thermal properties of selected materials for thermal insulation
TRANSCRIPT
THERMAL PROPERTIES OFSELECTED MATERIALS FOR
THERMAL INSULATION AVAILABLEIN UGANDA
BY
AYUGI GERTRUDE (B Sc. Ed, Mak)
Department of Physics
Makerere University
REG.NO:2009/HD13/15595U
A DISSERTATION SUBMITTED TO THE DIRECTORATE OF
RESEARCH AND GRADUATE TRAINING IN PARTIAL
FULFILLMENT FOR THE AWARD OF A DEGREE OF
MASTER OF SCIENCE (PHYSICS) OF MAKERERE
UNIVERSITY
DECEMBER 2011
Declaration
I certify that this dissertation which I now submit for examination for the award of Masters
of Science in Physics, is entirely my own work and has not been taken from the work of others
and to the extent that where such work has been cited, it has been acknowledged within the
text of my work.
Signature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ayugi Gertrude
2009/HD13/15595U
Supervisors
Signature:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prof. E. J. K. B. Banda
Department of Physics
Makerere University,
P.O Box 7062,
Kampala.
Signature:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dr. Florence Mutonyi D'ujanga
Department of Physics
Makerere University,
P.O Box 7062,
Kampala.
i
Dedication
This work is dedicated to my parents Mr. and Mrs Ogwal for their in-put in my education,
my late sister Diana Angwech, may her soul rest in eternal peace and my nephew Favor
Lubanga.
ii
Acknowledgments
I would like to express my deep appreciation and gratitude to the following people for helping
me complete this dissertation.
My �rst supervisor Prof. Eldad J.K.B. Banda at the Department of Physics Makerere Uni-
versity for his endless help, guidance and support throughout out the course of study.
My second supervisor Dr. Florence Mutonyi D'ujanga, the Head of Department of Physics
for her invaluable support and advice throughout the duration of this research.
All the Lecturers and Professors in the Department of Physics who taught me the �rst year
courses.
Mr. Benon Fred Twinamasiko, Assistant lecturer in the Department of Physics who allowed
me to access the keys to the project Laboratory anytime.
Mr. Dennis Okello , Assistant lecturer and a PhD. student at the Department of Physics
who helped me in various ways.
Mr. Micheal Okiror, the technician in charge of the project laboratory where the experiments
were carried out, Mr. Micheal Musoke , a technician in charge of the second year laboratory
and Mr. Ronald Nteziyaremye the technician in charge of the of the departmental workshop
for all their help during the time I was carrying out the experiments.
My brothers Robert Odong , Julius Elai, William Okello, Steven Ongwen and Geofrey Okulla
and sisters Teopista Akullo and Hellen Amongi for their support during the course of my
study as a postgraduate student.
I would also like to thank the sponsors of Millennium Science Initiative Project for having
iii
iv
provided some of the apparatus that was used during the experimental study.
Lastly, but most importantly, I extend my sincere appreciations to my sponsors NUFU project
`Small Scale Concentrating Solar Energy Systems ' for all the �nancial support without
which this work would have never become possible.
Contents
Declaration i
Dedication ii
Acknowledgments iii
Table of contents v
List of Figures viii
List of Tables x
Abstract xi
1 INTRODUCTION 1
1.1 Background of study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Statement of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Specif�ic objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.6 Signif�icance of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.7 Justif�ication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
v
CONTENTS vi
2 LITERATURE REVIEW 5
2.1 Thermal insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Benef�its of thermal insulation . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Types and Application . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Major thermal insulation materials used in thermal heat storage . . . . . . . 9
2.2.1 Calcium silicate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Mineral f�iber (rock and slag wool) . . . . . . . . . . . . . . . . . . . 9
2.2.3 F�ibre glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.4 Expanded silica, or perlite . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.5 Refractories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.6 Foamed plastic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.7 Insulating cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.8 Cotton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Thermal insulators available in Uganda . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 Clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Ash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3 Bagasse (Sugarcane f�ibres) . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.4 Banana f�ibres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.5 Sawdust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.6 Charcoal dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Important thermal properties of an insulating material . . . . . . . . . . . . 20
2.4.1 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 Specif�ic heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.3 Thermal dif�fusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.4 Other pertinent physical properties . . . . . . . . . . . . . . . . . . . 27
2.5 Measurement of thermal conductivity of insulators . . . . . . . . . . . . . . . 28
2.5.1 Steady state methods for measurement of thermal conductivity . . . . 28
CONTENTS vii
2.5.2 Transient state methods for measurement of thermal conductivity . . 31
2.6 Measurement of specif�ic heat capacity . . . . . . . . . . . . . . . . . . . . . 34
3 METHODS AND MATERIALS 39
3.1 Sample collection and preparation . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Measurement of thermal conductivity . . . . . . . . . . . . . . . . . . . . . 43
3.3 Measurement of thermal dif�fusivity . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Determination of specif�ic heat capacity . . . . . . . . . . . . . . . . . . . . . 48
4 RESULTS AND DISCUSSION 49
4.1 Thermal conductivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.1 Ef�fect of particle/f�ibre size on thermal conductivity . . . . . . . . . . 49
4.1.2 Ef�fect of compaction pressure on thermal conductivity . . . . . . . . 55
4.2 Thermal di�f�fusivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 Specif�ic heat capacity determination . . . . . . . . . . . . . . . . . . . . . . 69
5 CONCLUSIONS AND RECOMMENDATIONS 74
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 Recommendation for future work . . . . . . . . . . . . . . . . . . . . . . . . 75
Bibliography 76
Appendix I: Temperature response of the samples to a heat 84
List of Figures
2.1 Increase in thermal conductivity of polyurethane insulation material in the
f�irst 15 years of manufacture [26]. . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 The thermal conductivity of a mineral f�iber insulation versus packing density
[53]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Variation of Thermal conductivity with porosity of refractory bricks[54]. . . . 23
2.4 Variation of thermal conductivity with temperature for selected insulation
materials [55]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 Distribution and geometry of embedded material in continous phase. . . . . 25
2.6 Schematic diagram of the guarded hot plate apparatus . . . . . . . . . . . . 29
2.7 Lees' disk apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.8 Schematic representation of the dual-needle heat-pulse (DNHP) sensor . . . 36
2.9 Temperature response measured for a sample. . . . . . . . . . . . . . . . . . 37
2.10 A plot of the linearisation ln (δT ) against 1t. . . . . . . . . . . . . . . . . . . 38
3.1 Nested sieves on a mechanical vibrator . . . . . . . . . . . . . . . . . . . . . 41
3.2 Arrangement of a metal plate and a hollow rigid metal frame. . . . . . . . . 42
3.3 Hydraulic manual press type PW40 with die between its upper and lower plates. 43
3.4 Experimental set up for thermal conductivity measurement . . . . . . . . . . 44
3.5 Typical curves displayed on QTM-500 for small and large thermal conductivities 45
3.6 Display of the QTM-500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
viii
LIST OF FIGURES ix
3.7 Experimental set up for measurement of temperature response of a sample to
a heat pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1 Thermal conductivity against f�ibre size at various compaction pressures . . . 51
4.2 Thermal conductivity against particle size at various compaction pressures . 54
4.3 Variation of thermal conductivity with compaction pressure for di�f�ferent f�ibre
sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Variation of thermal conductivity with compaction pressure for di�f�ferent par-
ticle sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.5 Temperature response of the �brous samples to a heat pulse . . . . . . . . . 62
4.6 Temperature response of the particulate sample to a heat pulse . . . . . . . 66
4.7 Graphs of ln(δT ) versus 1/t for �brous samples . . . . . . . . . . . . . . . . . 68
4.8 Graphs of ln(δT ) versus 1/t for particulate samples . . . . . . . . . . . . . . . 72
List of Tables
2.1 Energy lost using mineral wool insulation [12] . . . . . . . . . . . . . . . . . 5
2.2 Thermal conductivity of insulating refractories [23]. . . . . . . . . . . . . . . 12
2.3 Thermal conductivity of gases used as blowing agents in foam plastic insula-
tion[24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Types of foamed plastics [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Average Bagasse Composition [41]. . . . . . . . . . . . . . . . . . . . . . . . 18
4.1 Thermal conductivity of the samples at di�f�ferent compaction pressures and
particle/f�ibre sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 RMSE values for the di�erent �ts for thermal conductivity variation with
particle/�bre size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Values of ε and β for dif�ferent particle/f�ibre sizes . . . . . . . . . . . . . . . 55
4.4 RMSE values for the di�erent �ts of thermal conductivity variation with com-
paction pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Values of ξ and γ for the di�f�ferent samples and particle/ f�ibre sizes . . . . . . 61
4.6 Constants ai, bi, ci for the di�erent samples . . . . . . . . . . . . . . . . . . . 67
4.7 Thermal dif�fussivities of the samples . . . . . . . . . . . . . . . . . . . . . . 69
4.8 Specif�ic heat capacity of the samples . . . . . . . . . . . . . . . . . . . . . . 69
x
Abstract
The use of thermal insulators is one of the most important aspect in thermal energy storage
systems. This dissertation presents investigations of thermal properties of selected materials
available in Uganda which can be used for thermal insulation. Thermal properties of seven
di�erent materials were measured. The materials studied were: sugar cane �bres, ash, banana
�bres, sawdust, clay, kaolin, and charcoal dust.The thermal properties investigated were,
thermal conductivity, thermal di�f�fusivity and speci��c heat capacity.
The Quick thermal conductivity meter which uses the hot wire method was used in the
measurement of thermal conductivity at room temperature (approximately 25oC). Thermal
di�f�fusivity was determined using the transient heat pulse technique and the speci�f�ic heat
capacity was calculated using the thermal conductivity, thermal dif�fusivity and density of
the samples.
The samples were prepared by sieving the dry materials to obtain smaller particles/ �bre sizes
in the ranges of 90-125, 125-150, 150-180, and 180-355µm. The powders were compacted at
pressures of 18.2, 36.4, 54.6, and 72.9MPa and dried in the oven at 100oC for 48h.
Graphical analysis using MATlab showed that the thermal conductivity:
(i) Increased with compaction pressure,P, for the di�erent particle sizes according to the
power law,κ = ξP γ. The values for γ were approximately 0.13 for ash, 0.08 for sawdust,
0.18 for clay and 0.08 for kaolin.
xi
ABSTRACT xii
(ii) Decreased with increasing particle size ,S, according to the equation κ = εSβ . The
values for β were approximately 0.04 for sugarcane �bres,0.26 for ash, 0.06 for sawdust,
0.20 for clay, 0.15 for kaolin and 0.25 for charcoal dust.
However, there was no clear variation of thermal conductivity with compaction pressure and
�bre diameter or length for the sugar cane and banana �bres.An attempt to �t the results
to a power law yielded values for γ of approximately 0.05 for sugarcane �bres and 0.04 for
banana �bres.
Particle/�bre sizes of ≤ 180µm were used in the determination of thermal di�usivity of
the samples. Using MATLab the graphs of temperature response to a heat pulse were �t-
ted using a Gaussian distribution and linerlisation of (δT )vs 1twas used to determine the
thermal di�usivity. The values for thermal di�usivity were 5.05x10−7m2s for sugarcane �bres,
3.67x10−7m2s for ash, 8.13x10−7m2s for banana �bres, 1.12x10−7m2s for sawdust,1.58x10−7m2s
for clay, 4.27x10−7m2s for kaolin and 6.90x10−7m2s for charcoal dust.
In the study the speci�c heat capacity was obtained from the relation, c = κρα .
From the samples studied, sugarcane �bres/ bagasse was the best insulating material with a
thermal conductivity ranging from 0.0840 to 0.1125Wm−1K−1, a thermal di�usivity 5.05×10−7m2s
of and a speci�c heat capacity of 1125 Jkg−1K−1at about 25oC.
Chapter 1
INTRODUCTION
1.1 Background of study
Solar energy is abundant and inexhaustible. This energy can be converted to thermal or
electrical energy. One of the most promising application of solar energy involves using solar
collectors, to heat water or air for domestic and industrial applications [1]. The production
of hot water is particularly an important application of solar energy using plane collectors
to heat water. In addition to its inexhaustible nature, solar energy has the advantage that
it is non polluting. However, solar energy utilisation is often inf�luenced by its intermittent
character and the signif�icant mismatch between the time of availability and that of intended
use. Early heat recovery systems used water as a storage medium [2]. However, solar energy
source and household demands in general, do not match each other at any time. This
necessitates the use of thermal energy storage (TES) systems to address this mismatch so
as to meet energy needs at all times [3]. There is a huge potential for the application of
thermal energy storage systems. TES systems can play an important role, as they provide
great potential for facilitating energy savings and reducing environmental impact [4].Energy
storage systems are not as widely used as they could due to several reasons. Some of these
systems are not yet economically competitive with fossil fuels and their long term reliability
1
INTRODUCTION 2
is not yet proven.
It is necessary to use thermal insulators around such storage systems to maintain high tem-
peratures inside by preventing heat losses to the surroundings [5]. There are varieties of
insulating materials which come in various forms like loose f�ill, rigid boards,pipe and foam.
Proper selection of the insulating material to be used is based on the thermal properties
which include the thermal conductivity, specif�ic heat capacity and thermal dif�fusivity. The
thermal insulation is provided by embedding insulation materials at least on the roof areas
and the vertical walls of the storage systems [6]. Poor thermal insulation of the heat storage
systems leads to high heat losses [7].
Rock wool and f�ibre glass are currently used as thermal insulation materials for the storage
systems. This is mainly due to their low thermal conductivity values leading to good thermal
insulation. However, these thermal insulators are expensive and also risky to human health
as a result of exposure during handling especially those in f�ibrous form [8]. Studies show that
people who manufacture f�ibre glass have 60% more f�ibre glass material in their lungs than
those who had not been exposed [9]. There is a need for f�inding alternative thermal insulating
materials which are cheap, readily available and do not pose a risk to human health and also
cheaply and readily available [10].
