Redesigning the ME 331 Heat Conduction Experiment
Prepared by Alan Guthrie, Michael Hartley,
Alex Moon, and Krista Simonson
Group E
Prepared for Mr. Shazib Vijlee, Mechanical Engineering PhD Student
University of Washington
June 2012
EXECUTIVE SUMMARY
This report provides a detailed discussion of the work completed by Group E in designing
and manufacturing a new heat conduction lab experiment for the ME 331 Heat Transfer
class at the University of Washington. The objective of this project is to design and test this
lab experiment that will test students’ understanding of heat transfer by conduction, while
producing consistent, accurate, and measurable results.
The final concept design that was selected is a cylindrical setup, where students are
required to measure the temperature difference across the radius of a cylindrical specimen.
The lab prototype consists of a heating rod, wrapped in the material to be tested and
suspended in the air with support blocks, made out of Temperlite insulation, on each end of
the rod. The power is controlled by a variac, which regulates the voltage received by the
heating rod. Data acquisition is performed with thermocouples attached to the inner and
outer surfaces of the specimen in coordination with Personal Daq View software. The
specimen being tested is ultra-flexible foam rubber pipe insulation with a literature thermal
conductivity value of 0.036 W/m-K. There is also a lab handout that will be handed to the
students that instructs them on how to collect the data and analyze it, testing their ability to
apply the conduction equation to a radial system. Additionally, a COMSOL pre-lab activity
was designed to enhance the students’ lab experience.
This design is a significant improvement to the conduction lab experiment currently in use
by the ME 331 Heat Transfer class instructors. The current system consistently gives
students a large percent error between measured and theoretical values. This new
cylindrical design eliminates much of the error due to multidimensionality that was present
in the old lab, and consistently produces results with a percent error of 10-15% for the
calculated thermal conductivity. The system is simple to operate, and the designed lab
handout adequately tests the students’ understanding of the fundamental concepts
surrounding heat conduction. The design is not as interesting or as complex as multilayered systems, but it produces accurate, consistent results.
If approved by the client and future instructors of the ME 331 Heat Transfer class, this lab
experiment could easily be incorporated into the class curriculum. It would make an
excellent addition to the course and would give students’ an opportunity to physically apply
the concepts they are being taught in the classroom.
ii TABLE OF CONTENTS
LIST OF FIGURES .............................................................................................................. v
LIST OF TABLES ................................................................................................................ v
INTRODUCTION ................................................................................................................. 1
Background ..................................................................................................................................... 1
Purpose ............................................................................................................................................ 1
DESIGN PROBLEM DEFINITION ................................................................................... 2
CURRENT TECHNOLOGY ............................................................................................... 3
CONCEPT GENERATION, EVALUATION, AND SELECTION ................................. 4
Overall Setup of New Lab .............................................................................................................. 4
Box Setup ..................................................................................................................................... 5
Cylindrical Setup ..........................................................................................................................5
Determining Material .....................................................................................................................6
Large Temperature Gradient ........................................................................................................ 6
Steady-State Arrival Time ............................................................................................................ 7
Availability and Machinability of Cylindrical Specimen .............................................................7
Multi-Layered System ....................................................................................................................7
In-Lab Experiment and Post-Lab Write-Up................................................................................8
Single Cylindrical Setup ............................................................................................................... 8
Compare Two Cylindrical Setups with Different Materials .........................................................8
Old vs. New Setup and Comparing Results for Same Material ...................................................8
COMSOL Pre-Lab Activity ........................................................................................................... 9
FINAL CONCEPTUAL DESIGN ....................................................................................... 9
General Description ........................................................................................................................9
Components ................................................................................................................................... 10
Heating Rod ................................................................................................................................10
Design .................................................................................................................................................... 10
Advantages/Disadvantages .................................................................................................................... 11
Ultra-Flexible Foam Rubber Pipe Insulation.............................................................................. 11
Design .................................................................................................................................................... 11
Advantages/Disadvantages .................................................................................................................... 11
Thermocouples ...........................................................................................................................12
Design .................................................................................................................................................... 12
Advantages/Disadvantages .................................................................................................................... 12
Temperlite Blocks.......................................................................................................................13
Design .................................................................................................................................................... 13
Advantages/Disadvantages .................................................................................................................... 13
Data Acquisition Setup and Power Supply.................................................................................13
Design .................................................................................................................................................... 13
Advantages/Disadvantages .................................................................................................................... 14
Lab Handout 1: Old vs. New Setup and Comparing Results for Same Material .......................14
Lab Handout 2: Single Cylindrical Setup ...................................................................................14
COMSOL Pre-Lab Activity........................................................................................................ 15
DETAILED DESIGN, PROTOTYPE MANUFACTURE AND EVALUATION ........ 15
MODELING AND ANALYSIS ......................................................................................... 16
ECONOMIC/COST EVALUATION ................................................................................ 19
iii CONSIDERATION OF THE BROADER CONTEXT OF DESIGN ............................ 20
Risk and Liability .........................................................................................................................20
Ethical Issues/Societal Impact ..................................................................................................... 20
Impact on Environment ............................................................................................................... 20
FUTURE WORK ................................................................................................................ 20
REFERENCES .................................................................................................................... 22
APPENDIX A: LAB HANDOUT FOR CURRENT CONDUCTION LAB .................. 23
APPENDIX B: MATLAB CODE ...................................................................................... 26
APPENDIX C: LAB HANDOUT INCORPORATING RECTANGULAR AND
CYLINDRICAL CONDUCTION LABS .......................................................................... 27
APPENDIX D: LAB HANDOUT FOR THE CYLINDRICAL CONDUCTION LAB 31
APPENDIX E: COMSOL PRE-LAB ACTIVITY ........................................................... 34
APPENDIX F: TESTING RESULTS ............................................................................... 41
iv LIST OF FIGURES
Figure 1. Current Conduction Lab Setup .......................................................................... 4
Figure 2. Schematic for the Current Conduction Lab...................................................... 5
Figure 3. Final Setup of the Redesigned Lab .................................................................... 10
Figure 4. Cylindrical Heating Rod with Tape .................................................................. 10
Figure 5. Cross Sectional View of the Foam Rubber Pipe Insulation ............................ 11
Figure 6. Placement of Thermocouples along Heating Rod ............................................ 12
Figure 7. Placement of Thermocouples along Outside of Insulation.............................. 12
Figure 8. Temperlite Block ................................................................................................. 13
Figure 9. Power Supply System ......................................................................................... 14
Figure 10. COMSOL Simulation of the Cylindrical Model ............................................ 15
Figure 11. May 22, 2012 Test of Foam Rubber: k vs. Distance From End of Specimen
............................................................................................................................................... 18
Figure 12. Range of Thermal Conductivities for Silicone Foams .................................. 19
LIST OF TABLES
Table I. Pugh Chart Comparing Characteristics of Different Materials ........................ 6
Table II. May 22, 2012 Test Results for Foam Rubber Insulation ................................. 17
Table F1. May 10 Testing Results ...................................................................................... 41
Table F2. May 11 Testing Results ...................................................................................... 41
Table F3. May 15 Testing Results ...................................................................................... 41
Table F4. May 17 Testing Results ...................................................................................... 41
Table F5. May 22 Testing Results ...................................................................................... 42
Table F6. May 16 Testing Results ...................................................................................... 42
Table F7. May 17 Testing Results ...................................................................................... 42
Table F8. May 21 Testing Results ...................................................................................... 42
v INTRODUCTION
Background
Mechanical Engineering students at the University of Washington are required by ABET
standards to complete a heat transfer class in order to obtain their Bachelor’s degree. This course
covers the conduction and convection modes of heat transfer with experiments. Due to extreme
experimental error, arising in no small part from incorrect assumptions about the directionality of
heat transfer, the laboratory experiment for conduction must be remade. Our client Shazib
Vijlee, a graduate student in the Mechanical Engineering department, believes that the error can
be mostly eliminated by switching from a rectangular model to a cylindrical one.
Conduction is the transfer of heat through solid surfaces. It is governed by the conduction
equation, which relates heat flow to the temperature gradient present, the physical dimensions of
the solid, and the thermal conductivity of the material. For uniaxial heat flow, the equation takes
!"
the form 𝑞 = −𝑘𝐴 !" , where q is equal to heat flow measured in Watts, k is the thermal
conductivity measured in W/m-K, A is the cross sectional area measured in m2, and dT/dx is the
change in temperature across the length of the specimen. Heat is always transferred in the
direction of decreasing temperature. The application of the conduction equation to a cylindrical
system is as follows:
𝑞=
2𝜋𝐿𝑘 𝑇!! − 𝑇!!
ln 𝑟! 𝑟!
