Finite Element Analysis of Heat Transfer in Single and Double Walled
Beverage Containers
by
Peter Tu
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2014
i
© Copyright 2014
by
Peter Tu
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
KEYWORDS .................................................................................................................... vi
SYMBOLS ...................................................................................................................... vii
ACKNOWLEDGMENT ................................................................................................ viii
ABSTRACT ..................................................................................................................... ix
1. INTRODUCTION ......................................................................................................... 1
2. THEORY & METHODOLOGY ................................................................................... 2
2.1 Theory .................................................................................................................... 2
2.2 Methodology .......................................................................................................... 3
3. RESULTS & DISCUSSION ......................................................................................... 7
3.1 COMSOL Heat Transfer in Solids Model – Single Walled Cup........................... 9
3.2 COMSOL Heat Transfer in Solids Model – Double Walled Cup ....................... 14
4. Conclusions.................................................................................................................. 19
5. References.................................................................................................................... 20
6. Appendices .................................................................................................................. 21
iii
LIST OF TABLES
Table 1: Material property constants or relationships used in the thermal analysis models
Table 2: Mesh convergence study results
iv
LIST OF FIGURES
Figure 1: Left - Single walled cup [5]; Right - Double walled cup [6]
Figure 2: Schematic of the heat transfer process: 1. Thermal conduction through inner
wall, 2. Convection via trapped gas, 3. Thermal conduction through outer wall, 4.
Energy lost to environment
Figure 3: Thermal model boundary conditions
Figure 4: Kiran Tea Glass by Teavana
Figure 5: Scale, digital caliper, and radius gages
Figure 6: Cross-section of the 3D models of the cup, air, and water
Figure 7: The cup, air, and water domains after importing and repairing in COMSOL
Figure 8: Thermal model at time = 30 minutes in COMSOL
Figure 9: Plot of the water and single walled glass cup temperature against time
Figure 10: Double walled cup thermal model at time = 30 minutes
Figure 11: Plot of the water and double walled glass cup temperature against time
Figure 12: Measured temperature of boiled water versus time in the Kiran Tea Glass
Figure 13: Graph of the temperature of boiled water in the Kiran Tea Glass
v
KEYWORDS
Singled walled cup, double walled cup, transient heat transfer, conjugate heat transfer,
axisymmetric, natural convection, heat transfer in solids, borosilicate glass, NX,
COMSOL
vi
SYMBOLS
𝑘 = thermal conductivity of the material (𝑊 ⁄𝑚 ∙ 𝐾)
ℎ = ℎ𝑎𝑖𝑟 (𝐿, 𝑝𝐴 , 𝑇𝑒𝑥𝑡 ) (𝑊 ⁄𝑚2 ∙ 𝐾)
L = plate height, length, or diameter (m)
𝑝𝐴 = Absolute pressure (Pa)
𝑇𝑒𝑥𝑡 = Externals temperature (K)
𝑄 = Energy added to the system (J)
t = time (s)
𝜌 = material density (kg/𝑚3 )
𝐶𝑝 = heat capacity at constant pressure (𝐽/(𝑘𝑔 ∙ 𝐾)
vii
ACKNOWLEDGMENT
I would like to acknowledge my family for their constant support and encouragement
throughout my career and studies. I would also like to acknowledge Professor Ernesto
Gutierrez-Miravete for his guidance and council as I conducted this final study.
viii
ABSTRACT
This project documents the analytical simulations that were created along with the
collection of data to confirm the validity of the claim that double walled beverage cups
keep hot liquids hotter for longer periods of time than single walled cups. Thermal
models of single walled and double walled cups of the same geometry were generated to
study and compare the behavior of the two systems. The thermal models feature
conduction heat transfer in solids with natural convection boundaries. The circulation
cells that occur in liquid water and gases were not modeled in these studies. The double
walled glass cup thermal model was also updated to mimic the data collection activity
that occurred to see how well the model could predict the behavior of an actual test
specimen. The project concludes in support of the claim that double walled cups keep
hot liquids hot longer than single walled cups of similar geometry. Further refinements
to the thermal models and potential uses are also offered for future reference.
ix
1. INTRODUCTION
The traditional cup is typically a single walled container formed to hold liquids. Rapid
loss or gain of thermal energy by the liquid depends on the cup geometry and materials
used. Handles are often added to cups as a feature to enable usage without exposing the
user to hot surfaces [1,2]. The desire for cups that are less prone to rapid heat transfer
has been addressed by the invention of double walled cups.