1.2 Statement of the problem
Thermal Energy storage systems are usually insulated with glass wool, f�ibre glass or rock
wool. The thickness of insulation used is large and ranges from 10 to 20 cm. Because of this,
the cost of the insulation represents a signif�icant part of the total cost of a thermal storage
system and means to reduce this cost need to be explored. There is need to investigate
thermal properties of cheap and readily available materials in Uganda . The properties
include thermal conductivity, thermal dif�fusivity and specif�ic heat capacity. This will make
INTRODUCTION 3
it possible to identify those materials that can be used as thermal insulators .
1.3 Objective
The main objective was to investigate the thermal properties of selected insulating materials
available in Uganda that can be used for thermal insulation.
1.4 Specif�ic objectives
The specif�ic objectives of this study are to investigate :
1. The thermal conductivity of selected materials available in Uganda.
2. T he thermal dif�fusivity of selected materials available in Uganda.
3. The specif�ic heat capacity of selected materials available in Uganda.
1.5 Scope
The investigation will cover the determination of thermal conductivity, thermal dif�fusivity
and specif�ic heat capacity of the following materials: clay, kaolin, ash, charcoal dust, sugar
cane f�ibre, banana f�ibre and saw dust.
1.6 Signif�icance of the study
This study is focused on identifying suitable materials in Uganda which can be used for ther-
mal insulation in thermal storage. In order to determine which material can best be used for
thermal insulation, their thermal properties, namely specif�ic heat capacity, thermal dif�fusiv-
ity and thermal conductivity will be studied. This investigation will provide an appropriate
INTRODUCTION 4
local material which can be used in thermal energy storage systems for insulation and hence
increase the economic ef�f�iciency of the systems.
1.7 Justif�ication
Materials currently in use for thermal insulation are mainly of synthetic origin. The com-
monly used materials are rock wool, f�ibre glass, polystyrene and the polyurethane. These
materials are expensive, required in large quantities and can sometimes be a health risk to
those handling them in �brous form [11]. The thermal characterization of insulating mate-
rials available in Uganda will allow identif�ication of those materials which can be used as
thermal insulators in place of existing ones therefore leading to reduction in the overall costs
of thermal energy storage systems.
Chapter 2
LITERATURE REVIEW
2.1 Thermal insulators
Thermal insulators are those materials or combinations of materials which retard the f�low of
heat energy. Installation of thermal insulation can signif�icantly reduce the thermal energy
(heat) lost from thermal heat storage system surfaces. The energy lost for an insulating
material depends on the the thermal properties and thicknesses of the insulation. Clausen [12]
calculated the energy lost for dif�ferent thickness of mineral wool insulation used in thermal
energy storage system and the results are shown in table 2.1. The thicker the insulation the
less the amount of heat loss.
Insulation materials can be made in dif�ferent forms including loose-f�ill form, blanket batt
or roll form, rigid form, foamed in place, or ref�lective form. The choice of the type and
Table 2.1: Energy lost using mineral wool insulation [12]
Insulation layer thickness [mm] Heat loss, 50 years [MJ]0 1995880 5424250 1855350 1338500 943
5
LITERATURE REVIEW 6
form of the proper insulation materials depends on where the insulation is to be applied as
well as the desired material's physical and thermal properties [13]. Some typical properties
of insulating materials that are considered as a must in terms of mechanical, physical and
thermal properties are: low thermal conductivity, prevention of water leak, ease of handling
and machining, durability and light weight, f�ire resistance, safety and installation. Identifying
the rate at which thermal energy (heat) is lost from an uninsulated surface provides the need
for installing thermal insulation. The basic requirement for thermal insulation is to provide a
signif�icant resistance path to the f�low of heat through the insulation material. To accomplish
this, the insulation material must reduce the rate of heat transfer by conduction, convection,
radiation, or any combination of these mechanisms.
The heat loss depends on a number of factors, such as the heating system or heat source
temperature, selection and thickness of insulation used, and exposure of insulated surfaces
to ambient conditions.
Heating systems may lose 2% to 5% of the total heat input through insulated surfaces. It
is not feasible or possible to eliminate all insulation-related heat loss, but it is possible to
reduce these losses by 10% to 25% [13]. To achieve this, one must:
(i) Review process requirements
(ii) Know the available and applicable insulation materials
(iii) Select materials to meet the process requirements
(iv) Properly design, install and precondition insulation systems
(v) Properly operate the equipment to avoid damage to the insulation
(vi) Perform periodic maintenance, repairs and replacement of the insulation
LITERATURE REVIEW 7
2.1.1 Benef�its of thermal insulation
Thermal insulation delivers the following benef�its.
Conservation of energy
Substantial quantities of heat energy are wasted daily in thermal energy storage plants be-
cause of under insulated and uninsulated heated and cooled surfaces. Properly designed and
installed insulation systems will immediately reduce the energy loss by the system. Insulation
helps in reducing heat loss or gain and maintaining process temperature to a pre-determined
value or within a predetermined range. The insulation thickness must be suf�f�icient to limit
the heat transfer in a dynamic system or limit the temperature change, with time, in a static
system.The benef�its to industry include enormous cost savings, improved productivity, and
enhanced environmental quality.
Protection of personnel
Thermal insulation is one of the most ef�fective means of protecting workers from second
and third degree burns resulting from skin contact for more than 5 seconds with surfaces of
hot piping and equipment operating at high temperatures. Insulation reduces the surface
temperature of piping or equipment to a safer level as required by Occupational Safety and
Health Administration (OSHA), resulting in increased worker safety [14].
Protection from f�ire
Insulation is used in combination with other materials in f�ire stop systems designed to pro-
vide an ef�fective barrier against the spread of f�lame, smoke, and gases at penetrations of f�ire
resistance rated assemblies by ducts, pipes, and cable [15].
LITERATURE REVIEW 8
Insulation materials fall into two broad categories: organic foams and inorganic materials.
Organic insulation are based on hydrocarbon polymers, which can be expanded to obtain
high void structures. The organic foams include materials such as polystyrene,
polyurethane, phenolic foam and polyethylene foam. Inorganic insulation is based on
siliceous/aluminous/calcium materials in f�ibrous, granular or powder forms. The inorganic
materials include mineral wool, calcium silicate, cellular glass, microporous silica, magnesia,
ceramic f�ibre, vermiculite, perlite and others. The materials selected for this study are
inorganic materials.
2.1.2 Types and Application
The insulation can be classif�ied into three groups according to the temperature ranges for
which they are used.
Low Temperature Insulators (up to 90oC)
This range covers insulating materials for refrigerators, cold and hot water systems, storage
tanks, etc. The commonly used materials are cork, wood, 85% magnesia, mineral f�ibers,
polyurethane and polystyrene .
Medium Temperature Insulators (90 - 325oC)
Insulators in this range are used in low temperature, heating and steam producing equipment,
steam lines, f�lue ducts etc. The types of materials used in this temperatures range include
85% magnesia, asbestos, calcium Silicate and Mineral f�ibers .
High Temperature Insulators (325oC and above)
These are used in systems like super-heated steam systems, oven dryers and furnaces. The
most extensively used materials in this range are asbestos, calcium silicate, mineral f�ibre,
mica and vermiculite based insulation, f�ireclay or silica based insulation and ceramic f�ibre.
LITERATURE REVIEW 9
2.2 Major thermal insulation materials used in thermal
heat storage
Many types of insulation materials are available which dif�fer with regard to thermal properties
and mechanical properties as well as cost. The following are major insulation materials used
in commercial and industrial installations.
2.2.1 Calcium silicate
In recent years, a variety of low-density calcium silicate-based material products have been
developed for high-temperature insulation and f�ire resistive material (FRM) applications [16].
Calcium silicate is one of the best inorganic light weight thermal insulation materials for high
temperatures [17]. It is a granular insulation made of lime and silica, reinforced with organic
and inorganic f�ibers and molded into rigid forms. Service temperature range covered is 400
to 9500C and the material is not deformed within this temperature range. Calcium silicate
is water absorbent, noncombustible, has high strength and is used primarily on hot piping
and surfaces.
Inhalation of excessive amounts of dust of calcium silicate may cause temporary upper respi-
ratory irritation [18] hence the product is harmful to human beings. Its thermal conductivity
is about 0.0462Wm−1K−1 at room temperature [17].
2.2.2 Mineral f�iber (rock and slag wool)
Rock and slag f�ibers are bonded together with a heat resistant binder to produce mineral
f�iber. The use of rock wool insulation provides a practical and cost ef�fective means of reducing
energy losses in TES. Rock wool derives its excellent thermal properties entirely from the air
trapped between the structures of the wool. As a result, the thermal qualities of rock wool
do not diminish over time and will continue to perform well through out.
LITERATURE REVIEW 10
Rock wool insulation is safe to manufacture and use, when proper guidelines are followed.
Decades of research have shown that it poses little to no health risk to humans, including
that of respiratory and other cancers. When mineral wool insulation is handled, the f�ibres
can cause skin irritations. These are caused by coarser f�ibres (with a diameter over 5µm),
which can pierce the skin owing to their rigidity and cause unpleasant itching.
F�ibrous dust is released during processing. Like any other mineral dust, the f�ibrous dust
from the mineral wool insulation can cause eye irritation. The material has a practically
neutral pH, is noncombustible, and has good sound control qualities. Rock and slag wool
insulation resists the growth of mould, fungi and bacteria because it is inorganic. The thermal
conductivity of rock wool is approximately 0.042Wm−1K−1 at room temperature [19].
2.2.3 F�ibre glass
F�ibre glass contains extremely f�ine f�ibres of glass. It is used as a reinforcing agent for many
polymer products; the resulting composite material is properly known as f�ibre reinforced
polymer (FRP) or glass-reinforced plastic (GRP). It is available as f�lexible blanket, rigid
board, pipe insulation and other pre-moulded shapes. By trapping air within, blocks of glass
f�ibre make good thermal insulation. The glass strands themselves are very poor conductors
of heat. In order for heat to be transferred through the f�ibre glass, then, it must be carried
convectively through the tiny air pockets. But the randomness of the strands means there
is no direct path through the material, so the heated air must take a very circuitous route
through [20]. The insulating properties of f�iberglass depend on this random path. If the
f�iberglass is compressed, the path becomes shorter, and the heat gets through quicker. That
is why the material is not tightly packed insulation.
Useful properties of f�iberglass insulation
The properties of f�iberglass insulation are as follows.
LITERATURE REVIEW 11
Moisture Absorption
F�iberglass does not absorb any moisture at all. The absorption of moisture by insulating
materials a�ects their thermal properties, which degrades their performance. Since f�iberglass
does not absorb moisture, it is benef�icial for use in moisture laden atmosphere.
Loss of Energy
F�iberglass insulation prevents air inf�iltration to a larger extent. Air inf�iltration refers to the
ability of an insulator to prevent the leakage of air, heat or energy through the walls
Corrosion Resistant
F�iberglass insulation is resistant to corrosion and it does not contain any chemicals that can
cause corrosion problem to wires or pipes.
Weight Issues
F�iberglass insulation is light in weight. It is easy to install in thermal energy storage systems.
F�ire Resistant
F�iberglass is non-combustible, that is, it does not support combustion. It does not need any
extra f�ire deterrent chemicals to be added to it.
Thermal conductivity
The thermal conductivity of f�ibre glass is of the order of 0.05Wm−1K−1[21] at room temper-
ature.
2.2.4 Expanded silica, or perlite
Perlite is a material that can be used for insulation. It is a very important material for
insulation due to its low heat conductivity of about 0.054Wm−1K−1 [19]. Perlite is made
from an inert siliceous volcanic rock combined with water. It is a vitreous substance that
contains 2-6% water. Binding materials such as cement, gypsum, lime, bitumen and clay are
LITERATURE REVIEW 12
needed for manufacturing perlite brick. Perlite/ clay bricks are some of the lightest ceramic
materials.
Perlite has low shrinkage and high resistance to substrate corrosion. Perlite is noncombustible
and operates in the temperature ranges 325oC and above. The product is available in rigid
pre-formed shapes and blocks. In addition to low thermal conductivity, perlite insulation is
relatively cheap and easy to handle and install.
2.2.5 Refractories
Refractory f�iber insulations are mineral or ceramic f�ibers, including alumina and silica, bound
with extremely high temperature binders. Low density ceramic materials, ceramic composites
and f�ibres are widely used in many high temperature applications. The materials provide low
thermal conductivity and high resistance to chemical attack. Refractories are manufactured
in blanket or rigid form. They are noncombustible and can withstand high temperatures of
3500C and above [22]. Refractory materials are made in varying combinations and shapes
and for dif�ferent applications. F�irebrick is the most common form of refractory material.
It is used extensively for thermal insulation in furnaces or kilns. Thermal conductivity
of refractories depends upon the chemical and mineralogical compositions as well as the
glassy phase contained in the refractory and the application temperature. The thermal
conductivities of some refractories are shown in Table 2.2 [23]
Table 2.2: Thermal conductivity of insulating refractories [23].
Type Thermal conductivity at 400 oC/Wm−1K−1
Diatomite solid grade 0.025Diatomite porous grade 0.014Clay 0.030High alumina 0.028Silica 0.040
LITERATURE REVIEW 13
2.2.6 Foamed plastic
These insulating materials are formed by blowing a gas of low thermal conductivity and the
type of gas blown inf�luences the thermal properties of the plastic. Table 2.3 [24] shows the
thermal conductivity of gases used as blowing agents in foam plastic insulation materials.
Foam plastics are composed of millions of tiny cells or bubbles. When the cells are completely
intact with no holes or spaces between the cells the material is called closed cell foam. When
the cells have holes connecting one cell to another the material is called open cell foam.