L is the length of the cylinder measured in meters, Ts1 is the temperature of the inner surface
measured in Kelvin, Ts2 is the temperature of the outer surface measured in Kelvin, r1 is the inner
radius in meters, and r2 is the outer radius in meters. This allows one to calculate the heat flow in
the radial direction of a cylindrical specimen, and it is the equation that was applied throughout
or design and evaluation of or product. [1]
Purpose
The University of Washington’s Mechanical Engineering Program requires all undergraduates to
complete the fundamental curricula in order to obtain a bachelor’s degree. Of these fundamental
curricula, the ME 331 course introduces students to the study of heat transfer by conduction,
convection, and radiation. The current course is taught by Professor Emery, who also oversees
the coursework, and is assisted by Shazib Vijlee. Sponsored by Professor Emery, Shazib Vijlee
has presented an opportunity to redesign the current ME 331 heat conduction lab exercise to
having a working lab that can provide accurate results as well as improve students’ connection to
the theory taught in class. The objective of this project is to design and test such a lab
experiment that will test students’ understanding of heat transfer by conduction, while producing
consistent, accurate, and measurable results.
1 DESIGN PROBLEM DEFINITION
The main objective of this project is to design and build a new conductive heat transfer
experiment for the ME 331 Heat Transfer class. The purpose of the new setup is to further
enforce the heat conduction theory through a physical model in which information can be
analyzed. Through the communication with our client, Shazib, we have established a list of
functional requirements that our client would like to be addressed through our project. Below,
these requirements have been ranked by the manner of importance:
1. Students should be able to match analysis of the experiment with a theory learned in
class.
2. The experiment must be safe, meaning it won’t catch fire and the external surface won’t
be so hot that it would cause serious injury to students who touched it.
3. Reduce heat flow in unwanted directions.
4. Experiment setup takes approximately 30 minutes to reach steady state.
5. Experiment is capable of measuring desired parameters.
6. Have working data acquisition system that provides accurate data.
7. Temperature must be measured at a minimum of two locations along in the desired
direction of conductive heat flow (at the heater-material interface and the external surface
of the material), but the more temperature measuring locations the better.
8. Choose materials so that there is a large change of temperature observed during the
experiment.
9. Write up a lab exercise with an answer key showing the expected results.
10. Use of COMSOL in the lab exercise. Students should model what they experienced in lab
and possibly model other materials unable to be tested in this lab setting.
11. Make experiment as “visual” as possible.
We realized that our client had given us two goals that are compliant with these functional
requirements; a realistic goal and an aggressive goal. The client’s realistic goal is that we design
and build a conductive heat transfer experiment but the aggressive goal is that along with
building a conductive heat transfer experiment, we test and create a working lab exercise with an
answer key. With this, our group has went along with completing the client’s aggressive goal.
However, with this in mind, there are constraints associated with this project that may limit our
ideas.
Our design constraints are fairly straightforward and simple. First of all, the design must be safe.
The operating temperature of the model must be at a level that would not cause any materials to
catch fire or cause any harm to students. In addition, the power setup must be constructed in a
way that protects the user from being electrocuted. With regards to materials, we plan on using
the current and voltage generators already supplied in the lab, so that is an additional design
constraint. Our client has estimated our budget for this project to be around $1000, so we must
design and construct our lab experiment in an economical fashion. Next, the consideration of the
physical size of the lab experiment was important to address. By having the physical size of the
lab experiment to be relatively small, we hope that this will allow it to have a spot in the heat
transfer lab area. There is plenty of space in the lab, but we plan on constructing something that
can sit on a single table. Time is also a limiting factor. Students that eventually run the lab
2 exercise must be able to complete all steps and obtain useful data in an hour or 1.5 hour session.
Since the data acquisition must occur while the model is at steady state, we need to design the
lab experiment to reach steady state in about one half hour. Finally, this lab must be something
that can be done repeatedly and produce similar results each time. Directions for conducting the
experiment and data analysis have to be simple enough for an undergraduate heat transfer class
of students to follow without difficulty.
CURRENT TECHNOLOGY
The current setup is intended to produce conductive heat transfer through solid materials in a
single direction. It consists of a plate heating element, on which rests a balsa wood block
sandwiched between two aluminum plates, all of which is surrounded by layers of insulation.
Thermocouples are attached to the top and bottom of the balsa wood block, and one is embedded
in its geometric center. The power input to the heating element is determined by the
multiplication of the voltage drawn and the current flowing through the element. The lab
handout that is currently given to students in coordination with this experiment is included in
Appendix A.
This setup produces unreasonably high experimental error, routinely being upwards of 250% [2].
One of the critical flaws is that a large fraction of the generated heat is transferred through the
insulation. The hole cut in the insulation to allow the balsa wood and aluminum to be inserted is
larger than these blocks, allowing convection to occur. The aluminum and balsa wood are
compressed by a heavy weight mounted on top, but there is nonetheless some contact resistance.
The experiment has been run a number of times, potentially altering the physical structure of the
balsa wood; the insulation shows visual evidence of heat damage. Figure 1 is a picture of this.
3 Figure 1. Current Conduction Lab Setup
CONCEPT GENERATION, EVALUATION, AND SELECTION
Overall Setup of New Lab
The client requested that our team improve the current heat conduction lab setup. The current
setup is made up of a box that measures the thermal conductivity through a balsa wood block. A
schematic of this lab setup is shown in Figure 2. The client did not give us any specific
requirements as to the overall setup of the lab but did suggest a cylindrical system. Therefore,
our team had the option of improving the current box setup or creating and testing a new
cylindrical one. Our team chose to continue working with the system that produced the most
accurate results for the thermal conductivity of a material when compared to its literature value.
4 Figure 2. Schematic for the Current Conduction Lab
Box Setup
The current setup, as described above, was arranged in a box where the thermal conductivity of a
balsa would block was measured. This was done by sandwiching the balsa wood block between
two metal plates with a heater placed below the bottom plate. The rest of the box was filled with
a hard insulation and the balsa wood block was surrounded by an insulation blanket in an effort
to direct heat flow through the balsa wood block. This current lab setup has many errors
associated with it due to multidimensionality, aging, and excess convection. With this old lab
setup, our team could find a way to better control the heat flow by trying to simulate a Guarded
Hot Plate Apparatus and by replacing aged materials. Past lab reports from previous quarters
have provided us with the results of this lab and the difference between the calculated thermal
conductivity values from the lab and the literature values.
Cylindrical Setup
A cylindrical setup was recommended to our team by our client. This kind of setup is essentially
in the shape of a long, narrow cylinder. Therefore, this design would include a cylindrical shaped
heater that would be wrapped with some kind of tubular shaped material. The idea is that the lab
setup would consist of a long enough heating specimen that the students could assume an infinite
rod and apply the heat conduction equation for a 1D cylindrical system. In order for the students
to be able to make this assumption, the heating rod would have to have a length to diameter ratio
greater than ten. Our team conducted many tests to determine the accuracy of this lab setup in
comparison to the old one.
5 Determining Material
When discussing what material to use for this project, our team considered three main
characteristics: 1) temperature gradient across the thickness of the material, 2) steady-state
arrival time, and 3) availability and/or machinablility of a cylindrical specimen. Some of the
materials we talked about were metals such as aluminum, copper, and stainless steel, clay, balsa
wood, pipe insulation (foam rubber and silicone foam), and Temperlite insulation. Some of these
materials are compared in a Pugh Chart in Table I.
Table I. Pugh Chart Comparing Characteristics of Different Materials
Materials
Metals
Characteristics
Large
Temperature
Gradient
Quick to
Steady-State
Availability
Machinability
Totals
Plus
Minus
Same
Score
Balsa
Wood
(0.055
W/m∙K)
Pipe Insulation
Aluminum
(237
W/m∙K)
Copper
(401
W/m∙K)
Stainless
Steels
(13.415.1
W/m∙K)
Clay
(1.3
W/m∙K)
Foam
Rubber
(0.036
W/m∙K)
Silicone
Foam
(0.056
W/m∙K)
Temperlite
Insulation
(0.06
W/m∙K)
D
A
T
U
M
-
-
-
S
S
S
S
+
+
+
S
S
S
S
S
+
S
+
S
+
-
+
+
+
+
+
-
-
2
1
1
1
2
1
1
1
2
1
1
1
0
2
2
-2
2
0
2
2
2
0
2
2
1
1
2
0
Large Temperature Gradient
One of our functional requirements was to ensure that there was a large change in temperature,
which we decided was 20°C or greater, across the thickness of the material. A temperature
gradient of 20°C or more creates a more interesting lab and more importantly, allows for more
accurate calculations of the thermal conductivity of the lab material. To find this we wrote a code
in MATLAB using the heat conduction equation for a 1D system. The code we used is shown in
Appendix B. By holding dimensions, power input, and material thickness constant and
experimenting with different materials and their literature thermal conductivity values, we were
able to find a relationship between thermal conductivity and the temperature gradient. We found
that in order to achieve a large temperature gradient the thermal conductivity of the material
should be less than about 1 W/m∙K. This means conductive materials such as metals would cause
very little to no change in temperature in the lab experiment.
6 Steady-State Arrival Time
Another one of our client’s requests was that our lab system reaches steady-state within a half an
hour of turning it on. Steady-state means that the temperature is no longer changing with time
and can be seen when the system reaches a maximum temperature and stays at this temperature
for an extended period of time. We attempted to explore the mathematical theory used to
calculate steady state time for various scenarios involving heat transfer, but it proved to be a
more complicated analysis than we originally expected. A complete analysis and computation
involves advanced differential mathematics that we felt was unnecessary given our project goals.