The first double walled cup patent was issued on July 22, 1969 under number 3456860
to William L. Janninck [3,4]. The original design featured plastic inner and outer walls
supported by circumferential and axial ribs that maintained structural integrity of the cup
while minimizing heat transfer from the inner to outer wall. Modern day double walled
cups can be fabricated from various materials and are delivered in many shapes and
sizes. Figure 1 depicts a typical single walled cup next to a typical modern day double
walled cup.
Figure 1: Left - Single walled cup [5]; Right - Double walled cup [6]
Based on similarity of double walled beverage cups to double paned windows, double
walled cups are expected to keep hot liquids hot longer than single walled cups. The
feature that makes double walled cups similar to double paned windows is the layer of
trapped gas between the inner and outer walls.
1
2. THEORY & METHODOLOGY
Double walled beverage cups are promoted as being able to keep hot drinks hot and cold
drinks cold for longer periods of time than single walled beverage cups. Much like
double pane windows, double walled mugs capture an insulating layer of air between
two layers of material and prevent thermal energy from being readily conducted through
to the other side.
2.1 Theory
The process of heat transfer can be simplified as follows and is depicted in Figure 2:
1. The inner most wall of the window obtains thermal energy and transfers the energy to
towards the second wall via thermal conduction
2. The gas in between the two walls then transfer the thermal energy to the second wall
through convection
3. The energy is then conducted through the second wall
4. Lost to the environment via convection
Figure 2: Schematic of the heat transfer process: 1. Thermal conduction through inner
wall, 2. Convection via trapped gas, 3. Thermal conduction through outer wall, 4.
Energy lost to environment
2
2.2 Methodology
Heat transfer is a process where thermal energy is exchanged between neighboring
systems in response to a temperature difference [7]. This is in accordance to
conservation of energy theory where the total energy of an isolated system remains
constant and the first law of thermodynamics where the change in internal energy of a
system is equal to the heat added to the system minus the work done by the system [7].
The heat transfer process is categorized into three modes: conduction, convection, and
radiation.
Heat conduction is heat transfer across a medium without any motion of the material as a
whole [4]. In a solid, the mechanism of conduction is the atomic activity in the form of
lattice vibration which contribution of the translational motion of electrons if the solid is
electrically-conducting. Heat conduction in a liquid or gas is due to the random motion
and interaction of the molecules. Examples of conductive heat transfer: the transfer of
heat energy down the axis of a metal rod when one end is a higher temperature than the
other; and the transfer of heat energy from a stove element through a metal pan into the
contents within.
Convective heat transfer occurs between systems by moving fluid past a wall of a
different temperature. Convection can be forced or natural - for the purposes of this
discussion and project, only natural will be described and used in the analysis model.
Natural convection occurs in accordance to the Ideal Gas Law, where a liquid that
increases in temperature also decreases in density and rises [7]. Due to the resulting
internal buoyancy force, circulating currents then transport the heat energy away from
the energy source.
