prototype with description of parts

4.2. Measurement of Solar Irradiation and Temperature

During the solar irradiation was measured using a pyranometer. The pyranometer was placed on
the plane of the collector glass and hence measures the tilted plane solar irradiation at 14 0 . The
solar irradiation measurement was taken at 10 min interval. Temperature was measured using
thermocouple for the ambient and water in storage tank. Temperature measurement was taken at
intervals of time coinciding with the solar irradiation measurement.

4.3.Performance of both arrangements

The prototype is arranged by putting a heat pipe on the absorber, properly fixing the glass and the
box. The condenser section of the heat pipe is inserted into the hot water tank. As the sun heats
the evaporator section of the heat pipe, the water inside vaporizes and moves up to condenser. As
it condenses inside the tank it heats up the water. Starting from morning until sunset
measurements of solar irradiation and temperature are taken at intervals of 10 minutes. The
experimental results for the heat pipe having wick is shown in the following graph The
experiments were conducted as per the procedure discussed earlier for both the wick and wickless
heat pipes.

46
 CHAPTER FIVE
5. Result and Discussion

5.1. Experimental result of heat pipe with wick and without wick collectors
The experiments were conducted in the month of May on the different days. The solar irradiation
on the plane of the collector and temperature at the tank were measured. Plots of the experimental
data are shown in the figures below.

Experimental results of heat pipe with wick

1200 60

1000 50

outlet water temprature(°c)

800 40
solar Irrdiation(w/m²)

600 30
outlet tmprature of
water
400 20
Irradiation

200 10

0 0
00 30 00 30 00 30 00 30 00 30 00 30 00 30 00 30 00
3: 3: 4: 4: 5: 5: 6: 6: 7: 7: 8: 8: 9: 9: 10: 10: 11:

Time

Figure 6.experimental data for heat pipe with wick on day one 18-09-2004

Figure 6 shows the data recorded for the heat pipe having wick. The solar irradiation increased
from about 554 w/m2 in the morning up to about 992 w/m2 at noon, is then gradually decreased
below 400 w/m2. The temperature of water in the storage tank steadily increased from 16.2°c in
the morning up to 56°c in the afternoon, it is then slowly decreased down to 47°c.

47
 Experimental Result for Heat pipe
80 1200
70

Tilted plane solar radiation(w/m²)

1000
outlet water temprature (ºc)

60
800 Evaporator section 1 (100mm from
50
the collector edge)
40 600 Evaporatior secion 2 (480 mm from
the collector edge)
30
400 condenseer secion
20 Irradiation
200
10
0 0
00 00 00 00 00 00 00 00 00
3: 4: 5: 6: 7: 8: 9: 10: 11:

Time

Figure 7. Shows different sections temperature for heat pipe with wick on 18-09-2004

Experimental results of heat pipe with wick

900 60
800 outlet temprature of water(ºc)
Tilted plane solar radiation(w/m²)

50
700
600 40
500
30
400 Outlet temprature of
water(ºc)
300 20
200 Irradiation(w/m2)
10
100
0 0
00 30 00 30 00 30 00 30 00 30 00 30 00 30 00 30 00
3: 3: 4: 4: 5: 5: 6: 6: 7: 7: 8: 8: 9: 9: 10: 10: 11:
Time

Figure 8.experimental data on heat pipe with wick on day 19-09-2004

48
Figure 8. Shows the data recorded for the heat pipe having wick second day. The solar irradiation
increased From about 424 w/m2 in the morning up to about 819 w/m2 at noon, then gradually
decreased below400 w/m2.But in this day, it was fluctuating due to cloud. The temperature of
water in the storage tank steadily increased From 18.2°c in the morning up to 49.5°c in the
afternoon, it is then slowly decreased down to 45.8°c.

5.2.Results and Discussion on Both Arrangements in the Same Day

The experiments were conducted as per the procedure discussed earlier for both the wick and
wickless heat pipes. The experiments were conducted in the month of May on the different days.

The solar irradiation on the plane of the collector and temperature at the tank were measured.
Plots of the experimental data are shown in the figures below.