The steady-state time was determined experimentally through our early testing. We were able to
graph the change in surface temperature versus time, and see where the temperatures leveled off.
Availability and Machinability of Cylindrical Specimen
An issue we ran into along the way was finding cylindrical shaped materials to conduct our
experiment with. Many of the materials we considered would have required special machining in
order to make them the right shape. Although machining a perfect cylinder would have been
difficult but doable, the bigger obstacle we ran into was being able to drill a hole the same
diameter and length as the heating rod. We would have had to cut the solid cylinder into sections
and drill a hole in each section individually. Then, the cylinder sections would have been stacked
together which could have led to more error due to convection if the sections were not stacked
tightly enough and the need to calculate contact resistances. These problems would be
experienced if we worked with any of the metals or balsa wood. Balsa wood would also require
special woodworking tools not readily available in the machine shop. Temperlite insulation
would have been approached in the same manner but also with different tools. However,
Temperlite creates a very big mess when handled, dispersing a powdery substance into the air
that should not be inhaled. Clay would have been difficult to work with because we did not know
how much we would need or how we would shape it. There are multiple ways to work with clay
like throwing it on a pottery wheel or casting it from a mold but it would have been hard to
control the exact measurements. The pipe insulations were easy to find and order off
McMaster.com and even came in the dimensions we needed. The foam rubber was easier to slide
onto the heating rod than the silicone foam, however.
Multi-Layered System
Our team discussed making a multi-layered system when we first began our concept generation,
since multiple layers would demonstrate the theory surrounding contact resistances and would
provide more extensive analysis in the lab write-up. To create a multi-layered system, we could
have wrapped the heating rod in two layers of the same material or two different materials.
However, as stated above, we had difficulty finding cylindrical materials with the right
dimensions and we did not have enough time to further explore adding additional material layers.
7 In-Lab Experiment and Post-Lab Write-Up
Our team had many ideas regarding how to enhance the students’ experience with this lab and to
test their understanding of the heat transfer theories learned in class. In order to test the students’
knowledge about heat transfer they must complete a formal lab report with their analysis of the
lab. The experiments we discussed for the students to complete were analyzing a single
cylindrical system, comparing two cylindrical systems with different materials, and comparing
the old lab setup vs. a new cylindrical setup when testing the same material.
Single Cylindrical Setup
In this lab experiment, the students would measure the temperature across the thickness, of a
tubular material. By knowing the dimensions of the specimen, the thickness, the power input,
and the change in temperature in the radial direction through the thickness of the material the
students can calculate the thermal conductivity of the material. They can then compare the
calculated thermal conductivity value with the literature one and determine the percent
difference. Students would also be asked to evaluate why the calculated thermal conductivity
value is different than the literature values and what aspects of the lab may contribute to the
difference. This lab experiment tests the students’ understanding of heat transfer concepts but
does not demand as much analysis as our team would like.
Compare Two Cylindrical Setups with Different Materials
This lab experiment would compare two different materials in the same cylindrical lab setup.
Analysis of the lab would still require students to calculate the thermal conductivities for each of
the materials and to compare them to the literature values. However, it would also ask the
students to compare the thermal conductivities of the different materials and tell the students to
describe why they might be so different or similar. This experiment obviously requires two
cylindrical specimens to measure the thermal conductivity of. Our team was in possession of two
such specimens, the foam rubber pipe insulation and the silicone foam pipe insulation, but testing
of the silicone pipe insulation did not provide very similar results for thermal conductivity in
comparison to the literature values. Therefore, in order to do this experiment a new material
would need to be found. In addition, the foam rubber and the silicone foam pipe insulations
looked alike and had similar thermal conductivities. It might be more fun for the students to
analyze if the two materials that were tested were more significantly different.
Old vs. New Setup and Comparing Results for Same Material
The comparison of the old box setup and the new cylindrical system when testing the same
material would be an interesting experiment. Like the lab experiments above, the main purpose
of this lab would be to measure the thermal conductivity of the material in both the lab setups.
Then the calculated thermal conductivity values would be compared to the literature values and
each other. The students would then be asked to explain why the calculated thermal
conductivities for each setup vary from each other and why they both may be different from the
literature values. This experiment would be the most comprehensive of the three proposed
experiments and formal lab write-ups but also requires that either our new cylindrical setup be
8 made with balsa wood or that the balsa wood in the old experiment be replaced with a new
material.
COMSOL Pre-Lab Activity
In addition to an in-lab experience with a post-lab formal write up, our team thought a COMSOL
pre-lab activity might make the experiment more engaging. COMSOL is an engineering, design,
and finite element analysis software program. This was also a suggestion given to us by the
client if we had time to investigate COMSOL. A COMSOL activity performed before the
experiment, where students could actually see a computer simulation of how the heat is
transferred through the material, would hopefully increase interest in the lab itself. Furthermore,
as graduating Mechanical Engineering students from the University of Washington, we feel that
we were not trained to use COMSOL very effectively and have not used it much since our first
introduction to it. A step-by-step COMSOL pre-lab activity would give students the chance to
become more familiar with the program.
FINAL CONCEPTUAL DESIGN
General Description
The final design our team chose to pursue in order to achieve the clients request to improve the
current heat conduction experiment utilized in ME 331: Heat Transfer was a cylindrical setup.
The setup is depicted below in Figure 3, which shows a photo of the final setup as observed by
the student as well as section view with labeled components. With this setup, a cylindrical
heating rod is covered with an ultra-flexible foam rubber pipe insulation sleeve. Thermocouples
are placed along the heating rod and the foam rubber sleeve to measure the temperature
difference across the radial thickness of the foam rubber pipe insulation. The ends of the heating
element and the rubber foam sleeve are supported and further insulated by two Temperlite
blocks. Two small holes were made in one of the Temperlite blocks to pass the heating rod leads
through, shown in the right picture of Figure 3, which carry power from the power supply to the
rod itself. The power input and temperature readings from the thermocouples are gathered and
displayed using the same data acquisition system, Personal Daq View, used in the old heat
conduction lab. Instructions for analyzing data provided by Personal Daq View are given in the
lab handout.
9 Figure 3. Final Setup of the Redesigned Lab
Discussed below, in further detail, are the heating rod, the ultra-flexible foam rubber, the
thermocouples, the Temperlite blocks, the data acquisition system and the power supply, and the
finalized lab handouts.
Components
Heating Rod
Design
The heating element used for this lab setup was a Steel HOTWATT Cartridge Heater,
Model Number #SC37-14.12 and rated at 50 watts. The rod has a diameter of 1 cm and is
36 cm long. Figure 4 shows the heating rods we used for testing. The blue and black
stripes are tape which is used for securing thermocouples. The expectation of the rod is
that it will heat up uniformly in the longitudinal direction. Heating of the rod occurs due
to a network of resistance coils established within the rod. When power is supplied to the
rod through the leads at one of the ends of the rod, the coils heat up and therefore the rod
heats up. When the foam rubber pipe insulation sleeve encases the rod, heat from the rod
is transferred to the foam rubber. [3]
Figure 4. Cylindrical Heating Rod with Tape
10 Advantages/Disadvantages
Beyond the fact that the heating element is cylindrical, the biggest advantage of this
heating cartridge is that the rod has a length to diameter ratio that is greater than ten
36 𝑐𝑚
1 𝑐𝑚 ≫ 10 . Since this aspect ratio is, in fact, greater than ten we can assume
the system is an infinite rod and can apply the conduction equation for a 1D cylindrical
system. The one disadvantage of this rod is that it does not heat up completely uniformly
because the resistance network within the rod is not perfect.
Ultra-Flexible Foam Rubber Pipe Insulation
Design
The material we chose to measure the thermal conductivity of was an ultra-flexible foam
rubber pipe insulation. This foam came in many dimensions but we ordered a sample
with an inner diameter of 3/8 inches, which is approximately equal to the diameter of the
heating rod, and a radial thickness of 3/4 inches. We cut a piece at 36 cm, the same length
as the heating rod, to use in the system. A temperature difference was calculated from the
inner diameter to the outer diameter of the material. Figure 5 shows a cross-sectional
view of the foam rubber.
Figure 5. Cross Sectional View of the Foam Rubber Pipe Insulation
Advantages/Disadvantages
The many advantages of this material include the fact that it was available in the desired
cylindrical shape and inner diameter dimension, it easily slides over the rod, it has a low
literature thermal conductivity value of 0.036 W/m∙K, and it produced calculated thermal
conductivity values that were similar to the literature values [4]. The silicone foam pipe
insulation that we also considered was much more difficult to slide onto the heating rod,
often displacing the thermocouples, and it produced less accurate calculated thermal
conductivity values when compared to literature ones. A disadvantage of the foam rubber
is that it does not fit as snugly around the heating rod as we would have liked. However,
this extra space allowed for the thermocouples to stay intact while the foam rubber was
slid onto the rod.
11 Thermocouples
Design
The thermocouples used in this lab system were Type K chromega-alomega 30 gage.
They measured the temperature at desired locations along both the heating rod and the
foam rubber insulation. Five thermocouples were placed approximately equidistant from
each other along the length of the heating rod, as seen in Figure 6. Another five
thermocouples were placed along the outside of the foam rubber insulation on the same
radial lines as the thermocouples on the heating rod. The thermocouples were attached to
both surfaces using flash tape, which is the blue tape visible in Figure 7. We used flash
tape to fasten the thermocouples to the heated surfaces because it does not burn or affect
the temperature readings of the thermocouples.