Foamed plastics are light weight with excellent moisture resistance. Foam plastic insulation
materials are considered to be inert materials with no recognized health ef�fects and have
not been linked to any respiratory problems or skin irritations as have some f�iber-based
insulations.
Table 2.3: Thermal conductivity of gases used as blowing agents in foam plastic insulation[24]
Type Gas thermal conductivityat 25oC W m−1 K−1
Air 0.0259Carbon dioxide 0.0162Cyclopentane 0.0130Hydro-chloro-�uoro-carbon (HCFC)-141b 0.0100
The common types of foam plastic insulation include, polyurethane and polystyrene .
Polyurethane
The high mechanical strength, high thermal resistance, ability to f�ill narrow cavities, low
water absorption and the excellent thermal insulation property of polyurethane makes it a
good material for thermal insulation. The insulation performance however will deteriorate
during the service life of a TES, due to gas dif�fusion processes leading to changes in the cell
gas composition. This is referred to as thermal conductivity aging and results in an increased
energy loss during transport of thermal energy which may reduce the prof�itability of a TES.
LITERATURE REVIEW 14
Long-term tests conducted on rigid polyurethane foam insulation boards showed that thermal
conductivity increases with time [25]. The thermal conductivity and cell gas composition
were determined periodically. F�igure 2.1 shows the change in thermal conductivity of rigid
polyurethane foam boards blown with pentane over a storage period of 15 years at room
temperature[26].
Figure 2.1: Increase in thermal conductivity of polyurethane insulation material in the f�irst15 years of manufacture [26].
Polystyrene
There are dif�ferent forms of polystyrene used for thermal insulation. The most common
type used is extruded polystyrene (XPS) foam plastic insulation which uses highly ef�f�icient
blowing agents specif�ically selected for low thermal conductivity and dif�fusivity. This helps
the insulation retain its properties. The durability of XPS foam plastic insulation is perhaps
the most important environmental consideration. The closed-cell structure and lack of voids
in extruded polystyrene foam plastic insulation not only impart the material's durability and
strength, but also help the foam resist moisture penetration.
Other types of polystyrene include molded polystyrene and injected polystyrene. The thermal
LITERATURE REVIEW 15
conductivities of foam plastics used for thermal insulation at room temperature are given in
table 2.4[19]
Table 2.4: Types of foamed plastics [19].
Foamed plastic Thermal conductivity/W m−1 K −1
1 Extruded polystyrene 0.0322 Molded polystyrene 0.0363 Injected polystyrene 0.0344 Polyurethane 0.024
2.2.7 Insulating cement
Insulating cement is a mixture of dry granular, f�ibrous or powdery material that develop
plasticity when mixed with water and when dried forms a coherent covering that produces
substantial resistance to heat transmission. It is used in insulation applications to f�ill voids,
joints and also as a f�inish to other insulation applications. According to the ASTM [27] the
thermal conductivity of insulating cements is 1.3Wm−1K−1 at 200oC.
2.2.8 Cotton
Cotton is one of the oldest �bres under human cultivation. In processing, the f�ibres (cotton
lint) are separated from the seeds by cotton ginning.
Cotton wool has thermal properties similar to those of f�ibre glass. It is environmentally
friendly for insulation and for use in the textile industry [28]. Cotton has disadvantages of
being hard to dry in case excessive moisture leaks into it and it can not seal cavities against
air movement since the material expands.
2.3 Thermal insulators available in Uganda
In Uganda there are many materials available for consideration as thermal insulators. These
materials are either available naturally or are obtained as industrial wastes. Due to the
LITERATURE REVIEW 16
environment concerns and the need to conserve energy, various research ef�forts have been
directed towards the utilization of waste materials around the world [29]. The potential of
these materials for thermal insulation is based on the following:
(i) Availability of the material
(ii) Thermal and physical properties of the material
(iii) Environmental and health impacts: the impacts from the processes of production of
waste materials into insulation board.
The locally available insulating materials in Uganda include clay, kaolin, ash, banana �bres,
sugarcane �bres, sawdust and charcoal dust.
2.3.1 Clay
Clay is a natural, earthy f�ine grained soil material that develops plasticity when mixed with
limited quantity of water. Clays are grouped into various forms based on the suitability of the
clay to meet user's purpose [30, 31]. The groups are kaolin, ball clay, stone-wave clay and red
earthen wave clays. Classif�ication of clays can be done using the yardsticks of their color and
availability; hence, there are red, gray, white and yellow clays. The variation in their mineral
contents such as kaolinite, montmorillonite, illite, chlorite and attapulgite contributes to the
dif�ferent colours of clays [31]. All refractory materials have a high specif�ic heat capacity,
meaning they can hold a lot of heat within themselves [32].
Thermal conductivities of clays have been previously investigated.
Mukwasibwe [33], using the Lee's Disk method studied the thermal conductivity of f�ired clay
samples from Seeta, Ntawo and Kigombya and the values obtained were in the range of 0.13
-0.30Wm−1K−1 at room temperature.
LITERATURE REVIEW 17
Owalu [34], used the hot wire method to investigate the thermal conductivity of kaolin
obtained from Buwambo quarry near Kampala. Values in the range of 0.3- 1.5Wm−1K−1
were obtained at room temperature.
No measurement of speci�c heat capacity were done hence there is need to study the specif�ic
heat capacity and thermal dif�fusivity to fully characterise the thermal properties of clay and
hence its insulation property.
2.3.2 Ash
Ash is residue powder left after the combustion of biomass. Properties of biomass di�er
hence the properties of ash will depend on biomass from which it is processed from. The
thermal properties of the ash deposits have a signif�icant inf�luence on the heat transfer rates
in furnace walls, super heater tubes, and other heat transfer surfaces. The in�uence largely
depends on the thickness, thermal conductivity, and emissivity of the deposits [35]. Ash
deposits are a complex, heterogeneous, multiphase, porous material. Like many porous
materials at high temperature, both conduction and radiation can contribute to the overall
heat transfer rate through the deposit. The radiative properties and thermal conductivity
of deposits have signif�icant inf�luence on the boiler performance deposit [36]. The ef�fective
thermal conductivity is used to characterize the overall heat transfer rate.
The thermal properties are strongly inf�luenced by the physical structures of the deposits,
particle size, porosity and sintered condition [37, 38]. Allen et al[35] reported that the
thermal conductivity of ash deposits in situ is 0.14Wm−1K−1.
2.3.3 Bagasse (Sugarcane f�ibres)
Bagasse is a f�ibrous residue left after extraction of sugar from the canes, and contains short
f�ibers.The average sugar content of the sugar canes is 9.3% [39] and the rest is mainly bagasse.
LITERATURE REVIEW 18
Basically, it is a waste product that causes mills to incur disposal costs. For example, every
metric ton of sugarcane generates about 280 kg of bagasse [40]. It consists of water, f�ibers,
and small amounts of soluble solids. Percent contribution of each of these components varies
according to the variety, maturity, method of harvesting, and the ef�f�iciency of the crushing
plant. In Table 2.5 [41] a typical Bagasse composition is presented.
Table 2.5: Average Bagasse Composition [41].
Item Bagasse % compositionMoisture 49.0f�iber 48.7Soluble solids 2.3
F�ibers in bagasse consist mainly of cellulose, pentosans, and lignin. The resultant sugar cane
f�iber bundles consist of several to hundreds of ultimate f�iber cells, with the width of the
f�iber bundles being dependent on extraction conditions and extraction processes. Nowadays
Bagasse is mainly used as a fuel in the sugar cane mill furnaces. The low caloric power
of bagasse makes this process of low ef�f�iciency . Also, the sugar cane mill management
encounters problems regarding regulations of "clean air" from the Environmental Protection
Agency, due to the quality of the smoke released in the atmosphere. Presently 85% of
Bagasse production is used as fuel in sugar cane mill furnace [42]. Even so, there is an excess
of Bagasse which is left to burn in the open.
Insulation materials containing bagasse have been produced. It is reported that their thermal
conductivity is in the range of 0.046 � 0.051 Wm−1K −1[43]. The thermal conductivity of
bagasse its self was not reported.
2.3.4 Banana f�ibres
Banana f�ibres are a renewable resource but have relatively poor mechanical properties and
have low densities. Matooke the fruit from bananas is one of the major foods in Uganda.
Bananas contribute up to 44.7 % of the total volume of food crops produced in Uganda [44].
LITERATURE REVIEW 19
Banana f�ibres are usually extracted manually from pseudo stems by peeling them of�f.
Presently banana f�ibres are used for making hand bags, table mats and ropes [45]. One of
the reasons for under utilization of these f�ibres is limited scientif�ic data on them. There have
been some studies of the chemical constituents and mechanical properties of these f�ibres [45].
These materials can also be easily employed for multi-function applications, as the hollow cel-
lular structure of plant f�ibers proved ef�fective in providing insulation against heat and noise.
Paul et al. [46] in their observations on the ef�fect of f�iber loading on banana/polypropylene
(PP) composite found that both the thermal dif�fusivity and thermal conductivity were de-
creasing on increasing f�iber loading (i.e., from 0.24Wm−1 K−1 for neat polypropylene matrix
to 0.217 and 0.157Wm−1 K−1 for 0.10 and 0.50 of volume fraction respectively).
2.3.5 Sawdust
Sawdust is the main by product of wood timber processing. Types of sawdust depend on the
varieties of wood from which it is obtained. Hence their thermal properties will dif�fer from one
to another. Ogunleye and Awogbemi [47] investigated the thermal and physical properties of
eight varieties of sawdust and found that they had dif�ferent thermal conductivity values.
Although many outlets are available for the utilization of this waste, economical disposal of
sawdust remains a problem of growing concern to the wood industry [48]. The saw mill sector
in Uganda currently disposes sawdust by burning which is environmentally inappropriate.
The use of sawmill residues must be carefully analyzed to of�fer the best technical, economic
and environmental alternative [49]. The thermal characterization of the sawdust generated
is essential in order to determine its possible use.
LITERATURE REVIEW 20
2.3.6 Charcoal dust
Charcoal dust is a residue from charcoal packing. It is a black powdery substance normally
found at the bottom of charcoal sacks, charcoal selling stores or in the charcoal making areas.
It results from the chip of�fs from the charcoal slates.
The properties of charcoal dust are highly dependent on the source and the process conditions
[50].
2.4 Important thermal properties of an insulating mate-
rial
A thermal insulating material must have the appropriate characteristics to retard the trans-
port of heat that occurs by conduction, convection and radiation. In order to decide which
material is best requires an understanding of the following thermal properties: thermal con-
ductivity, specif�ic heat capacity and thermal dif�fusivity.
2.4.1 Thermal conductivity
The thermal conductivity (κ) of a material is a measure of the ef�fectiveness of the material in
conducting heat [51]. Good heat insulators should have low thermal conductivities, in order
to reduce the total coef�f�icient of heat transmission.
The thermal conductivity of a material represents the quantity of heat that passes through
a metre thickness per square metre per second with one degree dif�ference in temperature
between the faces.
In a steady state, that is when the temperature at any point in the material is constant with
time, thermal conductivity is the parameter which controls heat transfer by conduction. The
LITERATURE REVIEW 21
rate of heat f�low, q, is given by Fourier's law:
q = −κA∂θ∂x
(2.1)
where κ is the thermal conductivity, A is the area of the test piece normal to the heat �ow,
and ∂θ∂x
is the temperature gradient.
Thermal conductivity is regarded as the most important characteristic of a thermal insulator
since it af�fects directly the resistance to transmission of heat that a material of�fers. The
lower the thermal conductivity value, the lower the overall heat transfer.
The thermal conductivity of insulating materials has been found to vary with: density,moisture
content, temperature, direction of heat f�low with respect to grain for f�ibrous materials,the
presence of defects in the material and porosity [52].
F�igures 2.2 [53] and 2.3 [54] show the variation of thermal conductivity with density and
porosity respectively in a mineral f�ibre.
The variation of thermal conductivity with temperature for common heat insulators is shown
in F�igure 2.4 [55]. It is observed that that the thermal conductivity does not vary appreciably
over a temperature range 0oC to 50oC.
Insulation levels are specif�ied by R-value. This is a measure of the resistance to heat f�low as
a result of suppression of conduction, convection and radiation. It depends on the material's
thermal conductivity, density and thickness [51]. It can be calculated from equation .
R =l
κ(2.2)
where l is the thickness and κ is the thermal conductivity of a material.
The higher the R-value the better the thermal performance of an insulator.
LITERATURE REVIEW 22
Figure 2.2: The thermal conductivity of a mineral f�iber insulation versus packing density[53].
Thermal conductivity of composites
The thermal conductivity of a composite material depends on its component materials and the
arrangement of the materials, It is possible to optimize the property through constitutional
and structural design.
Maxwell and Rayleigh [56] studied the ef�fective thermal conductivity as a function of the con-
stitutional and structural parameters and geometry (F�igure 2.5). Dif�ferent approximations
are used for various geometries.
For heterogeneous solids such as a material made of spheres of thermal conductivity κ0
embedded in a continuous phase of thermal conductivity κ1, the ef�fective thermal conductivity
κeff is given by Maxwell's and Rayleigh's equations 2.3 and 2.4, respectively [57, 58].
Assuming the spheres do not interact thermally (that is, small volume fraction φ as shown
in F�igure2.5a)
LITERATURE REVIEW 23
Figure 2.3: Variation of Thermal conductivity with porosity of refractory bricks[54].