Experimental result of wickless heat pipe

Tilted plane solar irradiatioon()w/m²

1000 60
outlet water temprature (ºc)
900
800 50
700 40
600
500 30
400 Irradiation(w/m²)
300 20 outlet water temprature(ºc)
200 10
100
0 0
00 00 00 00 00 00 00 0 0
3: 4: 5: 6: 7: 8: 9: :0 :0
10 11
Time

Figure 9.experimental data for heat pipe without wick on 30-09-2004

Figure 9shows the data recorded for the heat pipe without wick. The solar irradiation increased
from about 487.3 w/m2 in the morning up to about 875 w/m2 at noon, is then gradually decreased
below 48 w/m2. The temperature of water in the storage tank steadily increased from 16.2°c in the
morning up to 49.5°c in the afternoon, it is then slowly decreased down to 40°c.

49
 Experimental results on heat pipe with wick
Tilted plane solar irradiation(w/m²)

1000 50
900 45

outlet water temprature (ºc)

800 40
700 35
600 30
500 25 Irradiation(w/m²)
400 20 outlet water temprature (ºc)
300 15
200 10
100 5
0 0
00 00 00 00 00 00 00 0 0
3: 4: 5: 6: 7: 8: 9: :0 :0
10 11
Time

Figure 10.experimental data for heat pipe with wick on 30-09-2004

Figure 10 shows the data recorded for the heat pipe with wick. The solar irradiation increased
from about 487.3 w/m2 in the morning up to about 875 w/m2 at noon, is then gradually decreased
below 48 w/m2. The temperature of water in the storage tank steadily increased from 16.2°c in the
morning up to 48°c in the afternoon, it is then slowly decreased down to 42°c.

comparing the above figures it can be observed that the solar irradiation during the same day was
the same for both arrangements. however , the maximum temperature reached higher for heat
pipe with wick than wickless heat pipe. Hence the heat pipe type arrangement has better
performance.

50
 Experimental results on wickless heat pipe
Temprature at each secion of heat pipe(°c)
100
90
80
70
60 Evaporator section 1 (120mm from
50 the collector edge)
40 Evaporatior secion 2 (840 mm from
the collector edge)
30 condenseer secion
20
10
0
00 30 00 30 00 30 00 30 00 30 00 30 00 30 00 30 00
3: 3: 4: 4: 5: 5: 6: 6: 7: 7: 8: 8: 9: 9: 10: 10: 11:

Time

Figure 11.experimental data for heat pipe without wick on 30-09-2004

Figure 11 shows the data recorded for the heat pipe without wick at the three section of the
collector. The solar irradiation increased from about 487.3 w/m2 in the morning up to about 875
w/m2 at noon, then gradually decreased below 48 w/m2. The temperature of the evaporator first
section is 63°c in the morning then it reaches maximum temperature of 93°c at 6:00 then in the
afternoon it slowly decrease down to 34.3°c. The temperature of the evaporator second section is
68°c in the morning then it reaches maximum temperature of 87°c at 6:00 then in the afternoon it
slowly decrease down to 33.8°c. The temperature of the condenser section is 42°c in the morning
then it reaches maximum temperature of °c 82.6 at 6:00 PM, then in the afternoon it slowly
decrease down to 35.1°c.

Experimetal results of heat pipe at 3 section

90
80
70
60
Evaporator section 1 (100mm from
Temperature(°c)

50 the collector edge)

40 Evaporatior secion 2 (480 mm from
the collector edge)
30
condenseer secion
20
10
0
00 30 00 30 00 30 00 30 00 30 00 30 :00 :30 :00 :30 :00
3: 3: 4: 4: 5: 5: 6: 6: 7: 7: 8: 8: 951 9 10 10 11

Time
Figure 12.experimental data for heat pipe with wick on 30-09-2004

Figure 12 shows the data recorded for the heat pipe with wick at the three section of the collector.
The solar irradiation increased from about 487.3 w/m2 in the morning up to about 875 w/m2 at
noon, then gradually decreased below 48 w/m2. The temperature of the evaporator first section is
62°c in the morning then it reaches maximum temperature of 79°c at 4:30 then in the afternoon it
slowly decrease down to 36.1°c. The temperature of the evaporator second section is 50.9°c in
the morning then it reaches maximum temperature of 65.5°c at 8:30 then in the afternoon it
slowly decrease down to 35.1°c. The temperature of the condenser section is 49.5°c in the
morning then it reaches maximum temperature of 54.9°c .at 5:30 PM, then in the afternoon it
slowly decrease down to 41.9°c.

comparision of efficiencies
45
40
35
30
Efficiency(%)

25
20 wick
wickless
15
10
5
0
00 30 00 30 00 30 00 30 00 30 00 30 00 30 00 30 00
3: 3: 4: 4: 5: 5: 6: 6: 7: 7: 8: 8: 9: 9: 10: 10: 11:

Time

Figure 13.Comparison of the efficiency for heat pipe with wick and heat pipe without wick
structure

The above figure13,shows the comparison of the efficiency for the two types of arrangements.
The efficiency was calculated from the total gain [ ρVCp ( ¿−Ti ) ] divided by the solar energy input
during the time interval ( AcIt ∆ t ). This figure also shows the heat pipe arrangement with wick
structure has better efficiency compared to the heat pipe arrangement without wick structure.