Figure 6. Placement of Thermocouples along Heating Rod
Figure 7. Placement of Thermocouples along Outside of Insulation
Advantages/Disadvantages
Thermocouples provide accurate temperature readings within one or two degrees.
Fortunately, with this experiment, the change in temperature is significant enough that an
error of that degree will not affect the results much.
12 Temperlite Blocks
Design
The blocks used to support and further insulate the heated cylindrical specimen were
made of Temperlite 1200°. Temperlite has a nominal conductivity of 0.06 W/m∙K at
room temperature. It is a rigid, high temperature, water resistant molded perlite thermal
insulation available in many forms. Holes with the same cross-sectional area as the
cylindrical foam rubber specimen were cut into the Temperlite blocks where the foam
rubber and heating rod would later be inserted. On the opposite side of one of the blocks,
two small holes were made in order to let the electrical leads from the heating rod and the
thermocouple wires to connect to other systems. The Temperlite blocks were wrapped
with scotch tape to prevent them from creating a powdery mess whenever handled.
Figure 8 shows the block that had the power cords going into it.
Figure 8. Temperlite Block
Advantages/Disadvantages
The Temperlite blocks were readily available in the Heat Transfer Lab and were easy to
shape. However, Temperlite has a higher thermal conductivity than the foam rubber, and
therefore heat may be likely to travel in the direction of the Temperlite instead of radially
outward through the foam rubber. Also, Temperlite is very messy to work with and even
though it does not contain asbestos, it’s unhealthy to inhale.
Data Acquisition Setup and Power Supply
Design
Figure 9 shows the power setup for the lab experiment. The variac was used to control
the voltage going into the heating rod. The voltmeter and ammeter measured voltage and
current directly, which can be used by students to calculate power input. The
thermocouples were inserted into an external component connected to the computer and
the Personal Daq View software, allowing the user to read the temperature
measurements.
13 Voltmeter
Ammeter
Variac
Figure 9. Power Supply System
Advantages/Disadvantages
This setup is the exact same for the old box conduction lab, which allows for a simple
and easy changeover. If both lab setups are run in coordination with each other, as we
are suggesting, the leads connecting the heating units to the power supply would have to
be transferred to whichever system is being tested at the time. This allows for great
flexibility in how the lab experiments are run. There are no significant disadvantages to
this setup.
Lab Handout 1: Old vs. New Setup and Comparing Results for Same Material
The favored lab experiment for this lab setup is to compare the old box setup to the new
cylindrical one. Both labs would test the same material and the calculated thermal conductivities
would be compared against each other and the literature value. The analysis for this lab would be
very comprehensive, testing students’ understanding of multiple heat transfer concepts including
heat flow in a 1D rectangular system and a cylindrical system, calculating error caused by
convection, and analyzing why the systems act so differently. This lab handout is included in
Appendix C. In order to create this lab experiment, our team would need to replace the balsa
wood block in the current conduction lab setup. Unfortunately, we are not able to disassemble
the current lab because students will need it for experimentation it in the summer.
Lab Handout 2: Single Cylindrical Setup
Since we wanted to have a completed lab experiment for our client to be able to implement right
away, our team also wrote a lab handout for analyzing a single cylindrical setup. This lab asks
students to calculate the thermal conductivity across the radial thickness of the foam rubber
14 sheath. The calculated thermal conductivity value is compared to the gathered literature value for
the foam rubber. This lab handout is not as extensive as we would have liked but it is ready to be
handed over to students right away. This handout can be found in Appendix D.
COMSOL Pre-Lab Activity
Prior to doing the experiment, students will be asked to complete a COMSOL assignment that
models what will happen in the cylindrical system. The activity provides a step-by-step process
on how to create a simplified model of the cylindrical system that students will observe in the
lab. Figure 10 below shows the simulation students will be able to create on their own using our
COMSOL activity, which can be found in Appendix E.
Figure 10. COMSOL Simulation of the Cylindrical Model
Many students are uncomfortable operating COMSOL, since we do not use it much in our
Mechanical Engineering classes. When it is introduced in a class, instructions are often hard to
follow and require students to seek excess help from TAs or the professor. Our activity will give
them the confidence to explore the program on their own and to become more familiar with it.
DETAILED DESIGN, PROTOTYPE MANUFACTURE AND EVALUATION
The approach to the heat conduction through a radial system led to the final design concept of a
using a cylindrical heating rod and enclosing this heating rod with a cylindrical sleeve of a test
material. The goal of the lab experiment is to calculate the thermal conductivity of the specimen
using the measured temperature difference across the radius. Complications may be added to
this simple cylindrical system such as a multi-layered specimen, but we designed the simple
cylindrical system so as to provide a fundamental understanding of conduction in a radial system
in coordination with a working, reliable lab experiment.
Before construction of the lab prototype, we procured two possible specimens to test through the
website McMaster-Carr [5]. The two specimens selected were an ultra-flexible foam rubber pipe
insulation and a flexible tear-resistant silicone foam pipe insulation. The sizes of the insulation
were based off the cylindrical heating rods (Hot Watts) that were already available to us in the
Heat transfer lab area [3]. The thickness of the material that was ordered was based off of hand
15 calculations performed during the concept generation phase. The goal was to have a good
temperature gradient of at least 20 K. This led us to order the foam rubber with a thickness of
3/4" and the silicone foam with a thickness of 7/16”. Most of the components that made up our
conduction lab were sourced from the lab area to keep costs low. For example, we utilized the
current and voltage generators already in the lab. Along with this, the insulating supports on the
finalized design concept were constructed from blocks of Temperlite that was readily available
in the lab area. Also, the thermocouples were made in-house through the guidance of Bill
Kuykendall, the resident lab supervisor for the Mechanical Engineering Department.
Once the materials were gathered, the prototype of the radial heat conduction lab came together
rather quickly. Before building started, twenty five thermocouples were made in the heat
transfer lab. Next the insulation supports were manufactured with a simple hack saw and various
screwdrivers to dig fitment holes into the support blocks. Once the supports were made, the
attachment of thermocouples was put onto the surface of the heating rod, outer surface of the test
specimen, and in the insulation blocks.
Our evaluation of the prototype began with determining the time it took for the material to reach
steady state. Initial tests were longer than later trials because we needed to ensure that steady
state was obtained. Typically both materials took longer than one hour to reach steady state; of
which the ultra-flexible foam rubber took about 1.5 hours. Next the temperature gradient was
determined and the thermal conductivity, k, was determined. Due to having thermocouple pairs
along the length of the rod, we determined an overall k value by averaging the temperature
difference along the rod, and also calculated specific k values relating to each thermocouple pair.
To make sure consistent results could be measured, the prototype was tested various times to
ensure reliability of data. The results of this testing will be discussed in analysis portion of this
report.
MODELING AND ANALYSIS
Once the final concept was decided upon, we selected two different types of pipe insulation:
ultra-flexible foam rubber pipe insulation and flexible tear-resistant silicone foam pipe
insulation. Both of these had inner diameters of 3/8”, which was close to the 1 cm diameter of
the heating rod. The foam rubber had a manufactured thickness of 3/4” or 1.905 cm (actual
measured thickness was slightly less but calculations assume 3/8”). The silicone foam had a
manufactured thickness of 7/16” or 1.11 cm (actual measured thickness was slightly greater).
The foam rubber had a thermal conductivity given by the manufacture of 0.25 BTu-in/hr. ft2 °F,
or 0.036 W/m-K [4]. The silicone foam had a given thermal conductivity of 0.39 BTu-in/hr. ft2
°F, or 0.056 W/m-K [5]. Testing was done on both specimens across the span of about two
weeks. As explained above in previous sections, a section of each material was slipped onto the
heating rod, fully encasing it. Thermocouples were placed along the inside of the insulation and
along the outside so as to measure the temperature difference across the radius of the material.
The same process was carried out for each test. The dimensions of the two separate materials
remained constant throughout all tests. The amount of power supplied to the heating rod was
16 varied across tests to ensure that results remained consistent for different power levels. Data
acquisition was carried out up through steady state. It was important to collect final temperature
readings while the system was at steady state, so earlier tests were carried out over a longer
duration of time so that we could obtain an accurate picture of how long it took each specimen to
arrive at steady state.
At the end of each test, final temperature values and the power input value were recorded and
then used to calculate the thermal conductivity value via the heat conduction equation. This was
done with two different methods. First, the difference between the average outside surface
temperature and the average inside surface temperature was used to calculate k. The second
method was to calculate a k value for each pair of outside-inside temperature readings and then
average the k values. Both methods gave similar results, but it was deemed that the first method
was more accurate.
The test results for the foam rubber insulation were much more accurate than results obtained
from the old heat transfer lab. The percent error between the measured/calculated thermal
conductivity and the given manufacture value ranged between 10 and 15%. Table II shows the
final measured values obtained from a test conducted on May 22, 2012. The TC values are the
thermocouple measurements along the rod (1R-5R) and the outside surface (1O-5O). The
calculated k value for this test was 0.041 W/m-K when using the average temperature difference
to calculate k. This is a 12.94% error from the literature value.