κeffκ0
= 1 +3φ(
κ1+2κ0κ1−κ0
)− φ
(2.3)
Assuming large volume fraction φ(as shown in F�igure 2.5b)
κeffκ0
= 1 +3φ(
κ1+2κ0κ1−κ0
)− φ+ 1.569
(κ1−κ0
3κ1−4κ0
)φ10/3 + · · ·
(2.4)
For square arrays of long cylinders parallel to z axis(as shown in f�igure 2.5c) the thermal
conductivity is not the same in all directions. E�ective thermal conductivity is given by the
Rayleigh's derivation.
The e�ective thermal conductivity in the z-direction is given by equation 2.5 [59]
LITERATURE REVIEW 24
Figure 2.4: Variation of thermal conductivity with temperature for selected insulation mate-rials [55].
κeff,zzκ0
= 1 +
(κ1 − κ0κ0
)φ (2.5)
The e�ective thermal conductivity in the y-direction is given by equation 2.6 [59].
κeff,yyκ0
= 1 +2φ(
κ1+κ0κ1−κ0
)− φ+ 1.569
(κ1−κ03κ1+κ0
)(0.30584φ4 + 0.013363φ8 + . . .)
(2.6)
For unconsolidated granular beds as complex non-spherical inclusions in a continuous solid
phase as shown in f�igure 2.5d, the e�ective thermal conductivity is given by the complex
non-spherical approximation 2.7 [59].
LITERATURE REVIEW 25
(a) Spherical inclusion with a small volume fraction (b) Spherical inclusions with a large volume fraction
(c) Long cylinders parallel to z-axis (d) Complex nonspherical inclusions
Figure 2.5: Distribution and geometry of embedded material in continous phase.
κeffκ0
=(1− φ) + αφ (κ1/κ0)
(1− φ) + αφ(2.7)
where α = 13
∑3
k=1
[1 +
(κ1κ2− 1)gk
]−1and gk are �shape factors� for granules.
The values of gkrange from 0.7-0.98 [60].
For solids containing gas pockets, thermal radiation becomes important. The e�ective ther-
mal conductivity is now given by equation 2.8 [59].
κeffκ0
=1
1− φ+(κ1κ0φ
+ 4σT 3Lκ0
)−1 (2.8)
where σ is the Stefan-Boltzmann constant and L is the total thickness of the material in
direction of heat conduction
LITERATURE REVIEW 26
2.4.2 Specif�ic heat capacity
Specif�ic heat capacity is one of the important parameters for determining the insulation
property. Specif�ic heat capacity of a material is the amount of heat required to raise the
temperature of one kilogram of a material by one degree Celsius. The principal heat capacities
of a material are those at constant volume and constant pressure. The specif�ic heat capacity
at constant volume Cv, which is impossible to measure for solids , can be calculated from
equation (2.9).
Cp − Cv =TV τ 2
βT(2.9)
where Cp is the specif�ic heat capacity at contant pressure, which is the quantity normally
measured, T is the absolute temperature,τ is the coe�cient of thermal expansion, βT is the
isothermal compressibility and V is the volume.
In solids the volumetric heat capacity, which is the heat capacity per unit volume is the one
which can be determined experimentally.
A high specif�ic heat capacity value means high ability for heat retention and hence good
insulating materials should have a high speci�c heat capacity.
2.4.3 Thermal dif�fusivity
Thermal dif�fusivity, α, is the parameter which determines the temperature distribution in
non steady state or transient conditions. It is given by:
α =κ
ρCp(2.10)
where α is the thermal dif�fusivity, κ is thermal conductivity, Cp is specif�ic heat capacity at
constant pressure and ρ is the density.
Thermal dif�fusivity measures the ability of a material to transmit a thermal disturbance. It
LITERATURE REVIEW 27
indicates how quickly a material's temperature will change. Thermal dif�fusivity increases
with the ability of a body to conduct heat and decreases with the amount of heat needed to
change the temperature of a body. It is of little interest in many thermal insulation systems
since in these, approximately steady state conditions normally exist.There are few reports
which give direct measurement methods for thermal dif�fusivity of materials. Most of the data
is calculated from equation 2.10 .
Like thermal conductivity, specif�ic heat capacity and thermal dif�fusivity are functions of
temperature, porosity, density and particle sizes.
2.4.4 Other pertinent physical properties
Compression strength
This is the measure of the capacity of a material to withstand axially directed crushing forces.
The importance of this property is for maintaining press alignments. Typically, compression
strength of most insulating materials decreases as temperature increases [61]. In fact, a small
increase in temperature can result in a signif�icant decrease in compression strength in some
insulating materials.
Water absorption
This is def�ined as the amount of water absorbed by a material when immersed in water for
a period of time. Up to 98% of insulation system problems are caused by moisture or water
absorption.The common measure is the percent swell. The disadvantage of water absorption
to insulation is that swelling can cause misalignment and cracking. Also water absorption
causes solidif�ication of insulating materials in high-temperature thermal storage systems.
This leads to accelerated heat loss by a thermal storage system.
LITERATURE REVIEW 28
2.5 Measurement of thermal conductivity of insulators
The methods of measurement of thermal conductivity can be divided into steady state meth-
ods and transient or non steady state methods. Traditionally, steady state methods were
most widely used as they are mathematically simpler. For materials of low thermal conduc-
tivity, steady state methods can be very time consuming and involve expensive apparatus.
Transient methods have experimental advantages once the much more dif�f�icult mathematical
treatment has been worked out. Methods based on transient heat transfer have the potential
of directly determining thermal dif�fusivity, but they are not as accurate as steady state
methods with dry materials [62].
2.5.1 Steady state methods for measurement of thermal conductiv-
ity
Steady state methods of measuring thermal conductivity apply Fourier's law of heat con-
duction. Underlying all the dif�ferent steady heat f�low methods is the attempt to simplify
the mathematics by reducing the heat transfer problem to a one-dimensional problem. The
calculations use an inf�inite slab, the inf�inite cylinder or a sphere as models.
Guarded Hot Plate
The guarded hot plate is based on the inf�inite slab as the heat transfer model. Since sample
dimensions are f�inite, guard heaters are used to facilitate uni-directional heat f�low. It is
considered the most accurate and most widely used steady state method for the measure-
ment of thermal conductivities of poor conductors of heat [62]. It is most suitable for dry
homogeneous samples that can be formed into a slab.
The sample is sandwiched between a heat source and a heat sink as shown in f�igure 2.6.
LITERATURE REVIEW 29
Figure 2.6: Schematic diagram of the guarded hot plate apparatus
Thermal guards are kept at the same temperatures as their adjacent surfaces (heat source
and heat sink) to prevent heat leakage from heat source, sample and heat sink, thus ensuring
uni-directional heat f�low. The heat input is monitored. After steady state has developed, as
shown by stable temperatures of the heating and cooling plate, the thermal conductivity can
be calculated from the heat input, the temperature dif�ference across the sample, the sample
thickness and heat transfer area. Since steady state conditions may take several hours to
develop, this method is unsuitable for use with a material in which moisture migration may
take place. Equation (2.1) to determine the thermal conductivity of a material.
Radial Heat F�low Method
Whereas the guarded hot plate is generally used for measuring the thermal conductivity of
samples that can be formed into a slab, radial heat f�low steady state methods are more
commonly used with powdered or granular materials.
A cylindrical test device employs a central line (or cylindrical) heat source. End ef�fects are
assumed negligible due to either the large length or diameter ratio of the test apparatus or
the use of end guard heaters. After steady state has been established, the thermal conduc-
tivity can be calculated from the heating power, the length of the cylinder, the temperature
dif�ference between two internally (to the medium) located sensors and their radial position.
LITERATURE REVIEW 30
Alternatively, the cylindrical sample can be boardered by the heater on one side and a ref-
erence material on the other side. Temperatures on all surfaces are monitored. The thermal
conductivity of the test material is calculated from the temperatures, the radial position of
the sensors and the thermal conductivity of the reference material. Equation (2.1) is used to
determine the thermal conductivity of a material.
Lees' Disc
This apparatus consists of three copper (or any good conductor) plates (A, B and C) drilled
to accept liquid-in-glass thermometers and an electrical heater. The specimen to be studied
is sandwiched between the plates A and B and the heater is sandwiched between plates B
and C. After tightening the clamp screw to hold all the disks together as shown in f�igure 2.7.
The power to the heater is switched and
Figure 2.7: Lees' disk apparatus
the temperature gradient is measured when the apparatus reaches thermal equilibrium. This
allows the thermal conductivity to be calculated using equation 2.11
κ =ed
ε(TB − TA)(as
TA + TB2
+ 2aATA) (2.11)
LITERATURE REVIEW 31
where e is energy emitted from the exposed area of surface, aA, aS are the exposed surface
areas of the copper plates and specimen respectively, TA and TB are the temperatures of
the disks A and B, d is the thickness of the specimen and ε is the cross sectional area of the
specimen.
2.5.2 Transient state methods for measurement of thermal conduc-
tivity
The main disadvantage of steady state methods is the long measurement time involved. Con-
sequently, a steady state method will fail to measure representative thermal properties like
thermal dif�fusivity and specif�ic heat capacity. Therefore, transient methods are preferred for
measuring the thermal conductivity of materials. They are rapid as data are obtained in
minutes or even less compared to hours for a steady state measurement.
Steady state methods are only capable of measuring thermal conductivity. When the mea-
sured properties are to be used in the study of transient heat transfer, density and specif�ic
heat have to be found independently. They are combined with thermal conductivity to f�ind
the thermal dif�fusivity, For lack of accurate methods of direct measurement of thermal con-
ductivity, this approach is recommended [63]. Methods based on transient heat transfer have
the potential of directly determining thermal dif�fusivity, but they are not as accurate as
steady state methods applied to dry materials [62]
F�itch method
The Fitch method was developed by F�itch in 1935 [62] and uses a plane source of heat. It is
applicable to poor conductors of heat that can be formed into a slab. The F�itch apparatus
consists of a heat source and a heat sink. The heat source is a constant temperature vessel,
insulated on the sides and with a highly conductive bottom. The heat sink is a copper block,
insulated on all sides but the one facing the vessel. The heat transfer areas are made smooth
LITERATURE REVIEW 32
to minimize contact resistance. The roles of heat sink and heat source are reversed when the
vessel is maintained at a temperature lower than that of the copper block. Initially the sam-
ple is in thermal equilibrium with the copper block. Thermocouples record the temperature
history of the copper block, which is assumed to have a uniform temperature distribution,
and the temperature of the bottom of the vessel.
The model assumes a linear temperature prof�ile, negligible heat storage in the sample, and
negligible surface contact resistance. Heat transfer between the copper block and its insu-
lation is assumed negligible. Using these assumptions, an expression was derived for the
temperature of the copper block:
ln
(T0 − T∞T − T∞
)=
κA
LmcCct (2.12)
where A is the heat transfer area, κ is the thermal conductivity of sample, L is the thickness
of sample, mc is the mass of copper block, Cc is the specif�ic heat of copper, t is the time, T
is the temperature of copper block,T0 is the initial temperature and T∞ is constant temper-
ature of vessel bottom.
The plot of the dimensionless temperature(T0−T∞T−T∞
)against time on semilog paper is linear
with an initial curved part. The thermal conductivity of the sample is calculated from the
slope of linear part of this plot, the heat capacity of the copper block, the thickness and heat
transfer area of the sample.
This method is more accurate for thin samples.
Thermistor Based Method
A thermistor is a thermally sensitive resistor which exhibits a change in electrical resistance
with a change in temperature [64]. Those used for thermal property measurement have a
LITERATURE REVIEW 33
negative temperature coef�f�icient of resistance, indicating that their resistance will decrease
when their temperature is increased. Being resistive devices, a thermistor will heat up when
a current is passed through it. The thermistor is used both as a temperature sensor and as
a point heating source. The relationship between temperature and resistance is non-linear
and is usually described by the empirical Steinhart-Hart equation [64].
1
T= a0 + a1 + lnR + a2[lnR]
3 (2.13)
where T is the temperature, R is the resistance,a0, a1and a2 are derived constants.
At steady state (when the resistance has reached a constant value) the equation for measuring
thermal conductivity κ of a sample is given by [65]:
1
κ= 4πa
4TPss− 0.2
κb(2.14)
where 4T is the temperature change, P ss is the steady state power dissipation in the ther-
mistor required for maintaining 4T, a is the ef�fective probe radius and κb is the ef�fective
probe thermal conductivity.
Transient Hot Wire method
Transient hot wire is one of the most commonly used transient methods especially for gran-
ular materials [62]. It is also known as the line heat source method. The theory is based
on a linear heat source of inf�inite length and inf�initesimal diameter. The line heat source is
embedded in the material whose thermal conductivity is to be measured. From a condition
of thermal equilibrium, the heat source is energized and heats the medium with constant
power. The temperature response of the medium is a function of its thermal properties. The
thermal conductivity is found from the temperature rise measured at a known distance from
the heat source.
LITERATURE REVIEW 34
The value of the thermal conductivity κ is given by the following formula [66]:
κ =qln( t2
t1)
4π(T2 − T1)(2.15)
where q is heat generated per unit length of heating wire, t1 and t2 are the measured time
and T1and T2 are temperature at times t1 and t2 respectively.
2.6 Measurement of specif�ic heat capacity
Method of mixtures or the direct water immersion method
The method of mixtures consists of dropping a specimen of known mass and temperature
into a calorimeter of known specif�ic heat capacity containing a known mass of water at known
temperature. The unknown specif�ic heat capacity Cs is then calculated from a heat balance
equation after the thermal equilibrium has been attained [62].
Cs =CwWw(Te − Tw)− CcWc(Ti − Te)
Ws(Ti − Te)(2.16)
where, Cs, Cw and Cc are specif�ic heat capacity of sample, water and calorimeter respec-
tively; Ww, Wc, and Ws are weights of water, calorimeter and sample, respectively; Teis the
equilibrium temperature of the mixture, Tw is the initial temperature of water and Ti is the
initial temperature of the sample and calorimeter.