52
Though the calculation numerically suggests the efficiency 45% in the case of the case of heat
pipe , the experiment do not suggest it. It possible to obtain the calculated figure by adjusting or
improving the components so as to reduce the heat loss.

5.3.Comparison of Numerical and Experimental Results

The result of numerical analysis was discussed in the early section of this project, shows the
numerical results and experimentally obtained efficiencies for both arrangements. In the analysis,
experimentally obtained efficiencies are lower than numerical result. The reasons for the
difference are expected to be due to assumptions in the theoretical equations and error in
experimental measurement. The major factors are:

The error in assuming bond between the copper tube and aluminum absorber to be perfect. Since
there was, no means of measuring the bond conductance this assumption was introduced in the
collector heat loss coefficient. In practice, the bond is not perfect.

Errors were also introduced in the measurement of the hot water temperature. The temperature
was measured by inserting a thermocouple in to the storage tank. Due to stratification of the hot
water it is expected that some error is introduced. Measuring temperature this way also caused
heat loss as the hot water tank was opened to insert a thermocouple.

There was also some problems in insulation for heat pipe with wickless structure , that is it has no
insulation because it is plastic, where storage of heat pipe with wick is steel.

53
 CHAPTER SIX
6.1. Conclusion

This project computed solar energy resource data and this data could be used for further modeling
and analysis of solar energy technology. The data indicates that there is sufficient solar intensity
between the hours 3:00 up to 11:00 PM suitable for water heating.

The energy balance of a flat plate collector is modeled based on theoretical analysis from
literature. The energy balance between heat pipe arrangement with wick and without wick
structure is different. Their difference is that heat pipe with wick structure develop Surface pores
at the liquid vapor interface for the development of the required capillary pumping pressure and
there is a thermal loss because of the presence of this wick structure.

Numerical result based on dimension and parameters of the two prototype collector were carried
out. Result of the numerical calculation indicates that the efficiency of the heat pipe arrangement
with wick structure is higher by an average of about 2.2% and by a maximum of 4.8% compared
to the heat pipe arrangement without wick structure. Experiment conducted on the prototype also
shows that the efficiency of the heat pipe arrangement with wick structure was higher that than of
the heat pipe arrangement without wick structure.

Comparing the experimental data with the numerical analysis, the experimentally obtained
efficiency in both arrangements were lower than the numerical result. The reasons for the
difference are the uncertainties of the temperature measuring instruments during measuring the
temperature of the hot water and the heat loss because of poor insulation.

54
 6.2. Recommendation

The study made under this project has indicated promising result in both type of arrangement. Its
recommended that future study should focus on the manufacture of heat pipe in addition to
improvement in efficiency heat pipe collectors will have advantage in reducing corrosion of
copper tube and improvement in maintaining the temperature of the hot water during night.
Future studies should simplify the manufacture of heat pipes and the study of different working
fluids.

The application of solar collectors for domestic consumption mainly depends on cost. The
technology can be introduced by working with small workshop owners. Future work is suggested
in this regard. Here the tasks may include preparing workshop drawings, conducting training and
promoting the solar collector to the public.

Since heat pipe is a new technology as compared to other types in the area of water heating using
solar energy, there are a few studies conducted up to now , so further investigations should be
under taken on the heat pipe and on the collector in general to achieve better efficiency.

55
6.3. References

1. Dunn, P.D and Reay, D.A. 1994. Heat pipes. 4th Edition, Pergamon, Great Britain
2. Faghiri, Amir. 1998. Heat pipe Technology. Taylor and Francis, USA
3. S.W.chi, 1995. Heat pipe theory and practice,2nd Edition McGraw-Hill book company,
Great Britain
4. Dr. Mulu Bayray. 2008. Research Review(on solar water heating employing heat pipe),
volume 3
5. E.AZAD,F. BAHAR and F.MOZTARADEH, 1987, Solar Water Heater Using Gravity –
Assisted Heat pipe, vol.7, Pergamon Journals Ltd.

56