Table II. May 22, 2012 Test Results for Foam Rubber Insulation
TC
TC
TC
TC
TC
TC
TC
TC
TC
TC
1R
2R
3R
4R
5R
1O
2O
3O
40
50
Power
°C
°C
°C
°C
°C
°C
°C
°C
°C
°C
W
87.82 85.35
80.47 76.68
70.53
31.87 32.88
32.11 32.07 31.56
2.81
When examining how the k values changed along the length of the specimen, we noticed some
reoccurring observations throughout all the tests. Temperatures at the end of the cylinder, where
the power cords were attached, were noticeably lower, causing the k value calculated at the ends
to have a greater difference from the literature value than the other measured k values. This led
us to examine the heating elements in greater depth and conduct further research into their
design. We found that the rods consisted of resistance coils spread throughout that are supposed
to uniformly heat the rod. However, there is a space between the end and the start of the coils,
which explained why there were lower temperature readings at the end. Figure 11 shows how
the k values varied over the length of the rod for the May 22 test. The points on the right are the
measurements taken from the end of the rod where the power is attached.
17 Thermal Conductivity k (W/m-K)
0.06000
0.05000
0.04000
0.03000
0.02000
0.01000
0.00000
0
50
100
150
200
250
300
350
Distance From End of Rod (mm)
Figure 11. May 22, 2012 Test of Foam Rubber: k vs. Distance From End of Specimen
The average of the k values for this specific test was 0.045 W/m-K, which is a 25% difference
from the given manufacture value. This caused us to use the first calculation method of using the
average surface temperatures as our primary method of calculation. The difference in k values
across the length of the rod can be attributed to the design of the rod and how the power is
transferred into heat. It is obvious based on our results that uniform heating is not taking place
throughout the length of the rod. The lab exercise that we designed for students to carry out
causes them to examine this unexpected result and account for the sources of error. The hope is
that they would research the design of the heating rod as we did.
We had greater difficulty in obtaining accurate results with the silicone foam insulation. The
range of percent error throughout testing was much greater for this material, and ranged from
75% to 80%. This was strange to us, because the testing was producing similar results each trial
for various power inputs. It led us to research the given thermal conductivity from the
manufacture in greater detail. Both materials were purchased on McMaster-Carr, an online site
from which various materials and construction supplies can be purchased for lab projects. We
were able to confirm the k value given on McMaster-Carr for the foam rubber specimen with the
original manufacturer, but we were unable to find information on the manufacturer of the
silicone rubber. We did manage to find a range of literature values collected for silicone foam,
and our measured k value of about 0.10 W/m-K is within that range. Figure 12 shows this range
of values. This led us to the conclusion that McMaster-Carr may not have completely accurate
specifications on all its different products.
18 Figure 12. Range of Thermal Conductivities for Silicone Foams [6]
As a result of our testing, it was concluded that the lab exercise should be designed for the foam
rubber specimen because we had a good literature value for the thermal conductivity, and testing
results produced a reasonable percent error between the measured k value and the literature
value. The silicone foam system was also constructed and may be used, but a more accurate
literature value for the thermal conductivity should be found.
All testing results can be found in Appendix F.
ECONOMIC/COST EVALUATION
The experiment setup requires systems for generating heat, recording data, and channeling heat.
On the generation side, it requires a Variac (a controllable voltage source), a voltmeter, an
ammeter, and a cartridge heater. The data recording system is composed of a data acquisition
module and ten type K thermocouples, plus leads for the voltmeter and ammeter. The heat
leaves the cartridge heater via the specimen material and two side blocks of Temperlite.
Most of these materials were readily available in the heat transfer lab space. The specimen
material had to be purchased. Two specimens were acquired, one made of foam rubber ($5.13
for a 6-foot specimen, plus $16.80 for a quarter-inch thick sheet needed for the old setup to be
19 rebuilt), and the other of silicone foam ($54.80 for six feet, which was much higher than
expected) [5]. With shipping costs included, the entire cost to the group was $94.82, much lower
than the client’s initial budget estimate of $1,000.
CONSIDERATION OF THE BROADER CONTEXT OF DESIGN
Risk and Liability
There are two ways the setup could pose danger to people around it. The first is through thermal
damage—either burning people directly, or starting fires. Fire danger is mitigated by keeping the
cartridge heater’s outer temperature below the maximum operating temperature of the material
specimen. For the foam rubber, this was about one hundred degrees Celsius, and this
temperature was only slightly increased for the silicone foam. A person cannot directly
experience this temperature due to the layer of insulation. We found that the outer temperature
was between 30 and 50 degrees Celsius, not enough to cause harm to a person.
The second mode of peril is through electrical shock. However, the power delivered to the
cartridge heater is around 4 watts, removing any real danger of electrocution.
Ethical Issues/Societal Impact
The original motivation of modifying the current conduction experiment was that the
experimental error was out of control. Such an inaccurate experiment does not engender a sense
of trust and professional responsibility in the students who perform it. It is perhaps not entirely
ethical to claim to have taught something to someone when the method of teaching does not
actually demonstrate what should have been taught. Therefore, with the considerably lower
percent error we achieved, we have acted ethically.
Impact on Environment
The amount of waste involved in creating the experiment setup was relatively low. Leftover
insulation will remain in the heat transfer lab and hopefully be usable in another project. The
amount of energy consumed by the experiment setup is negligible, and regardless is supplied
primarily by clean hydropower thanks to Washington’s extensive dam system.
FUTURE WORK
The lab experiment that we designed is fully ready to be incorporated into the ME 331 Heat
Transfer class curriculum, but there are many things that could be done to improve or modify the
lab experience.
20 It is highly recommended that the cylindrical system and the corresponding lab exercise that we
designed be made part of the existing heat conduction lab. We have included a lab handout in
Appendix C that achieves this goal. The plan is that students would be able to compare the
accuracy of the box system to that of the cylindrical system. The large sources of error in the
box system would become more evident, and the students would be able to conduct a more
fruitful analysis. In order to make this modification, the balsa wood that is the current specimen
in the box system must be replaced with flat sheets of the foam rubber insulation to be consistent
with the cylindrical system. We have purchased sheets of this material and cut it into suitable
sections ready to be inserted into the box system. We were advised by our client not to
dismantle the current setup in case it is used as it is for summer classes, so we were not able to
finalize this step. It would take a few days to dismantle the current setup, replace the balsa wood
with the rubber foam, insert thermocouples throughout the system, and replace the insulation
surrounding the specimen. This should be done upon approval by the ME 331 instructor.
Additionally, we have several recommendations for future work in regards to improving the
cylindrical system and making the lab exercise more interesting to students. The system is setup
so that cylinders of different materials can be swapped in and out. Research should be done into
procuring a cylindrical specimen made out of balsa wood, to match the current box system
specimen, as well as a ceramic specimen. Thermal conductivity values for ceramics are
generally higher than those for the pipe insulation that we used, but are still low enough to
produce a measurable temperature difference in the specimen. Because of the higher
conductivity value, the specimen would reach steady state faster, which would potentially allow
the students to conduct the entire experiment themselves. With the pipe insulation, it takes about
1.5 hours for the system to reach steady state, which is too long for students to sit in the lab
waiting for results. Using a ceramic would hopefully shorten that waiting time, allowing the
students to turn on the system themselves and observe the entire conduction process from start to
finish.
Another complication that should be considered is the inclusion of multiple layers. Using
multiple layers of the same material, or even different materials, would allow students to plot the
changes in temperature across the total radius of the system. It would also introduce the concept
of contact resistance, which would result in a more intricate analysis for the students.
It is also recommended that further research be conducted into the theoretical calculation of the
time it takes for a cylindrical conduction system to reach steady state. This goes beyond what is
required for the undergraduate curriculum as it involves a higher level of understanding of
difficult mathematical concepts, but it would be helpful to be able to accurately predict the
steady state time for the system.
21 REFERENCES
[1] F. P. Incropera et al., Introduction to Heat Transfer, 5th ed. Hoboken, NJ: Wiley, 2007.
[2] M. R. Buckley et al., “Conduction Heat Transfer Lab,” Heat Transfer Class, Univ.
Washington, Seattle, WA, June 2011.
[3] Hotwatt: Heaters For Every Application [Online]. Available: http://www.hotwatt.com
[4] “ ‘R’ Value for AP Armaflex,” Armacell Engineered Foams, Mebane, NC, Nov. 2010.
[5] McMaster-Carr [Online]. Available: http://www.mcmaster.com/#
[6] H. Zhang and A. Cloud, “New Advances in Silicone-based Thermal Insulation,” Arlon
Silicone Technologies, Bear, DE.
22 APPENDIX A: LAB HANDOUT FOR CURRENT CONDUCTION LAB
CONDUCTION HEAT TRANSFER EXPERIMENT
The purpose of this experiment is to determine the thermal conductivity of low k materials
through direct measurement.