The heat losses to the surroundings is the greatest concern in such experimental units [67].
To avoid heat losses the calorimeter should be maintained at the same temperature as that
of the surroundings and also a cooling correction should be made.
LITERATURE REVIEW 35
Dif�ferential scanning calorimeter (DSC)
The DSC is the most suitable equipment for measuring speci�c heat capacity but it is ex-
pensive [68]. As discussed by Mohesnin [62], the DSC produces a thermogram in accordance
with the heat energy gained or lost by the sample. This is done by a scanner which scans the
sample at the desired rate over a specif�ied temperature level of interest. The test material
and the reference material are held in a cell. They are heated by individual heaters but
maintained at the same temperature and the amount of heat energy required to maintain
this temperature is recorded.
The dual-needle heat-pulse (DNHP) sensor
Campbell et al. [69] developed a dual-needle heat pulse (DNHP) probe that can determine
simultaneously C, κ and α. In addition to its economical advantage, measurements are
rapid. The DNHP has successfully been used to rapidly and accurately measure the thermal
properties of soils [69, 70].
The Dual-Needle Heat-Pulse (DNHP) sensor consists of two 304 stainless steel parallel needles
spaced 6mm apart (F�igure 2.8). One needle contains a line heat source and the other contains
a thermocouple.
A short duration pulse is applied to the heater and the temperature of the thermocouple is
monitored. The thermocouple's temperature response to the heat pulse is used to simultane-
ously determine the thermal conductivity κ and thermal dif�fusivity α, and to calculate the
volumetric heat capacity, Cρ,which is the product of the heat capacity and the density, of
the sample.
This method was developed from the transient heat pulse technique. This technique is com-
LITERATURE REVIEW 36
Figure 2.8: Schematic representation of the dual-needle heat-pulse (DNHP) sensor
monly used because of its convenience, applicability to a variety of sample types and ability
to determine specif�ic heat capacity, thermal conductivity and thermal dif�fusivities in a single
measurement . The technique is based on the application of a heat pulse to a line source
and analysis of the temperature response at the line source or at some distance from the line
source [71].
Two equivalent solutions to the heat dif�fusion equation for an inf�inite slab of thickness a,
which is excited by an instantaneous input heat pulse are given below [71].
δT =
(Q
2πwCραt
)exp (−x2/4αt) +
(1 + 2
∑n=1
exp (−n2a2/αt)
)(2.17)
δT =
(Q
2awCρ (παt)1/2
)exp (−x2/4αt) +
(1 + 2
∑n=1
exp (−n2π2αt/a2)
)(2.18)
where Q is the total heat input, x is the distance between the heater and the thermocouple
and w, α, Cρ are the width, thermal dif�fusivity and volumetric specif�ic heat capacity of the
sample respectively.
The second terms in the brackets of equations 2.17 and 2.18 are negligible for short and long
measurement times. Initially the heat pulse dif�fuses outward in two dimensions as though
the sample was semi inf�inite but for long measurement times one observes one-dimensional
LITERATURE REVIEW 37
Figure 2.9: Temperature response measured for a sample.
heat f�low.
There are two ways of determining the specif�ic heat capacity and thermal dif�fusivity of the
sample.
One can plot a graph of temperature response measured for the sample (F�igure 2.9) . From
the graph the maximum temperature Tmax , attained and the time, tmax taken to reach that
temperature are recorded .
From equation (2.17)
α = x2/4tmax (2.19)
and
Cρ = 2Q/δTmaxπwex2 (2.20)
where δTmax is the maximum temperature change.
The second way to obtain α and Cρ is by plotting a graph of ln (δT )against 1/t . The graph
LITERATURE REVIEW 38
Figure 2.10: A plot of the linearisation ln (δT ) against 1t.
gives a straight line with a negative slope f�igure 2.10. α is determined from the slope while
Cρ is determined from the intercept.
The operation of the transient heat pulse technique is based on the following assumptions:
1. The heating wire is long enough so that the end ef�fects are negligible.
2. The size of the sample is su�ciently large to allow the heat pulse to propagate without
reaching any boundary during the time the measurement takes place.
3. No movement of any kind is induced during the measurement.
The analysis of error [72] showed that assuming an inf�inite length for a heat source of f�inite
length caused errors < 2% and assuming the cylindrically shaped heater to be a line heat
source caused errors of < 0.6% in the measurement of thermal properties. In order to minimise
errors in measurement in this study, the wire used as a heater was wound in cylindrical form.
Chapter 3
METHODS AND MATERIALS
3.1 Sample collection and preparation
Sample collection
In this study, the materials used include: clay, kaolin, ash, charcoal dust, saw dust, banana
f�ibres and sugar cane f�ibres.
The clay samples used in the study were collected from Ntawo in Mukono District and kaolin
was obtained from Buwambo in Wakiso district.
Ash was collected from the deposits at the bottom of local stoves used for cooking. It is a
waste material from combustion of mainly agricultural products in Uganda. The biomass
which was burned to produce this ash used in this study was not put in consideration.
The charcoal dust was collected from local charcoal selling sites. The type of wood from
which the charcoal was processed was not considered.
The sawdust was collected from carpentry workshops as a waste material from processing of
wood timber. The timber from which the sawdust waste was obtained was not considered in
this study.
The banana f�ibers were extracted from pseudo banana stems by hand. The f�ibres were then
39
METHODS AND MATERIALS 40
washed and dried in sunlight for about 12 hours.
The sugar cane f�ibres were obtained from sugar cane vendors after the juice has been extracted
by the customers from the sugar canes. The f�ibres were then dried.
The banana f�ibres and sugar cane f�ibres were f�irst ground to obtain f�ibres of smaller sizes
which were used in the measurement.
Sample preparation for thermal conductivity measurement
The clay and kaolin collected from the deposit were soaked in water and massive particles
were separated by gravity sedimentation. Thereafter, the samples were sun dried for three
days then placed inside the oven and further dried for a period of eight hours at a temperature
of 50oC. The dried samples were f�inally crushed down to smaller sizes.
The clay, kaolin, saw dust, ash and charcoal dust were sieved through a 500µm sieve to
remove coarse particles and foreign materials which are larger than 500µm that might have
been present in the samples.
Sieving by hand is dif�f�icult to perform because it is both time consuming and labor intensive
and the results are somewhat subjective. A mechanical test sieve shaker or vibrator was used
in the study.
A stack of sieves of f�ive dif�ferent sizes was mounted on the vibrator and covered at the top
so that the stack can be easily secured in the shaker as shown in f�igure 3.1. Care was taken
to ensure that there were no loose sieves on the shaker.The top sieve had the largest screen
openings of 355µm. Each lower sieve in the column had smaller openings than the one above.
At the base is a round pan, called the receiver.
A small quantity of about 200g of a sample was introduced in the top sieve at a time. The
process timer knob was rotated clockwise and set to run for 60 seconds. The sieve shaker
was set into vibrations by switching it on and the excitation produced was strong enough to
produce the desired particle sizes.
METHODS AND MATERIALS 41
Figure 3.1: Nested sieves on a mechanical vibrator
After the set time of 60 seconds, the vibrator stops and the contents from each sieve were
removed and graded.
The particle sizes obtained were in the range <90µm, 90 -125µm, 125 - 150µm , 150 -180µm
and 180 - 355µm.
Banana and sugar cane f�ibres samples were sieved in the same way to obtain dif�ferent f�ibre
sizes
Fabrication of the rectangular plates
According to the principle of hot wire method, inf�initely long and rectangular plates are
desired for measurement. These samples should be large enough so that the heat from the
hot wire is not lost through the surrounding hence leading to errors in measurement. These
rectangular plates of the samples were achieved through the following steps.
METHODS AND MATERIALS 42
Figure 3.2: Arrangement of a metal plate and a hollow rigid metal frame.
(i) A rectangular mould was obtained by assembling the rectangular metal block, hollow
rigid metal frame and a metal plate fabricated from mild steel as shown in the �gure .
(ii) A sample of mass 200g was poured in the mould and then covered with a metal plate.
The sample was then compacted slowly and gently using a hydraulic manual press type
PW40 (�gure 3.2) available in the department to avoid cracking of the samples. These
samples were compacted until a set pressure was attained. When the set pressure was
attained, it was maintained for about 5 minutes to allow the pressure to stabilize. The
press was then released and the rectangular blocks were then removed. As required
by the hot wire measurement, rectangular samples of 10x5x2 cm, were obtained after
compacting the powdered samples at di�erent pressures.
(iii) The samples were dried for 8h in the oven at 100oC to remove the moisture present .
(iv) The samples were then ready for thermal conductivity measurements.
To study the ef�fect of compaction pressure on the thermal conductivity, the samples were
compacted at pressures of 18.2, 36.4, 54.6 and 72.9 MPa.
When the charcoal dust sample was compacted, a weakly cohesive structure was formed so
the sample was not removed from the mould otherwise it would break. Thermal conductivity
measurements were done when the sample was still in the mould. To study the ef�fect of
METHODS AND MATERIALS 43
Figure 3.3: Hydraulic manual press type PW40 with die between its upper and lower plates.
particle sizes on the thermal conductivity, the dif�ferent particle sizes of the graded charcoal
dust samples were compacted at a pressure of 54.6MPa.
3.2 Measurement of thermal conductivity
Thermal conductivity measurement is relatively complicated for some materials under real
conditions. The main problem in most cases lies in the preparation of test samples whose
characteristics will be identical to those of the actual material. With regard to the preparation
of test samples and their properties, problems may arise due to the cohesion of a material
which depends on the forces acting between the particles.
The Quick thermal conductivity meter (QTM-500) which uses the hot wire method was used
in the study. It does quick and easy measurement on all kinds and types of sample materials.
Measurements of thermal conductivity using QTM-500 are carried out on test samples shaped
as rectangular plates of dimensions of about 5cm x10 cm and thickness between 2 to 4 cm.
METHODS AND MATERIALS 44
The QTM-500 has a sensor probe which consists of a constantan wire heater and a chromel-
alumel thermocouple. The heating wire is used to supply heat to the test sample and the
thermocouple monitors the heat f�low rate.
The measurement of thermal conductivity involved placing the rectangular block sample in
the probe box and then placing the sensor probe (PD-11) on sample surface (f�igure 3.4).
Figure 3.4: Experimental set up for thermal conductivity measurement
The Quick thermal conductivity meter was then switched on. The meter displays �Meas.
wait� on the LCD display (f�igure 3.6a) if the temperature of the probe is not in equilibrium
with the sample. This stabilization process takes about 30 minutes. When the temperature of
the meter has stabilized it displays on the screen �Meas. Ok�on the LCD display (f�igure 3.6b)
and the measurement is started by pressing the �START� button. When START button is
pressed, the heater is supplied with constant power by the heater current.
During the measurement, temperature of the wire against time curve is plotted on the display.
This curve is exponential and the angle of the curve is large with low conducting samples
because the temperature of the wire rises rapidly The angle becomes smaller with a sample
of high conductivity as shown in f�igure 3.5. The temperature rise, 4T , of the sample probe
METHODS AND MATERIALS 45
Figure 3.5: Typical curves displayed on QTM-500 for small and large thermal conductivities
from the start to the end of the measurement aganist time is also displayed by the meter
(f�igure 3.6c).
The measurement result is shown on display immediately after the measurement is f�inished
in 60s (f�igure 3.6d).
METHODS AND MATERIALS 46
(a) Stand by mode (b) Ready to start measurement
(c) Graph during measurement (d) Measurement result
Figure 3.6: Display of the QTM-500
3.3 Measurement of thermal dif�fusivity
Sample preparation
Samples were sieved to obtain particle/�bre sizes of <180 µm. In order to obtain large
rectangular block samples to allow the heat pulse to propagate without reaching any boundary
during the time of the measurement, the samples were mixed with water. The ratio of mass
of sample to volume of water was 5:2 /gcm−3 for clay, ash , kaolin and charcoal dust while
for sawdust, bagasse and banana �bres was 1:4 /gcm−3 . Rectangular boxes of dimensions
of 12×7× 6cm were used as moulds in which the mixture was poured.
A nichrome wire (heater) was embedded in the middle of the sample. The wire was selected
as a heating element in the study because of its high resistivity and high melting point of
about 1400o C.
METHODS AND MATERIALS 47
Figure 3.7: Experimental set up for measurement of temperature response of a sample to aheat pulse
At the opposite sides of the embedded nichrome wire, holes were drilled at equal distances,
x, from the heater recorded in Table 4.7 . During measurements the thermocouples were
inserted to measure the temperature response of the samples to a transient heat pulse.
Samples were then dried in the oven at 100oC for about 48h to remove all the moisture content.
After the drying,the samples were then removed from the oven, weighed and their masses
were recorded. Also the dimensions of the samples were measured and used in calculating
the volume. Using the values obtained from mass and volume of the samples the density was
obtained.
Measurement of thermal dif�fusivity
The block sample was clamped at both ends to prevent movement of any kind. The thermo-
couples were then inserted in the holes drilled at the opposite sides of the heater. Figure 3.7
shows the experimental set up for the measurement of temperature response of a sample to
a supplied heat pulse.
An instantaneous heat pulse was introduced into the sample by energising the heater with a
METHODS AND MATERIALS 48
voltage pulse.
After every 30 seconds the temperature on the thermocouples was noted. This was done
until a steadytemperature was attained.
Graphs of lnδT vs 1/t were drawn for the samples and their slopes determined. The thermal
di�usivities were calculated from equation (3.1).
α = − x2
4slope(3.1)
3.4 Determination of specif�ic heat capacity
. Volumetric heat capacity was obtained from the thermal di�usivity and thermal conduc-
tivity of the samples using equation (3.2) [21].
Cρ =κ
α(3.2)
Speci�c heat capacity (C) for the samples was calculated from equation (3.3).