For the purposes of this study, only natural convection heat transfers from the cup and
water surfaces exposed to the surrounding environment were simulated. To simplify the
heat transfer model and to avoid any complications with a conjugate heat transfer model,
the heat transfer where the interfaces between the water, cup, and air gap were analyzed
3
as time dependent conductive heat transfer in solids. These simplifications were
necessary to demonstrate that the thermal models were well behaved and that the inputs
or model geometry did not influence the calculations and predictions. The equation for
time dependent heat transfer in solids is as follows:
𝜌𝐶𝑝
𝜕𝑇
= ∇ ∙ (𝑘∇𝑇) + 𝑄
𝜕𝑡
Where:
𝑄 = Energy added to the system (J)
t = time (s)
𝑘 = thermal conductivity of the material (𝑊 ⁄𝑚 ∙ 𝐾)
𝜌 = material density (kg/𝑚3 )
𝑇 = temperature (K)
𝐶𝑝 = heat capacity at constant pressure (𝐽/(𝑘𝑔 ∙ 𝐾)
The convective heat transfer boundary conditions in this study were simplified into
natural convection from a horizontal and vertical plate. The assumption is that the cup is
on a level surface and the cup geometry can be approximated by a vertical wall. For a
time dependent study, the natural convection across a vertical or horizontal plate is
represented by the following equation:
−𝑛 ∙ (−𝑘∇𝑇) = ℎ ∙ (𝑇𝑒𝑥𝑡 − 𝑇)
Where:
ℎ = ℎ𝑎𝑖𝑟 (𝐿, 𝑝𝐴 , 𝑇𝑒𝑥𝑡 ) (𝑊 ⁄𝑚2 ∙ 𝐾)
L = plate height, length, or diameter (m)
𝑝𝐴 = Absolute pressure (Pa)
𝑇𝑒𝑥𝑡 = External temperature (K)
4
Thermal radiation is a form of energy emitted by matter at a nonzero temperature and
can be considered to be the propagation of electromagnetic waves or particles. For the
purpose of this project, this form of heat transfer will be considered insignificant.
Using the above equations to generate the boundary conditions that will be applied to the
thermal models results in the following Figure 3.
Figure 3: Thermal model boundary conditions
The material properties used in this work were taken from the COMSOL built-in
materials library. Table 1 provides the values for each property. The material properties
for air and liquid water are temperature dependent; therefore no single value is listed in
the table.
5
Silica Glass
Property
Name
Heat Capacity at constant pressure
Cp
Density
rho
Thermal conductivity
k
Air
Property
Name
Heat Capacity at constant pressure
Cp
Density
rho
Thermal conductivity
k
Water, liquid
Property
Name
Heat Capacity at constant pressure
Cp
Density
rho
Thermal conductivity
k
Value
703
2203
1.38
Units
J/(kg*K)
kg/m^3
W/(m*K)
Value
Cp(T[1/K])
rho(pA[1/Pa],T[1/K])
k(T[1/K])
Units
J/(kg*K)
kg/m^3
W/(m*K)
Value
Cp(T[1/K])
rho(T[1/K])
k(T[1/K])
Units
J/(kg*K)
kg/m^3
W/(m*K)
Table 1: Material properties used in the thermal analysis models
6
3. RESULTS & DISCUSSION
The test specimen obtained for this project is the Kiran Tea Glass distributed exclusively
by Teavana [8]. The cup is double walled, made from borosilicate glass, and holds 8
ounces or 235 milliliters of liquid. The cup can be procured from any Teavana retail
store or from the company’s internet website. Figure 4 is a picture of the cup.
Figure 4: Kiran Tea Glass by Teavana
The reason for selecting this cup model is due to its design being simple, axisymmetric,
and being made from a clear glass material. This simplifies not only the analysis, but
also eliminates complications from the analysis model.
A two-dimensional sketch of the cup was created using NX 6.0, the computer-aided
design software package formerly known as NX Unigraphics. The inputs used to model
the cup were gathered using a scale, digital caliper, and radius gages. Dimensions that
7
could not be measured such as the thickness of the glass were estimated. Also, flaws in
the glass itself like bubbles or uneven surface profiles were not incorporated into the
model. All dimensions were gathering in the United States customary system units then
converted to metric using NX. Figure 5 is a picture of the tools used to gather the
dimensions of the cup being analyzed.
Figure 5: Scale, digital caliper, and radius gages
To facilitate the analysis model, two-dimensional sketches of the water and air were
created using the curves from the two-dimensional cup sketch. As with the cup, the air
and water were created in the United States customary system units then converted to
metric using NX. Imperfections such as uneven wall profiles and scratches were not
incorporated into the model.
8
These sketches were then revolved around a datum axis to generate a three dimensional
model. The following Figure 6 is a picture of the three models nested and crosssectioned.