INTRODUCTION AND BACKGROUND
The basis for analysis of conduction heat transfer situations is known as Fourier's Law Of Heat
Conduction. The “Law” which is so glibly pronounced as an obvious truth was submitted as part
of a 234 page paper by Joseph Fourier in 1807. The work was controversial, and it remained
unpublished until 1822. Compare this publication rate with that of any assistant professor today!
No tenure for Joseph. The empirical law that he stated is “The heat flux resulting from thermal
conduction is proportional to the magnitude of the temperature gradient and opposite to it in
sign”. Note that he did not state that heat flux is directly proportional to the first power of the
gradient: it is just proportional. This experiment is designed to measure the value of the
proportionality factor through knowledge of the heat flux, temperature difference, and the
distance of conduction.
APPARATUS
The apparatus if very straightforward and simple. An electric heater, which is potted in silicone,
is used to heat the bottom aluminum plate whose inner surface has thermocouples set in to it. The
paper stack is covered by the top aluminum plate having thermocouples on its inner surface. A
thermocouple is also located in the geometric center of the stack. The stack is insulated on the
bottom with Temperlite 2000 insulation and on the four sides with an insulation blanket. The
applied heating current and electric potential are measured with meters, and the power generated
by the heater can be determined by the relation P = IV, where I is current, and V is potential. A
single thermocouple is mounted in the vicinity of a glass thermometer to measure ambient
temperature. The overall thickness of the paper stack is 1.00 inches and it is sandwiched between
the two 0.25 inch thick aluminum plates for a total stack thickness of 1.50 inches (one inch is
0.0254 m).
MEASUREMENTS
Measurements are taken with a data acquisition system which measures 10 temperatures and the
power to the heater is calculated by using the potential from the power source and the current
from the multimeter. When taking measurements, be sure and note on paper the time of the
experiment and the following: 1) the ambient temperature as indicated by the meter on the shelf
above the experiment; 2) the electric potential across the heater as indicated by the leftmost
voltmeter above the experiment; 3) the current through the heater as indicated by the rightmost
voltmeter. These values will be used to check the heater power measured by the DAQ and the
ambient temperature. Three temperatures on the bottom plate (tc 1, 2, 3), in the middle of the
paper (tc 4), on the top plate (tc 5, 6, 7), and the ambient temperature (tc 8). Average the
temperatures over time and on each plate and express the result as some nominal value centered
within uncertainty (±) limits. You can judge the uncertainty of the measurements by watching
the fluctuations of the readings. Record at least 10 sets of measurements in order to get some
statistical idea of the fluctuations.
23 THERMOCOUPLE LAYOUT ON TOP AND BOTTOM PLATES
Thermocouples are Type K chromel-alumel 60 gage
Typical variation in an isothermal environment at room temperature is +/-0.5 ° F The heater is
"FLEXIBLE SILICONE RUBBER FIBERGLASS INSULATED" from OMEGA Engineering.
Model number SRFG-206 rated at 10 watts/in 2 , but the power limitation is due to the maximum
temperature for silicone which is 450°F.
The insulation below the heater is Temperlite 1200° with a nominal conductivity of 0.06 W/m °C
at room temperature. It is a rigid, high temperature, water resistant molded perlite thermal
insulation available in many forms. It contains no asbestos. The insulation around the paper has a
nominal conductivity of 0.05 W/m °C.
The stack is insulated by a 4 inch thick layer of Temperlite below the heater and an
insulation blanket on each of the four sides. The top aluminum plate is open to the ambient
air and has a rod compressing it with a 10 pound load squeeze out air and limit contact
resistance.
24 ANALYSIS AND DISCUSSION
1. Assuming that the mid-stack thermocouple is exactly centered between the aluminum
plates, if the mid-stack temperature is not exactly at the mid-point temperature calculated
from the aluminum plate temperatures explain why. Describe an experiment(s) that could
be conducted to justify your reasoning.
2. Calculate the thermal conductivity of the paper sample. State what assumptions you have
made in computing the heat loss.
3. Compare the measured values of thermal conductivity for the paper sample with values
published in the open literature (at least three cited sources. Sources can be found in the
engineering library). Do the values seem reasonable?
4. If the measured thermal conductivity values are higher than the average of the published
values, then perhaps heat loss effects in the experiment were underestimated. Accounting
for heat loss effects beneath the heating pad, by how much would the measured values of
thermal conductivity change?
5. If the measured thermal conductivity values are less than the average of the published
values, then perhaps contact resistance between adjacent paper layers influenced the
results. If the results exhibit this behavior, assume that the actual thermal conductivity of
the paper sample (composed of 200 layers) is the average of the three published values
and calculate the contact resistance between adjacent paper layers in m2-K/W based on
the actual heat transfer rate through the paper stack. Are the results seen reasonable when
compared to typical contact resistance values tabulated in Table 3.2 from the textbook?
6. The experiment was conducted with insulation (ki = 0.05 W/m K) surrounding the
aluminum plate/paper stack, except for the outer surface of the top plate which was
exposed to atmospheric air (ka = 0.03 W/m K). Even though as air is a better insulator
than the blanket insulation used (air has a lower thermal conductivity), why weren’t the
four side walls of the stack exposed to atmospheric air during the experiment to lower the
heat loss through these walls? Justify your answer with back-up calculations.
25 APPENDIX B: MATLAB CODE
%Conduction experiment simulation
clc
clear all;
%All units in meters, watts, Celsius
%Total length, l
L = 0.15;
%cartridge heater generation capability, qgen
qgen = 20;
%estimated convection coefficient
h= 100;
%Ambient temperature
tamb = 25
%Conduction resistant calculation
%copy and alter variables as needed for multi-layer
%Outer section outer radius
osor = 12.7E-3;
%outer section inner radius
osir= 6.355E-3;
%outer section conductivity (k)
osk = 13.4;
%outer section thermal resistance
ro = (log(osor/osir))/(2*pi*osk*L);
%convection resistance
rh = 1/(h*2*pi*osor*L);
%total resistance
rtot = ro + rh;
%Highest allowable temperature for surface of cartridge heater
tch = qgen*rtot + tamb
%outer surface area (for reference)
A = osor*2*pi*L
%Surface temperature of outer layer
ts = qgen/(h*A) + tamb
26 APPENDIX C: LAB HANDOUT INCORPORATING RECTANGULAR AND
CYLINDRICAL CONDUCTION LABS
CONDUCTION HEAT TRANSFER EXPERIMENT
The purpose of this experiment is to determine the thermal conductivity of low k materials
through direct measurement.
INTRODUCTION AND BACKGROUND
The basis for analysis of conduction heat transfer situations is known as Fourier's Law of Heat
Conduction. The “Law” was submitted as part of a 234 page paper by Joseph Fourier in 1807,
but was not published until 1822. The empirical law that he stated is:
“The heat flux resulting from thermal conduction is proportional to the magnitude of the
temperature gradient and opposite to it in sign”.
Note that he did not state that heat flux is directly proportional to the first power of the gradient:
it is just proportional. This experiment is designed to measure the value of the proportionality
factor through knowledge of the heat flux, temperature difference, and the distance of
conduction.
APPARATUS
Two apparatuses will be used and compared in this experiment.
1. The first apparatus consists of an electric heater, potted in silicone, which is used to heat
the bottom aluminum plate whose top surface has thermocouples set into it. The rubber
foam insulation sheet is sandwiched between the two aluminum plates with the top
aluminum plate having thermocouples set into its bottom surface. A thermocouple is also
located in the geometric center of the sheet of insulation. The sheet is insulated on the
bottom with Temperlite 1200° insulation and on the four sides with an insulation blanket.
The overall thickness of the rubber foam insulation sheet is 1.00 inches that is
sandwiched between the two 0.25 inch thick aluminum plates for a total thickness of 1.50
inches (one inch is 0.0254 m).
2. The second apparatus has a cylindrical set-up. The electric heater used is in the shape of a
cylinder rod with a diameter of 0.393 inches (1 cm) and a length of 14.173 inches (36
cm). Thermocouples are attached along the heating element in the axial direction. The
heater is covered by a tubular-shaped rubber foam pipe insulation that slides directly onto
the heating rod. The rubber foam insulation has an inner diameter approximately equal to
the diameter of the heating element and a thickness of 0.75 inches. Another set of
thermocouples are attached to the outer surface of the rubber foam insulation. The ends
of the heating rod and cylindrical rubber foam insulation are supported and insulated by
blocks of Temperlite 1200°.
27 The applied heating current and electric potential for both apparatuses are measured with meters,
and the power generated by the heater can be determined by the relation P = IV, where I is
current, and V is potential. A single thermocouple is mounted in the vicinity to measure ambient
temperature.
MEASUREMENTS
Measurements are taken with a data acquisition system which measures seven temperatures from
the first apparatus, ten temperatures from the second, and the ambient temperature. The power to
the heaters is calculated by using the potential from the power source and the current from the
multimeter.
When taking measurements for both apparatuses, be sure and note on paper the time of the
experiment and the following: 1) the electric potential across the heater as indicated by the top
voltmeter above the experiment and 2) the current through the heater as indicated by the bottom
voltmeter. These values will be used to check the heater power measured by the DAQ.
Apparatus 1
Thermocouple locations: three on the bottom plate (TC 1, 2, 3), one in the middle of the
insulation sheet (TC 4), and three on the top plate (TC 5, 6, 7). Average the temperatures over
time and on each plate and express the result as some nominal value centered within uncertainty
(±) limits.