C =Cρρ
(3.3)
This approach was taken because heat losses would not permit determination of volumetric
heat capacity from the intercepts of the graphs of lnδT vs 1/t .
Chapter 4
RESULTS AND DISCUSSION
Introduction
This chapter discusses the various results obtained for thermal conductivity (κ), thermal dif� -
fusivity (α) and speci�c heat capacity (C) of seven dif�ferent types of materials that included:
clay, kaolin, ash, charcoal dust, sugar cane f�ibre, banana f�ibre and saw dust.
4.1 Thermal conductivity tests
The measured thermal conductivity values are presented in Table 4.1. All measurements
were carried out at room temperature (approximately 25oc).
4.1.1 Ef�fect of particle/f�ibre size on thermal conductivity
The measured thermal conductivity values (Table 4.1) conf�irm that thermal conductivity is
related to particle/f�ibre size. F�igures 4.1 and 4.2 show the variation of thermal conductivity
with f�ibre/particle size for the samples respectively.
49
RESULTS AND DISCUSSION 50
Table 4.1: Thermal conductivity of the samples at di�f�ferent compaction pressures and parti-cle/f�ibre sizes
Thermal Conductivity,κ ±0.005 /Wm−1K−1
Sample Average particle/ 18.2 MPa 36.4 MPa 54.6 MPa 72.9 MPaf�ibre size (µm)
Sugar cane f�ibres/ 125 0.104 0.107 0.111 0.113bagasse 150 0.103 0.105 0.105 0.111
180 0.103 0.104 0.108 0.107355 0.084 0.078 0.076 0.086
Ash 90 0.301 0.318 0.343 0.361125 0.286 0.299 0.324 0.338150 0.272 0.288 0.314 0.326180 0.250 0.263 0.281 0.297
Banana f�ibres 125 0.317 0.318 0.327 0.338150 0.290 0.296 0.313 0.320180 0.287 0.300 0.294 0.304355 0.275 0.275 0.276 0.276
Saw dust 90 0.200 0.216 0.222 0.240125 0.198 0.212 0.219 0.232150 0.195 0.211 0.215 0.226180 0.190 0.202 0.211 0.218355 0.185 0.199 0.209 0.213
Kaolin 90 0.518 0.527 0.542 0.554125 0.505 0.513 0.529 0.537150 0.486 0.491 0.512 0.523180 0.466 0.472 0.493 0.500
Clay 90 0.240 0.275 0.295 0.308125 0.232 0.268 0.292 0.298150 0.217 0.257 0.288 0.291180 0.210 0.236 0.272 0.285
Charcoal dust 90 0.219125 0.213150 0.192180 0.184355 0.158
RESULTS AND DISCUSSION 51
(4.1a) Sugar cane f�ibres/bagasse
(4.1b) Banana f�ibre
Figure 4.1: Thermal conductivity against f�ibre size at various compaction pressures
RESULTS AND DISCUSSION 52
(4.2a) Ash
(4.2b)Sawdust
RESULTS AND DISCUSSION 53
(4.2c) Kaolin
(4.2d) Clay
RESULTS AND DISCUSSION 54
(4.2e) Charcoal dust
Figure 4.2: Thermal conductivity against particle size at various compaction pressures
F�itting the results using MatLab software indicates that the best f�it could be obtained when
the relationship between the thermal conductivity and f�iber /particle size is of the form
κ = εs−β (4.1)
where s is the f�ibre/particle size, ε is a constant which is independent of the processing
conditions of a material and β is a constant which shows the bonding power of a material.
This �t was chosen because the data provided the lowest average Root Mean Square Error
(RMSE) values compared to linear polynomial, Gaussian and Weibul �ts. The average RMSE
values obtained for the di�erent �ts are presented in Table 4.4.
This same trend has been observed in many studies in the literature [33, 34] for the variation
of thermal conductivity with particle size. Thermal conductivity generally increases with
decreasing particle size. This could be explained by the fact that small particles interlock
RESULTS AND DISCUSSION 55
Table 4.2: RMSE values for the di�erent �ts for thermal conductivity variation with parti-cle/�bre size.
Fit Average RMSE valuePower 0.00418
linear polynomial 0.00482Gaussian 0.00551Weibul 0.37885
Table 4.3: Values of ε and β for dif�ferent particle/f�ibre sizes
SampleCompa- Bagasse Ash Banana Saw- Clay Kaolin Charcoalction f�ibres dust Dust
pressure(MPa) ε β ε β ε β ε β ε β ε β ε β
18.2 0.12 0.02 0.95 0.25 0.54 0.12 0.26 0.06 0.58 0.20 1.03 0.1536.4 0.12 0.03 1.01 0.26 0.43 0.07 0.29 0.06 0.69 0.20 1.08 0.1654.6 0.13 0.04 1.10 0.26 0.51 0.10 0.27 0.05 0.47 0.10 0.98 0.13 0.68 0.2572.9 0.14 0.04 1.18 0.26 0.58 0.12 0.31 0.07 0.51 0.11 1.04 0.14
closely leading to low porosity.
However no clear variation between thermal conductivity and f�ibre sizes (Figure 4.1) could
be ascertained. This could be due to the orientation or alignment of the f�ibres in the sample
with respect to direction of heat �ow. The f�ibres can be aligned horizontally, vertically or
inclined at an angle to the direction of heat �ow. Highest thermal conductivity is expected
when the f�ibres are aligned horizontally and lowest when aligned vertically [73].
Statistical analysis was done to study the ef�fect of particle/f�ibre size on the constants ε and
β . The results are presented in Table 4.3. The range of ε is between 0.12 to 1.08 and β
ranges from 0.02 to 0.26 for the samples.
4.1.2 Ef�fect of compaction pressure on thermal conductivity
Values of thermal conductivity obtained for the di�f�ferent samples were used to analyse the
ef�fect of compaction pressure on thermal conductivity. F�igures 4.3 and 4.4 show the ef�fect of
RESULTS AND DISCUSSION 56
compaction pressure on the the di�f�ferent f�ibres and particle sizes respectively.
RESULTS AND DISCUSSION 57
(4.3a) Sugar cane f�ibres
(4.3b) Banana f�ibres
Figure 4.3: Variation of thermal conductivity with compaction pressure for di�f�ferent f�ibresizes
RESULTS AND DISCUSSION 58
Generally, results obtained show that thermal conductivity increases with increase in com-
paction pressure. This thermal conductivity increase is attributed to reduction in porosity
with increase in compaction pressure. The reduction in porosity is due to the fact that
increase in compaction pressure increases the particle - particle contact area. Materials gen-
erally have a higher thermal conductivity than that of air and hence increasing the particle-
particle contact area reduces the air spaces between and thus increasing the heat transfer in
the material.
This analysis was not performed on the charcoal dust sample because this sample could not
be compacted to form rectangular blocks.
The graphs in Figure 4.3 for the di�f�ferent f�ibre sizes do not show any marked variation of
thermal conductivity with compaction pressure. Thermal conductivity of large �bre sizes
was almost constant. This is because the �bres could not stay in the compacted state for
long. The block samples of the �bres could relax after the pressure has been released leading
to increase in air within the sample.
Analysis of the graphs in f�igure 4.3 and 4.4 show that thermal conductivity varies with
compaction pressure according to equation 4.2 .
κ = ξP γ (4.2)
where P is the compaction pressure, ξ is a constant which is independent of the processing
parameters of the sample and γ reperesents the bonding power of a material.
The power �t was preferred on the basis of lowest average RMSE compared to other �ts
obtained with the measured data. The average RMSE values obtained for the di�erent �ts
are presented in the Table 4.4.
The values of ξand γ for the di�f�ferent samples are given in Table 4.5. The value of ξ ranges
from 0.08 to 0.45 and γ ranges from 0.04 to 0.23.
RESULTS AND DISCUSSION 59
(4.4a) Ash
(4.4b) Sawdust
RESULTS AND DISCUSSION 60
(4.4c) Clay
(4.4d) Kaolin
Figure 4.4: Variation of thermal conductivity with compaction pressure for di�f�ferent particlesizes
RESULTS AND DISCUSSION 61
Table 4.4: RMSE values for the di�erent �ts of thermal conductivity variation with com-paction pressure
Fit Average RMSE valuePower 0.00510
linear polynomial 0.00589Gaussian 0.00778Weibul 0.38678
Table 4.5: Values of ξ and γ for the di�f�ferent samples and particle/ f�ibre sizes
SampleDiameters/ Bagasse Ash Banana Saw- Clay Kaolinsizes/µm f�ibres dust
ξ γ ξ γ ξ γ ξ γ ξ γ ξ γ
90 0.20 0.13 0.15 0.11 0.14 0.18 0.45 0.05125 0.08 0.06 0.19 0.13 0.28 0.04 0.16 0.08 0.14 0.18 0.44 0.05150 0.09 0.05 0.18 0.14 0.23 0.07 0.16 0.08 0.12 0.21 0.41 0.05180 0.09 0.04 0.17 0.13 0.26 0.04 0.15 0.09 0.10 0.23 0.39 0.05355 0.09 -0.01 0.24 0.05 0.14 0.10
4.2 Thermal di�f�fusivity tests
The measured values for temperature response for the di�f�ferent samples are presented in
AppendixI. The maximum error in temperature recorded was 0.05 oC and the maximum
error in time was 1s. F�igure 4.5 and 4.6 show the temperature response of the f�ibrous and
particulate samples respectively.
The analysis showed that the curves of best f�it could be obtained using the Gaussian relation
in equation (4.3).
T =∑i
ai exp
(−((t− bi)ci
))2
(4.3)
where T is the temperature, t is the time and ai, bi, ci are constants and i = 1, 2, 3 · · · , labels
the samples.
The constants ai, bi, ci obtained for each sample are presented in Table 4.6
RESULTS AND DISCUSSION 62
(4.5a)Sugarcane �bres
(4.5b) Banana �bres
Figure 4.5: Temperature response of the �brous samples to a heat pulse
RESULTS AND DISCUSSION 63
Thermal di�f�fusivities of the samples were obtained using slopes of F�igure 4.7 for the f�ibres
and F�igure 4.8 for the particulate samples. Results of thermal di�f�fusivities obtained are of
the order of 10−7m2s which shows that all the samples have a low response to temperature
change.
RESULTS AND DISCUSSION 64
(4.6a) Ash
(4.6b) Sawdust
RESULTS AND DISCUSSION 65
(4.6c) Clay
(4.6d) Kaolin
RESULTS AND DISCUSSION 66
(4.6e) Charcoal dust
Figure 4.6: Temperature response of the particulate sample to a heat pulse
RESULTS AND DISCUSSION 67
Table 4.6: Constants ai, bi, ci for the di�erent samples
Sample i ai bi ciSugar cane �bres 1 34.33 3723 8103
2 -10.87 867.2 11693 10.21 918.1 10054 -2.166 140.9 328.95 2.226 1758 1174
Ash 1 33.86 3700 56852 2.398 1282 1031
Banana �bres 1 38.28 7937 115102 4.534 1998 11073 3.503 1067 739.44 3.017 563 14115 1.756 562 311.5
Sawdust 1 37.98 3036 43022 2.922 926 497.93 4.004 574.3 326.24 3.51 1414 8505 2.723 321 198
Clay 1 55.38 12310 84032 2.998 4125 10883 17.38 1923 15104 28.41 4364 40615 10.06 619.8 867.2
Kaolin 1 50.81 24010 55572 72.21 14680 82953 40.98 6036 48534 21.67 2828 26795 9.993 1224 1505
Charcoal dust 1 38.53 11230 162702 4.076 1630 12283 1.47 32.2 5694 2.948 3455 1399
RESULTS AND DISCUSSION 68
(4.7a) Sugarcane �bres
(4.7b) Banana �bres
Figure 4.7: Graphs of ln(δT ) versus 1/t for �brous samples
RESULTS AND DISCUSSION 69
Table 4.7: Thermal dif�fussivities of the samples
Sample x± 0.05× 10−3/m slope ±3.2/s−1 α± 0.23× 10−7/m2s
Sugarcane �bres 3.50 606.2 5.05Ash 3.50 834.8 3.67
Banana �bres 3.50 376.8 8.13Sawdust 3.50 255.5 1.12Clay 1.50 355.7 1.58Kaolin 3.50 716.7 4.27
Charcoal dust 3.50 503.2 6.09
Table 4.7 shows the values of the thermal dif�fusivities of the samples obtained using the slopes
from the graphs in f�igures 4.7 and 4.8 and x (distance between heater and thermocouple).
The values for thermal dif�fusivities obtained show that the samples have a very low response
to heat.
4.3 Specif�ic heat capacity determination
The specif�ic heat capacities of the samples could not be obtained using the intercepts from
the �gures 4.7 and 4.7 and the quantity of heat supplied (q = ivt) because of the heat losses
which could not be accurately measured. Using the density, thermal dif�fusivities, and thermal
conductivities of the samples, the specif�ic heat capacities of the samples were obtained using
equation (3.2). Table 4.8 shows the determined specif�ic heat capacities of the sample.
Table 4.8: Specif�ic heat capacity of the samples
Sample κ± 0.005/ α± 0.23× 10−7 ρ± 0.3 C ± 17Wm−1K−1 /m2s /kgm−3 /Jkg−1K−1
Sugarcane �bres 0.110 5.05 194.0 1125Ash 0.280 3.67 863.0 900
Banana �bres 0.270 8.13 380.0 874Sawdust 0.230 11.2 218.0 942Clay 0.240 1.58 1650.0 919Kaolin 0.480 4.27 1665.0 677
Charcoal dust 0.220 6.09 450.0 800
Results obtained show that sugarcane �bres have the highest specif�ic heat capacity therefore
RESULTS AND DISCUSSION 70
(4.8a) Ash
(4.8b) Sawdust
RESULTS AND DISCUSSION 71
(4.8c) Clay
(4.8d) Kaolin
RESULTS AND DISCUSSION 72
(4.8e) Charcoal dust
Figure 4.8: Graphs of ln(δT ) versus 1/t for particulate samples
RESULTS AND DISCUSSION 73
has a high capacity to retain heat and kaolin has the lowest specif�ic heat capacity.