Figure 6: Cross-section of the 3D models of the cup, air, and water
While the three-dimensional models of the cup, air, and water were not necessary for the
study, they were useful for predicting what the two-dimensional-axisymmetric thermal
model would look like based on the two-dimensional NX model.
3.1 COMSOL Heat Transfer in Solids Model – Single Walled Cup
COMSOL Multiphysics 4.2a was used to create and solve the finite element analysis
models for both the single walled and double walled cup. Since the two models are
geometrically the same, the procedure used to create and set up the thermal analysis was
common for both models. The geometry created using NX was imported into COMSOL
via a Drawing Exchange Format (DXF) file which is one of the default export files from
NX. The heat transfer module was then used to generate time-dependent Heat Transfer
in Solids studies and apply the boundary conditions. The COMSOL mesh generator and
analysis solver were used to set up the remainder of the simulations.
9
After importing, the cup, air, and water geometry were united and repaired to
compensate for any approximations that were made when the NX files were converted to
the appropriate measurement systems and file formats. The relative repair tolerance
function in COMSOL was utilized to perform the geometry repair. The repair tolerance
was set to 1e-3 millimeters. Figure 7 is a picture of the cup, air, and water domains after
being imported and repaired in COMSOL.
Figure 7: The cup, air, and water domains after importing and repairing in COMSOL
For the single walled cup thermal study, the air domain was set to the same material
properties as the cup domain. This eliminated any potential analytical discrepancies a
single walled cup of different geometry would have when drawing comparison
conclusions between single and double walled cups. The material property values for the
glass and water were from the built-in library in COMSOL.
10
The thermal models are two-dimensional axisymmetric. It is important to note that
utilizing an axis of symmetry simplifies the thermal model by eliminating the need to
account for any uneven heat transfer perpendicular to the axis of symmetry and the
amount of detail that needed to be taken into account when generating the 2D sketch in
NX.
In heat transfer in solids models, any curves between materials are set to conductive heat
transfer by default. Insulating boundary conditions were added to the bottom and axis of
symmetry. Natural convection boundary conditions were added to the top of the water
and outer wall of the cup. Refer to Figure 4 an overall sketch of the boundary conditions
and their ruling equations.
Zero heat energy is lost to the surrounding environment from the while normal
convection heat transfer occurs at the sides and top surface of the water. Convection past
a vertical wall were applied to the sides of the of the glass cup model. Convection past a
horizontal plate was applied to the exposed surface of the water model.
In both natural convection boundary conditions the atmospheric pressure and
temperature were set to 1 atm and 293.15 K, respectively. The initial temperature value
of the water was set to 373.15 Kelvin. The initial temperature value of the cup was set to
294.26 Kelvin. This would simulate boiled water added to the single walled glass cup at
room temperature. The rest of the variables in the thermal equations are satisfied by the
material properties and their temperature dependent relationships listed in Table 1.
COMSOL offers the user the opportunity to use meshes of incrementing coarseness. In
order to confirm that the thermal model would not be influenced by the mesh, a mesh
coverage study was performed. Based on the convergence study, the mesh size bears no
influence on the calculations and a mesh of normal element size would be appropriate
for this study. The following Table 2 displays the results of the convergence study.
11
Element Size
Extremely
Coarse
Extra Coarse
Coarser
Coarser
Normal
Fine
Finer
Extra Fine
Extremely Fine
Element
Count
Degrees of
Freedom
Final Water Temp
(K)
725
862
1139
1685
2544
2645
3621
5917
18078
1534
1813
2380
3500
5255
5462
7442
12082
36595
351.3
351.65
351.22
352.03
351.89
351.8
351.8
352.14
352.27
Table 2: Mesh convergence study results
The thermal model for the single walled glass cup is a time dependent study. The study
duration was for thirty minutes and with each solver step size no larger than 60 seconds.
Figure 8 is a picture of the single walled glass cup thermal model at time = thirty
minutes in COMSOL.