THERMOCOUPLE LAYOUT ON TOP AND BOTTOM PLATES
Thermocouples are Type K chromel-alumel 60 gage
The heater is "FLEXIBLE SILICONE RUBBER FIBERGLASS INSULATED" from OMEGA
Engineering. Model number SRFG-206 rated at 10 watts/in2, but the power limitation is due to
the maximum temperature for silicone which is 450°F.
The rubber foam insulation sheet is insulated by a 4 inch thick layer of Temperlite below the
heater and an insulation blanket surrounding the four sides. The Temperlite 1200°, the insulation
28 below the heater, has a nominal conductivity of 0.06 W/m∙K at room temperature. It is a rigid,
high temperature, water resistant molded perlite thermal insulation available in many forms. It
contains no asbestos. The insulation blanket has a nominal conductivity of 0.05 W/m∙K. The top
aluminum plate is open to the ambient air and has a rod compressing it with a 10 pound load to
squeeze out air and limit contact resistance.
Apparatus 2
Thermocouple locations: five on the heating rod (TC 9, 10, 11, 12, 13) and five on the exterior
surface of the rubber foam insulation (TC 14, 15, 16, 17, 18). Average the temperatures over
time and on the heating rod and outer surface of the insulation and express the result as some
nominal value centered within uncertainty (±) limits.
THERMOCOUPLE LAYOUT ON HEATER AND OUTER SURFACE OF INSULATION
Thermocouples are Type K chromega-alomega 30 gage
The heater is a Stainless Steel HOTWATT Cartridge Heater. Model number #SC37-14.12 rated
at 50 watts, but the power limitation is due to the maximum temperature for rubber foam
insulation which is 220°F.
The cylindrical set-up is supported on each end by two Temperlite 1200° blocks with the same
properties as listed above.
The ambient temperature is measured by TC 8. Typical variation in an isothermal environment at
room temperature is +/-0.5 ° F. You can judge the uncertainty of the measurements listed above
for both apparatuses by watching the fluctuations of the readings. Record at least 10 sets of
measurements in order to get some statistical idea of the fluctuations.
29 ANALYSIS AND DISCUSSION
Part A: Apparatus 1
1. Calculate the thermal conductivity of the rubber foam sample. State what assumptions
you have made in computing the heat loss.
2. Compare the measured values of thermal conductivity for the rubber foam sample with
values published in the open literature. Note: the rubber foam insulation is manufactured
by Armaflex. Do the values seem reasonable?
3. Account for any differences between the measured values of thermal conductivity and the
literature values? What potential sources of error are there? Estimate the heat loss due to
each potential source.
4. The experiment was conducted with insulation (ki = 0.05 W/m K) surrounding the
aluminum plate/rubber foam stack, except for the outer surface of the top plate which was
exposed to atmospheric air (ka = 0.03 W/m K). Even though as air is a better insulator
than the blanket insulation used (air has a lower thermal conductivity), why weren’t the
four side walls of the stack exposed to atmospheric air during the experiment to lower the
heat loss through these walls? Justify your answer with back-up calculations.
Part B: Apparatus 2
1. Calculate the thermal conductivity of the rubber foam sample using two methods:
a. Take an average of the outside surface temperatures and an average of the inside
surface temperatures. Use the difference between these two to calculate a total k
value.
b. Calculate separate k values for each pair of thermocouples. Average these k values.
2. Compare the measured values of thermal conductivity for the rubber foam sample with
values published in the open literature. Do the values seem reasonable?
3. Account for any differences between the measured values of thermal conductivity and the
literature values? What potential sources of error are there? Estimate the heat loss due to
each potential source.
4. Construct a graph of temperature vs. longitudinal distance for the outside surface
thermocouples and the inside surface thermocouples. Set x=0 for the end of the cylinder
that is attached to the power supply. Does temperature vary in the longitudinal direction?
Comment on why this may be.
Part C: Compare and Contrast the Two Systems
Are the measured k values different for the two apparatuses? Does one system produce more
accurate results than the other? Which one? Why do you think this is? Analyze the differences
and similarities between the two systems. What stays constant in both setups? What changes?
How does this affect your calculations?
30 APPENDIX D: LAB HANDOUT FOR THE CYLINDRICAL CONDUCTION LAB
CONDUCTION HEAT TRANSFER EXPERIMENT
The purpose of this experiment is to determine the thermal conductivity of low k materials
through direct measurement.
INTRODUCTION AND BACKGROUND
The basis for analysis of conduction heat transfer situations is known as Fourier's Law of Heat
Conduction. The “Law” was submitted as part of a 234 page paper by Joseph Fourier in 1807,
but was not published until 1822. The empirical law that he stated is:
“The heat flux resulting from thermal conduction is proportional to the magnitude of the
temperature gradient and opposite to it in sign”.
Note that he did not state that heat flux is directly proportional to the first power of the gradient:
it is just proportional. This experiment is designed to measure the value of the proportionality
factor through knowledge of the heat flux, temperature difference, and the distance of
conduction.
APPARATUS
The apparatus has a cylindrical set-up. The electric heater used is in the shape of a cylinder rod
with a diameter of 0.393 inches (1 cm) and a length of 14.173 inches (36 cm). Thermocouples
are attached along the heating element in the axial direction. The heater is covered by a tubularshaped rubber foam pipe insulation that slides directly onto the heating rod. The rubber foam
insulation has an inner diameter approximately equal to the diameter of the heating element and
a thickness of 0.75 inches. Another set of thermocouples are attached to the outer surface of the
rubber foam insulation. The ends of the heating rod and cylindrical rubber foam insulation are
supported and insulated by blocks of Temperlite 1200°. The applied heating current and electric
potential for the both apparatus are measured with meters, and the power generated by the heater
can be determined by the relation P = IV, where I is current, and V is potential. A single
thermocouple is mounted in the vicinity to measure ambient temperature.
MEASUREMENTS
Measurements are taken with a data acquisition system which measures eleven temperatures and
the power to the heaters is calculated by using the potential from the power source and the
current from the multimeter.
When taking measurements, be sure and note on paper the time of the experiment and the
following: 1) the electric potential across the heater as indicated by the top voltmeter above the
experiment and 2) the current through the heater as indicated by the bottom voltmeter. These
values will be used to check the heater power measured by the DAQ.
Thermocouple locations: five on the heating rod (TC 1, 2, 3, 4, 5), five on the exterior surface of
the rubber foam insulation (TC 6, 7, 8, 9, 10), and one in the vicinity of the experimental set-up
31 to measure ambient temperature. Typical variation in an isothermal environment at room
temperature is +/-0.5 ° F. Average the temperatures over time and on the heating rod and outer
surface of the insulation and express the result as some nominal value centered within
uncertainty (±) limits. You can judge the uncertainty of the measurements listed above by
watching the fluctuations of the readings. Record at least ten sets of measurements in order to get
some statistical idea of the fluctuations.
THERMOCOUPLE LAYOUT ON HEATER AND OUTER SURFACE OF INSULATION
Thermocouples are Type K chromega-alomega 30 gage; thermocouple pairs are mounted at same
axial coordinates.
The heater is a Stainless Steel HOTWATT Cartridge Heater. Model number #SC37-14.12 rated
at 50 watts, but the power limitation is due to the maximum temperature for rubber foam
insulation which is 220°F.
The cylindrical set-up is supported on each end by two Temperlite 1200° blocks. Temperlite has
a nominal conductivity of 0.06 W/m∙K at room temperature. It is a rigid, high temperature, water
resistant molded perlite thermal insulation available in many forms. It contains no asbestos.
32 ANALYSIS AND DISCUSSION
1. Calculate the thermal conductivity of the rubber foam sample using two methods:
c. Take an average of the outside surface temperatures and an average of the inside
surface temperatures. Use the difference between these two to calculate a total k
value.
d. Calculate separate k values for each pair of thermocouples. Average these k values.
2. Compare the measured values of thermal conductivity for the rubber foam sample with
values published in the open literature. Note: the rubber foam insulation is manufactured
by Armaflex. Do the values seem reasonable?
3. Account for any differences between the measured values of thermal conductivity and the
literature values? What potential sources of error are there? Estimate the heat loss due to
each potential source.
4. Construct a graph of temperature vs. longitudinal distance for the outside surface
thermocouples and the inside surface thermocouples. Set x=0 for the end of the cylinder
that is attached to the power supply. Does temperature vary in the longitudinal direction?
Comment on why this may be. Hint: how are the heating rods designed?
5. In general, how are thermal conductivities measured to obtain the literature values? How
does this apparatus compare to other methods?
33 APPENDIX E: COMSOL PRE-LAB ACTIVITY
Comsol Guide
1. Open the program Comsol 4.1
2. Take notice of the program layout. There are three “tabs” which will be important in
navigating through Comsol. First your “Model Build” tab will act as your “road map” of
the actions you’ve taken. Next the “Settings” tab is used to input or adjust data that is
selected from the Model Build. Finally, the “Graphics” tab will have the graphical
representation of your model.