Chapter 5
CONCLUSIONS AND
RECOMMENDATIONS
5.1 Conclusions
Thermal conductivity at room temperature, thermal dif�fusivitiy and specif�ic heat capacity
have been determined for the selected samples.
The results show that all the samples studied are good insulating materials because they
have:
(i) Low thermal conductivities hence the rate of heat transfer in these samples is low.Their
thermal conductivities ranged from 0.08 to 0.55Wm−1K−1.
(ii) Low thermal di�usivities of the order of therefore these samples have a low response to
a heat pulse.
(iii) Moderate speci�c heat capacity which means that these materials have the ability to
retain heat. The speci�c heat capacity of the samples obtained were in the range of 900
to 1125 Jkg−1K−1 for clay, ash, sawdust and sugarcane �bres and 677 to 872Jkg−1K−1
for kaolin, charcoal dust and banana �bres .
74
CONCLUSIONS AND RECOMMENDATIONS 75
It has also been noted that among the materials studied, sugarcane f�ibres can provide the
best thermal insulation for thermal energy storage systems (TES) since it has the lowest
thermal conductivity and highest specif�ic heat capacity.
The variation of thermal conductivity with particle/f�ibre size and with compaction pressure
has been clearly established. Thermal conductivity increases with decreasing particle size
and increases with increasing compaction pressure due to a decrease in porosity.
5.2 Recommendation for future work
This study has covered only seven materials. There are other materials available in Uganda
which can be used as thermal insulating materials such as sisal, paper, cotton lint and others.
The thermal properties of these materials would be studied so as to obtain the best thermal
insulating material.
To fully characterise the studied materials as insulating materials, properties like compressive
strength and water absorption should be investigated.
Also a study to consider application of the recommended material (sugarcane f�ibres) as a
thermal insulation material using life cycle analysis to evaluate environmental and health
impacts need be carried out.
There is need to investigate the appropriate form in which sugarcane f�ibres can be used for
insulation in TES systems. This study should analyse whether sugarcane f�ibres are best used
for insulation as dried crushed samples or just dried.
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APPENDIX I 84
Appendix I: Temperature response of the samples to a heat pulse.
pulse.AVERAGE TEMPERATURE±0.05oCTime/s Sugarcane �bres Banana �bres Ash Sawdust Clay Kaolin Charcoal dust
0 24.4 24.8 23.5 24.2 25.1 25.1 25.130 24.4 24.8 23.5 24.2 25.1 25.1 25.160 24.4 24.9 23.5 24.4 25.3 25.1 25.190 24.4 25.0 23.5 25.2 25.8 25.2 25.2120 24.5 25.1 23.5 26.0 26.6 25.3 25.3150 24.6 25.4 23.6 26.9 27.7 25.7 25.4180 24.8 25.7 23.6 27.8 28.7 26.0 25.6210 25.1 26.0 23.7 28.8 29.8 26.6 25.8240 25.4 26.4 23.8 29.8 30.6 27.3 26.0270 25.6 26.8 24.1 30.4 31.6 28.0 26.2300 25.9 27.1 24.2 31.2 32.5 28.8 26.3330 26.2 27.6 24.5 31.9 33.1 29.5 26.5360 26.5 28.0 24.7 32.5 33.8 30.4 26.7390 26.9 28.3 25.0 33.0 34.6 31.2 27.1420 27.2 28.7 25.2 33.4 35.3 31.7 27.3450 27.5 29.1 25.4 33.9 35.8 32.4 27.5480 27.8 29.5 25.6 34.2 36.3 33.3 27.7510 28.2 29.8 25.9 34.5 36.8 33.9 27.9540 28.5 30.0 26.2 34.8 37.3 34.6 28.1570 28.8 30.3 26.4 35.1 37.7 35.2 28.2600 29.0 30.5 26.6 35.2 38.2 35.8 28.4630 29.3 30.7 26.8 35.5 38.6 36.3 28.6660 29.6 30.8 27 35.6 39.0 36.8 28.8690 29.8 31.0 27.2 35.8 39.4 37.4 29.0720 30.0 31.2 27.4 35.9 39.8 37.8 29.2750 30.1 31.3 27.8 36.1 40.2 38.3 29.5780 30.3 31.5 28.1 36.3 40.6 38.9 29.7810 30.5 31.6 28.2 36.4 40.9 39.3 29.8840 30.7 31.8 28.4 36.4 41.3 39.7 30.0870 30.9 31.9 28.6 36.5 41.7 40.2 30.1900 31.0 32.1 28.9 36.5 42.1 40.7 30.2930 31.2 32.2 29.0 36.6 42.5 41.2 30.3960 31.4 32.4 29.3 36.7 42.8 41.6 30.5990 31.5 32.45 29.7 36.7 43.1 42.1 30.61020 31.6 32.6 29.8 36.8 43.5 42.4 30.61050 31.8 32.8 29.9 36.8 43.8 42.9 30.61080 31.9 32.9 30 36.8 44.2 43.4 30.71110 32.0 33.0 30.1 36.9 45.1 43.9 30.71140 32.1 33.1 30.1 37.1 45.2 44.3 30.81170 32.2 33.3 30.3 37.2 45.4 44.7 30.91200 32.4 33.4 30.4 37.2 45.6 45.2 31.01230 32.4 33.5 30.7 37.3 45.9 45.6 31.11260 32.5 33.7 30.8 37.3 46.1 46.0 31.11290 32.6 33.8 30.9 37.4 46.2 46.4 31.21320 32.7 34.0 30.9 37.4 46.5 46.8 31.41350 32.8 34.1 30.9 37.5 46.7 47.2 31.61380 32.9 34.2 30.9 37.6 46.9 47.5 31.61410 33.0 34.2 31.0 37.6 47.1 47.9 31.81440 33.0 34.3 31.0 37.6 47.2 48.3 31.81470 33.1 34.4 31.0 37.6 47.5 48.8 31.81500 33.1 34.5 31.1 37.7 47.7 49.1 31.9
Apendix I: Temperature response of the samples to a heat pulse 85
AVERAGE TEMPERATURE ±0.05/OCTime/s Sugarcane �bres Banana �bres Ash Sawdust Clay Kaolin Charcoal dust
1530 33.2 34.6 31.1 37.7 47.8 50.0 31.9
1560 33.2 34.7 31.3 37.7 47.9 50.3 32.0
1590 33.3 34.8 31.5 37.8 48.1 50.7 32.0
1620 33.4 34.8 31.6 37.8 48.3 51.0 32.0
1650 33.4 34.9 31.8 37.9 48.5 51.3 32.1
1680 33.5 35.0 31.6 37.9 48.7 51.7 32.1
1710 33.5 35.1 32.0 37.9 48.8 52.0 32.2
1740 33.6 35.1 31.9 38.0 49.0 52.3 32.1
1770 33.6 35.1 31.7 37.9 49.1 52.6 32.2
1800 33.7 35.2 31.8 37.9 49.3 52.8 32.2
1830 33.7 35.2 31.8 38.0 50.0 53.1 32.4
1860 33.8 35.3 31.9 38.0 50.1 53.4 32.5
1890 33.8 35.4 32.1 38.0 50.4 53.7 32.5
1920 33.9 35.4 32.2 38.0 50.5 54.0 32.6
1950 33.9 35.4 32.2 38.0 50.6 54.3 32.7
1980 34.0 35.4 32.2 38.1 50.8 54.6 32.7
2010 34.0 35.5 32.4 38.0 51.0 54.8 32.7
2040 34.0 35.5 32.5 38.0 51.1 55.1 32.7
2070 34.0 35.5 32.7 38.0 51.1 55.4 32.7
2100 34.0 35.6 32.8 38.1 51.2 55.6 32.7
2130 34.0 35.6 32.9 38.1 51.3 55.8 32.7
2160 34.0 35.6 33.1 38.1 51.7 56.0 32.7
2190 34.0 35.7 33.0 38.1 51.7 56.3 32.7
2220 34.0 35.8 32.9 38.1 51.9 56.6 32.8
2250 34.2 35.8 33.0 38.1 51.9 56.8 32.9
2280 34.2 35.8 33.0 38.0 52.0 57.0 32.8
2310 34.2 35.8 32.8 38.0 52.0 57.2 32.9
2340 34.2 35.9 32.9 38.0 52.1 57.4 33.0
2370 34.2 36.0 33.0 38.0 52.2 57.7 33.1
2400 34.3 36.0 33.0 38.0 52.0 58.0 33.1
2430 34.3 36.1 33.0 38.0 52.0 58.2 33.3
2460 34.3 36.1 33.1 38.1 51.9 58.4 33.3
2490 34.2 36.1 33.2 38.1 52.0 58.6 33.4
2520 34.3 36.2 33.1 38.1 52.4 58.8 33.4
2550 34.5 36.2 33.1 38.1 52.5 59.0 33.4
2580 34.5 36.2 33.1 38.2 52.4 59.2 33.6
2610 34.5 36.2 33.2 38.2 52.3 59.4 33.5
2640 34.5 36.2 33.1 38.2 52.3 59.6 33.5
2670 34.5 36.2 33.1 38.2 52.7 59.8 33.5
2700 34.5 36.3 33.2 38.2 52.9 60.1 33.4
2730 34.5 36.3 33.2 38.2 52.8 60.4 33.4
2760 34.5 36.3 33.1 38.1 52.7 60.6 33.3
2790 34.5 36.3 33.1 38.1 52.7 60.8 33.2
2820 34.5 36.4 33.3 38.1 53.3 60.9 33.4
2850 34.5 36.4 33.4 38.1 53.3 61.0 33.4
2880 34.5 36.4 33.4 38.1 53.1 61.2 33.7
2910 34.5 36.4 33.3 38.0 53.1 61.4 33.7
2940 34.5 36.4 33.3 38.0 53.0 61.5 33.7
Apendix I: Temperature response of the samples to a heat pulse 86
AVERAGE TEMPERATURE ±0.05OCTime/s Sugarcane �bres Banana �bres Ash Sawdust Clay Kaolin Charcoal dust
2970 34.5 36.4 33.4 38.0 53.0 61.8 33.7
3000 34.5 36.4 33.4 38.0 53.1 61.8 33.7
3030 34.5 36.4 33.5 38.0 53.7 62.1 33.7
3060 34.6 36.4 33.6 38.0 53.5 62.4 33.6
3090 34.6 36.4 33.6 38.0 53.3 62.4 33.6
3120 34.6 36.4 33.7 38.0 53.2 62.5 33.6
3150 34.6 36.5 33.7 38.0 53.2 62.7 33.7
3180 34.5 36.5 33.7 38.0 53.2 62.8 33.7
3210 34.5 36.6 33.8 38.0 53.2 62.9 33.8
3240 34.5 36.6 33.8 38.0 53.9 63.0 33.8
3270 34.5 36.6 33.9 38.0 53.8 63.3 33.9
3300 34.5 36.6 33.9 53.6 63.8 33.8
3330 34.5 36.7 33.9 53.9 63.9 33.9
3360 34.5 36.7 34.0 53.4 63.9 33.9
3390 34.5 36.7 33.8 53.4 63.9 33.9
3420 34.5 36.7 33.6 53.4 64.0 34.0
3450 34.5 36.7 33.8 53.4 64.1 34.1
3480 34.5 36.7 33.9 53.4 64.3 34.3
3510 34.5 36.7 34.1 53.4 64.5 34.2
3540 34.5 36.7 34.0 53.4 64.6 34.3
3570 34.5 36.7 33.8 53.5 64.6 34.1
3600 34.5 36.8 33.7 53.7 64.7 34.1
3630 34.5 36.7 33.8 54.3 64.8 34.3
3660 34.5 36.7 33.5 53.3 64.9 34.2
3690 34.4 36.8 33.4 53.8 65.0 34.2
3720 34.4 36.9 33.4 53.7 65.1 34.2
3750 34.4 36.9 33.4 53.6 65.2 34.2
3780 34.4 36.9 33.5 54.4 65.3 34.2
3810 34.4 36.9 33.7 54.7 65.4 34.2
3840 34.4 36.9 33.6 54.7 65.5 34.2
3870 34.4 36.9 33.6 54.6 65.6 34.2
3900 34.4 36.9 33.5 54.6 65.8 34.2
3930 36.9 33.4 54.5 65.9 34.2
3960 37.0 33.6 54.5 66.0 34.3
3990 37.0 33.8 54.6 66.1 34.3
4020 37.0 33.9 54.6 66.2 34.3
4050 37.0 34.0 54.7 66.4 34.3
4080 37.0 33.9 54.7 66.6 34.3
4110 37.0 33.9 54.8 66.9 34.3
4140 37.0 34.0 54.8 66.9 34.3
4170 37.0 34.1 54.9 66.9 34.3
4200 37.0 33.8 54.9 67.0 34.2
4230 37.0 33.8 54.9 67.0 34.2
4260 37.1 33.6 55.0 66.9 34.1
4290 37.1 33.5 55.1 66.9 34.2
4320 37.1 33.5 55.2 67.1 34.2
4350 37.0 55.3 67.2 34.2
4380 37.0 55.5 67.4 34.2
4410 37.0 55.5 67.4 34.2
4440 37.0 55.4 67.5 34.1
4470 36.9 55.4 67.6 34.2