Model Wizard
1. The Model Wizard will open up to a “Select Space Dimension” which you can decide on
what dimension to work in. For this example, select “3D” then press the arrow pointing
to the right.
2. Now in the “Add Physics” section, expand the “Heat Transfer” tab and select “Heat
Transfer in Solids” then press the arrow on the top pointing to the right.
3. Now in the “Select Study Type”, select “Stationary” under the Preset Studies tab. Click
the checkered flag to finish the Model Wizard.
Geometry [Builds Model]
1. As you press the checkered flag on the Model Wizard, the “Geometry” settings will
appear. Choose the “Length unit” to be in “inches”
2. Next in the “Model Build” tab, right click on “Geometry 1” which is tiered under “Model
1”
3. Choose the cylinder shape, and this will bring up the “settings” tab
4. Select the Radius to be 0.2 inches and the Height to be 15 inches. The Position section
determines the placement of the center of the cylinder face. Leave/change the Position to
x = 0 inches, y = 0 inches, and x = 0 inches
5. Next for the “Axis”, we want the cylinder to be parallel with the x-axis, so choose the
“Axis type” as Cartesian and choose x to be 1 leave y and z as 0
6. Look above the “Cylinder” heading, there are two blue buttons
that will “build”
your model with your inputs. The first blue button with a red square is the Build Selected
34 and will build only what is currently selected. The other blue button is the Build All
which will build everything in the Model Build path
7. Press either of the blue buttons and the cylinder will appear in the Graphics tab
8. Right-click on Geometry 1 again in the Model Build and select the cylinder again. Set
the Radius and Height as 0.95 inches and 15 inches
9. Set the position and the axis to the same as in steps 4 and 5. Then Select Build All
10. Go to the “Model Build” tab and find “Cylinder 1” under Geometry 1 and right click to
rename as “Heating Element”. Do the same for “Cylinder 2” but rename as Rubber
Insulation.
11.
Materials
1. Locate “Materials” under the Model Build tab and right click. Select “Material” and the
Settings Tab will come up with the Material heading.
2. Set the Geometric Entity Level as Domain, and Selection as Manual.
3. Click on the model and press the
Plus sign next to the box to add the
material to selected section. To
remove a material assignment, select
the corresponding number in the
Selection Box and press the minus
sign to remove. Remove the “2”
from the selection, which
corresponds with the heating element
4. Expand the Basic Properties section,
is going to be based in a steady state
and select the thermal conductivity.
system, the density and heat capacity
To add, press the plus button below
values are not necessary.
the Material Properties box and
assign the Thermal conductivity
value of 0.036 in the Material
Contents box. Note: Since our model
35 5. Repeat step 1 to add another material. Repeat step 2. In step 3, this time remove “1” from
the selection box. For step 4, add the thermal conductivity value of 200 [W/(m*K)]
6. Re-label Material 1 to Rubber Insulation and Material 2 to Heating Rod in the Model
Builder.
Heat Transfer
1. Locate “Heat Transfer” under the Model Build tab
2. Expand the Heat Transfer path, and select Initial Values 1 and under the Initial Values
section, set T as 350 K.
3. Right-click on Heat Transfer in the Model Builder and select “Boundary Heat Source”
a. This is a bit tricky. For the “Boundary Heat Source”, it is necessary to select the
boundaries of the heating rod and not the heating rod itself. {Explain reason}.
b. Select the zoom box
button under the Graphics tab, and zoom box the left
hand side or the “origin” of the model. Also, to go back to your default 3d view
select the
button in the Graphics tab.
c. Clicking the center of the rod with select the entire rod, we don’t want this
(example below left). Keep clicking around the edges of the inner rod until an
36 edge is highlighted red. Go to the Settings tab and press the Plus button on the
side of the selection box (Right Click will also add the red highlighted portion to
the selection box). The red highlighted portion will now turn blue once added.
No! We don’t want this
Yes! We want only the edges
37 d. Repeat this until the edges of the inner cylinder are selected (example top
right)
e. Now in the “boundary heat source” in the settings tab, set Qb as 265
[W/m^2]
4. Right-click on Heat Transfer in the Model Builder and select “Convective Cooling”
a. Select all of the outer surfaces and end surfaces of the model and add to the
selection box in the settings tab. (Only unselected surface should be on face
on the origin)
b. In the Heat Flux section, set h as 15 [W/(m^2*K)] and the Text as 298.15 [K].
Mesh
1. Go to the Model Builder Table and select “Mesh 1”.
2. The settings tab will open up and you can adjust the Mesh Settings. Leave the
Sequence type in “Physics-controlled mesh” and adjust the Element Size to “Fine”
3. Press the Build All button to start the mesh sequence
38 Study
1. Find “Study 1” in the Model Builder tab.
2. Right click and press Compute.
Results
1. Once the solver finishes computing, a plot of the temperature of the model will be
shown
2. Expand the “Results” tab in the Model Builder
3. Select the 3D Plot Group 2 to open up a the slice view of the temperature of the
model
39 4. Right click the Results and select “3D Plot Group”. The created one should be
called “3D Plot Group 3”
5. Right click on “3D Plot Group 3” and “Splice”
6. In the Settings tab, change the data set to “Solution 1”, then change the Plane under
Plane Data to “xy-planes”
7. Change the Entry Method to “coordinate” and set the z-coordinate to 0.45 [in]
8. Press the Plot button
to plot
40 APPENDIX F: TESTING RESULTS
Testing Results for Foam Rubber Insulation
The dimensions for the cylindrical setup with the foam rubber insulation remained constant
throughout testing:
r0=0.005 m r1=0.02405 m L=0.36 m
Tables F1 through F5 show the results of the various tests done on the foam rubber
specimen. Note that the thermocouple setup changed slightly throughout testing as we
started analyzing the collected data. We modified the acquisition procedure slightly over
time.
Table F1. May 10 Testing Results
TC1R TC2R TC3R TC1O TC2O Power k
% Error
°C
°C
°C
°C
°C
W
W/(m-K)
99.36 95.58 69.51 36.31 35.00
3.51
0.039
9.66
Table F2. May 11 Testing Results
TC
1R
TC
2R
TC
3R
TC
4R
TC
5R
TC
1O
TC
2O
TC
3O
TC
40
TC
50
°C
100
°C
103
°C
95.1
°C
89.7
°C
69.4
°C
33.6
°C
34.8
°C
33.1
°C
°C
33.1 34.2
W
3.54
P
P
k
W/(m
*K)
0.039
%
Error
7.97
Table F3. May 15 Testing Results
TC
1R
TC
2R
TC
3R
TC
4R
TC
5R
TC
1O
TC
2O
TC
3O
TC
40
TC
50
°C
66.5
°C
68.1
°C
63.7
°C
60.9
°C
50.0
°C
32.7
°C
32.5
°C
32.0
°C
°C
32.1 31.8
W
1.85
TC
1O
TC
2O
TC
3O
TC
40
TC
50
P
°C
34.1
°C
°C
35.0 33.4
°C
33.3
°C
31.9
W
3.07
k
W/(m
*K)
0.040
%
Error
10.08
Table F4. May 17 Testing Results
TC
1R
TC
2R
TC
3R
TC
4R
TC
5R
°C
90.0
°C
93.1
°C
86.1
°C
°C
81.3 63.5
41 k
W/(m
*K)
0.040
%Err
or
10.21
Table F5. May 22 Testing Results
TC
1R
TC
2R
TC
3R
TC
4R
TC
5R
TC
1O
TC
2O
°C
87.8
°C
85.3
°C
80.5
°C
76.7
°C
70.5
°C
°C
31.9 32.9
TC
3O
TC
40
TC
50
P
°C
32.1
°C
32.1
°C
31.6
W
2.81
%
Error
k
W/(m
*K)
0.041
12.94
Testing Results for Silicone Foam
The testing procedure for the silicone foam specimen was the same, but the dimension of
the outer radius differed slightly:
r0=0.005 m r1=0.016 m L=0.36 m
Tables F6 through F8 show the results of the various tests done on the silicone foam.
Table F6. May 16 Testing Results
TC
1R
TC
2R
TC
3R
TC
4R
TC
5R
TC
1O
TC
2O
TC
3O
TC
4O
P
°C
54.8
°C
54.1
°C
54.7
°C
55.8
°C
46.6
°C
32.9
°C
35.0
°C
36.5
°C
36.3
W
3.78
k
W/(m
*K)
0.10
%
Error
76.8
Table F7. May 17 Testing Results
TC
1R
TC
2R
TC
3R
TC
4R
TC
5R
TC
1O
TC
2O
TC
3O
TC
4O
P
°C
°C
°C
°C
°C
°C
°C
°C
°C
W
57.3
56.2
56.8
57.8
47.6
33.0
36.2
36.9
36.5 4.10
k
W/(m*
K)
0.10
%
Error
75.6
Table F8. May 21 Testing Results
TC
1O
TC
2O
TC
3O
TC
4O
TC
1R
TC
2R
TC
3R
TC
4R
TC
5R
P
°C
45.4
°C
46.8
°C
47.2
°C
46.9
°C
98.0
°C
99.3
°C
96.6
°C
93.9
°C
90.8
W
9.60
42 k
W/(m*
K)
0.10
%
Error
79.2