4500 37.0 55.3 67.6 34.1
Apendix I: Temperature response of the samples to a heat pulse 87
AVERAGE TEMPERATURE±0.05OCTime±1/s Banana �bres Clay Kaolin Charcoal dust
4530 36.9 55.2 67.6 34.2
4560 36.8 55.0 67.7 34.2
4590 36.8 55.0 67.8 34.2
4620 36.8 55.0 67.9 34.2
4650 36.9 55.0 68.1 34.1
4680 37.0 55.0 68.2 34.0
4710 37.0 55.1 68.2 34.0
4740 37.0 55.3 68.2 34.1
4770 37.0 55.3 68.3 34.1
4800 37.0 55.4 68.3 34.1
4830 37.0 55.4 68.3 34.2
4860 37.0 55.4 68.4 34.2
4890 37.1 55.4 68.5 34.2
4920 37.0 55.5 68.8 34.2
4950 36.9 55.5 68.7 34.2
4980 36.9 55.5 68.7 34.1
5010 36.9 55.5 68.8 34.1
5040 36.9 55.6 69.1
5070 55.5 69.1
5100 55.5 69.2
5130 55.4 69.3
5160 55.4 69.3
5190 55.4 69.3
5220 55.6 69.4
5250 55.6 69.4
5280 55.6 69.5
5310 55.6 69.5
5340 55.6 69.6
5370 55.7 69.6
5400 55.7 69.7
5430 55.7 69.7
5460 55.7 69.7
5490 55.7 69.7
5520 55.7 70.0
5550 55.7 70.0
5580 55.7 70.0
5610 55.7 70.1
5640 55.8 70.1
5670 55.8 70.1
5700 55.9 70.1
5730 55.9 70.1
5760 55.9 70.1
5790 55.9 70.3
5820 55.9 70.6
5850 55.8 70.7
5880 55.9 70.7
5910 55.9 70.7
5940 55.9 70.9
5970 56.0 71.1
6000 56.1 71.1
Apendix I: Temperature response of the samples to a heat pulse 88
Time±1/s Clay Kaolin Time±1/s Clay Kaolin Time±1/s Clay Kaolin
6030 56.0 71.0 7530 54.9 72.6 9030 55.5 73.7
6060 56.0 71.0 7560 54.9 72.6 9060 55.5 73.7
6090 55.9 70.9 7590 54.9 72.7 9090 55.5 73.6
6120 55.9 70.9 7620 54.7 72.6 9120 55.5 73.6
6150 56.1 70.9 7650 54.7 72.5 9150 55.5 73.5
6180 56.1 70.8 7680 54.7 72.5 9180 55.5 73.5
6210 56.0 70.9 7710 54.8 72.5 9210 55.4 73.5
6240 56.0 70.9 7740 54.8 72.6 9240 55.4 73.4
6270 55.9 71.0 7770 54.8 72.8 9270 55.5 73.3
6300 56.0 71.0 7800 54.9 72.8 9300 55.5 73.3
6330 56.1 71.0 7830 55.0 72.8 9330 55.5 73.2
6360 56.0 71.2 7860 55.1 72.9 9360 55.5 73.1
6390 56.0 71.2 7890 55.2 72.9 9390 55.4 73.1
6420 56.0 71.2 7920 55.2 72.9 9420 55.4 73.2
6450 55.9 71.2 7950 55.2 72.8 9450 55.4 73.2
6480 55.8 71.2 7980 55.3 72.8 9480 55.4 73.2
6510 55.4 71.3 8010 55.6 72.8 9510 55.4 73.2
6540 55.7 71.2 8040 55.6 72.9 9540 55.4 73.2
6570 55.6 71.2 8070 55.6 72.9 9570 55.5 73.5
6600 55.7 71.3 8100 55.6 72.9 9600 55.5 74.0
6630 55.6 71.4 8130 55.6 72.9 9630 55.5 74.1
6660 55.6 71.4 8160 55.7 72.9 9660 55.5 74.1
6690 55.8 71.4 8190 55.7 72.9 9690 55.4 74.0
6720 55.9 71.5 8220 55.6 72.9 9720 55.5 73.9
6750 55.8 71.5 8250 55.6 73.0 9750 55.5 73.7
6780 55.9 71.5 8280 55.6 73.0 9780 55.5 73.7
6810 56.0 71.6 8310 55.5 73.0 9810 55.4 73.6
6840 55.1 71.6 8340 55.4 73.0 9840 55.4 73.6
6870 56.0 71.7 8370 55.3 73.1 9870 55.4 73.6
6900 55.9 71.7 8400 55.3 73.1 9900 55.4 73.6
6930 55.7 71.8 8430 55.3 73.1 9930 55.3 73.6
6960 55.9 71.9 8460 55.2 73.1 9960 55.3 73.5
6990 55.9 71.8 8490 55.2 73.2 9990 55.5 73.5
7020 55.7 71.8 8520 55.2 73.2 10020 55.4 73.5
7050 55.7 71.9 8550 55.2 73.2 10050 55.4 73.4
7080 55.8 72.1 8580 55.2 73.1 10080 55.5 73.4
7110 55.7 72.3 8610 55.2 73.1 10110 55.5 73.5
7140 55.7 72.6 8640 55.1 73.1 10140 55.4 73.5
7170 55.6 72.6 8670 55.2 73.2 10170 55.5 73.5
7200 55.5 72.6 8700 55.3 73.4 10200 55.4 73.7
7230 55.4 72.4 8730 55.3 73.3 10230 55.5 73.7
7260 55.6 72.4 8760 55.3 73.4 10260 55.6 73.6
7290 55.7 72.4 8790 55.3 73.4 10290 55.6 73.9
7320 55.7 72.5 8820 55.3 73.5 10320 55.5 73.9
7350 55.6 72.5 8850 55.4 73.5 10350 55.5 73.9
7380 55.4 72.5 8880 55.4 73.5 10380 55.5 73.8
7410 55.4 72.5 8910 55.5 73.5 10410 55.5 73.7
7440 55.3 72.6 8940 55.5 73.7 10440 55.6 73.6
7470 55.2 72.5 8970 55.4 73.9 10470 55.6 73.5
7500 55.0 75.6 9000 55.4 73.8 10500 55.6 73.7
Apendix I: Temperature response of the samples to a heat pulse 89
Time±1/s Clay Kaolin Time±1/s Kaolin Time±1/s Kaolin Time±1/s Kaolin
10530 55.5 74.3 12000 74.7 13470 76.2 14940 77.1
10560 55.6 74.5 12030 74.6 13500 76.2 14970 77.0
10590 55.6 74.4 12060 74.6 13530 76.2 15000 76.9
10620 55.6 74.2 12090 74.8 13560 76.1 15030 76.9
10650 55.6 74.2 12120 74.9 13590 76.1 15060 77.0
10680 55.5 74.0 12150 74.8 13620 76.2 15090 77.0
10710 55.5 73.9 12180 74.9 13650 76.2 15120 77.1
10740 55.5 73.7 12210 74.9 13680 76.1 15150 77.1
10770 55.5 73.7 12240 74.9 13710 76.2 15180 76.9
10800 55.4 73.6 12270 75.0 13740 76.2 15210 76.9
10830 55.4 73.7 12300 74.9 13770 76.2 15240 77.1
10860 55.4 73.7 12330 74.9 13800 76.1 15270 77.1
10890 55.5 73.7 12360 75.0 13830 76.2 15300 77.2
10920 55.6 73.7 12390 75.0 13860 76.2 15330 77.1
10950 55.7 73.8 12420 75.1 13890 76.2 15360 77..0
10980 55.7 73.8 12450 75.1 13920 76.1 15390 77.1
11010 55.8 73.8 12480 75.2 13950 76.0 15420 77.0
11040 55.8 73.8 12510 75.2 13980 76.1 15450 76.9
11070 55.9 73.9 12540 75.2 14010 76.2 15480 77.0
11100 55.9 74.1 12570 75.3 14040 76.2 15510 77.1
11130 55.9 74.4 12600 75.3 14070 76.2 15540 77.2
11160 55.9 74.4 12630 75.3 14100 76.3 15570 77.1
11190 55.8 74.3 12660 75.4 14130 76.3 15600 77.2
11220 55.7 74.3 12690 75.4 14160 76.4 15630 77.1
11250 55.8 74.2 12720 75.4 14190 76.4 15660 77.2
11280 55.9 74.2 12750 75.4 14220 76.3 15690 77.1
11310 56.0 74.0 12780 75.4 14250 76.4 15720 77.1
11340 56.0 74.0 12810 75.5 14280 76.4 15750 77.2
11370 56.1 74.1 12840 75.4 14310 76.5 15780 77.1
11400 56.1 74.1 12870 75.4 14340 76.4 15810 77.2
11430 56.1 74.3 12900 75.4 14370 76.6 15840 77.2
11460 56.2 74.4 124930 75.5 14400 76.9 15870 77.1
11490 56.2 74.5 12960 75.5 14430 76.8 15900 77.4
11520 56.4 74.6 12990 75.5 14460 76.8 15930 77.4
11550 56.5 74.7 13020 75.7 14490 76.7 15960 77.4
11580 56.6 74.8 13050 75.7 14520 76.5 15990 77.4
11610 56.7 74.7 13080 75.7 14550 76.5 16020 77.5
11640 56.7 74.6 13110 75.7 14580 76.5 16050 77.5
11670 56.7 74.6 13140 75.7 14610 76.5 16080 77.5
11700 56.6 74.5 13170 75.7 14640 76.5 16110 77.4
11730 56.6 74.5 13200 75.7 14670 76.6 16140 77.5
11760 56.6 74.5 13230 75.8 14700 76.6 16170 77.5
11790 74.6 13260 75.8 14730 76.5 16200 77.5
11820 74.6 13290 75.7 14760 76.7 16230 77.5
11850 74.7 13320 75.7 14790 76.7 16260 77.4
11880 74.6 13350 75.7 14820 76.7 16290 77.4
11910 74.6 13380 75.7 14850 76.8 16320 77.4
11940 74.7 13410 75.8 14880 77.0 16350 77.4
11970 74.8 13440 76.1 14910 77.0 16380 77.5
Apendix I: Temperature response of the samples to a heat pulse 90
Time±1/s Kaolin Time±1/s Kaolin Time/s Time±1/s Time±1/s Kaolin Time±1/s Kaolin
16410 77.5 17880 77.5 19350 77.5 20820 78.5 22290 76.9
16440 77.4 17910 77.6 19380 77.6 20850 78.6 22320 76.8
16470 77.4 17940 77.6 19410 77.6 20880 78.6 22350 76.8
16500 77.5 17970 77.7 19440 77.5 20910 78.5 22380 76.8
16530 77.7 18000 77.7 19470 77.6 20940 78.6 22410 76.8
16560 77.7 18030 77.7 19500 78.4 20970 78.4 22440 76.7
16590 77.6 18060 77.6 19530 78.4 21000 78.4 22470 76.7
16620 77.5 18090 77.6 19560 78.3 21030 78.4 22500 756.7
16650 77.7 18120 77.5 19590 78.1 21060 78.3 22530 76.7
16680 77.6 18150 77.4 19620 78.1 21090 78.3 22560 76.7
16710 77.5 18180 77.4 19650 78.0 21120 78.4 22590 76.7
16740 77.6 18210 77.5 19680 78.1 21150 78.8 22620 76.6
16770 77.6 18240 77.7 19710 78.1 21180 78.7 22650 76.5
16800 77.6 18270 77.7 19740 78.0 21210 78.9 22680 76.5
16830 77.5 18300 77.6 19770 78.0 21240 79.0 22710 76.5
16860 77.6 18330 77.6 19800 78.0 21270 78.9 22740 76.5
16890 77.5 18360 77.6 19830 78.0 21300 79.2 22770 76.5
16920 77.6 18390 77.6 19860 78.0 21330 78.8 22800 76.4
16950 77.6 18420 77.6 19890 78.0 21360 79.0
16980 77.6 18450 77.5 19920 78.0 21390 78.8
17010 77.6 18480 77.6 19950 78.0 21420 78.8
17040 77.6 18510 77.5 19980 78.0 21450 78.6
17070 77.5 18540 77.5 20010 78.0 21480 78.3
17100 77.5 18570 77.4 20040 78.0 21510 78.3
17130 77.6 18600 77.4 20070 78.0 21540 78.1
17160 77.7 18630 77.4 20100 78.1 21570 78.3
17190 77.8 18660 77.4 20130 78.0 21600 78.3
17220 77.7 18690 77.2 20160 77.8 21630 78.2
17250 77.7 18720 77.2 20190 77.9 21660 78.2
17280 77.7 18750 77.1 20220 78.1 21690 78.0
17310 77.8 18780 77.2 20250 78.1 21720 78.0
17340 77.7 18810 77.2 20280 78.1 21750 77.9
17370 77.7 18840 77.2 20310 78.2 21780 77.8
17400 77.7 18870 77.2 20340 78.2 21810 77.8
17430 77.7 18900 77.2 20370 78.1 21840 77.8
17460 77.8 18930 77.2 20400 78.2 21870 77.7
17490 77.8 18960 77.3 20430 78.2 21900 77.7
17520 77.7 18990 77.3 20460 78.2 21930 77.7
17550 77.6 19020 77.4 20490 78.4 21960 77.6
17580 77.7 19050 77.4 20520 78.4 21990 77.5
17610 77.8 19080 77.4 20550 78.3 22020 77.5
17640 77.8 19110 77.4 20580 78.4 22050 77.4
17670 77.7 19140 77.5 20610 78.4 22080 77.3
17700 77.7 19170 77.5 20640 78.4 22110 77.3
17730 77.7 19200 77.5 20670 78.4 22140 77.2
17760 77.7 19230 77.4 20700 78.4 22170 77.2
17790 77.6 19260 77.5 20730 78.5 22200 77.1
17820 77.4 19290 77.6 20760 78.4 22230 77.1
17850 77.5 19320 77.5 20790 78.5 22260 77.0