Figure 8: Thermal model at time = 30 minutes in COMSOL
12
After thirty minutes, the water temperature dropped approximately 22 degrees and the
cup temperature rose approximately 34 degrees. The lip of the cup is the coolest spot in
the model and the middle of the water retained the most heat. The following graph in
Figure 9 is the water and single walled cup wall temperature over the course of the 30
minute study. The thermal analysis model appears to be well behaved and utilized the
applied boundary conditions appropriately.
Figure 9: Plot of the water and single walled glass cup temperature against time
Note the spike in thermal heat transfer between the water and cup in the first several
minutes of the study. As expected, the top surface of the water loses energy out to the
environment while the middle of the water domain remains the hottest spot in the model.
The cup temperature peaks around four minutes then steadily drops for the rest of the
study. The temperature throughout the wall of the cup is fairly uniform and there is little
difference between the inner and outer surfaces of the single wall. The water and glass
cup wall steadily drop in temperature in a fairly linear fashion once the initial spike of
heat transfer occurs.
13
3.2 COMSOL Heat Transfer in Solids Model – Double Walled Cup
The second thermal model created in COMSOL was another time-dependent Heat
Transfer in Solids study for the double walled glass cup. The same cup, air, and water
geometry used in the single walled study were imported into COMSOL and united. The
same relative repair tolerance function in COMSOL was utilized to perform the
geometry repair. The repair tolerance was set to 1e-3 millimeters.
The material properties for the glass, air, and water were added to their respective
domains from the built-in library in COMSOL. See Figure 8 for the location of each
material domain. Much like the singled walled glass cup, the thermal model for the
double walled glass cup is two-dimensional axisymmetric and features all the same
boundary conditions summarized in Figure 3.
Zero heat energy is lost to the surrounding environment from the while normal
convection heat transfer occurs at the sides and top surface of the water. Convection past
a vertical wall were applied to the sides of the of the glass cup model. Convection past a
horizontal plate was applied to the exposed surface of the water model.
In both natural convection boundary conditions the atmospheric pressure and
temperature were set to 1 atm and 293.15 K, respectively. The initial temperature value
of the water was set to 373.15 Kelvin. The initial temperature value of the cup was set to
294.26 Kelvin. This would simulate boiled water added to the single walled glass cup at
room temperature. The rest of the variables in the thermal equations are satisfied by the
material properties and their temperature dependent relationships listed in Table 1.
Since the model geometry did not change, the same mesh convergence study performed
for the single walled glass cup applies. Based on the convergence study, the mesh size
bears no influence on the calculations and a mesh of normal element size would be
appropriate for this study. See Table 2 for the results of the convergence study.
14
Like the single walled glass cup study, a stepped time dependent study was performed.
The duration was for thirty minutes and with 60 seconds for the maximum step size.
Figure 10 is of the results of the thermal model at time = thirty minutes.
Figure 10: Double walled cup thermal model at time = 30 minutes
After thirty minutes, the water temperature dropped approximately 12 degrees and the
cup temperature rose approximately 30 degrees. The lip of the cup is the coolest spot in
the model and the middle of the water retained the most heat. The following graph in
Figure 11 is the water, air, and double walled cup wall temperature over the course of
the 30 minute study. The thermal analysis model appears to be well behaved and utilized
the applied boundary conditions appropriately.
15
Figure 11: Plot of the water and double walled glass cup temperature against time
Note the spike in thermal heat transfer between the water and cup in the first several
minutes of the study. This same behavior was also noted in the single walled cup study.
However, due to the air gap there is a significant difference in temperature between
points C and D throughout the study in the double walled glass cup versus the single
walled glass cup. The cup temperature peaks around ten minutes, significantly later than
the single wall glass cup. The water, air, and cup temperatures steadily drop in a fairly
linear fashion once the initial spike of heat transfer occurs. Also note that the air trapped
between the two walls of glass eventually remains hotter than the top surface of the
water.
3.2 Measured Data versus Analytical Model
Boiled water was added to the Kiran Tea Glass on hand and the water temperature was
measured incrementally as it cooled off. The double walled glass cup was placed on a
cork trivet and the room temperature was measured with a digital thermometer [9].
Water was boiled in an electric kettle along with the digital thermometer to bring both
the water and the thermometer up to the same starting temperature. The boiled water and
thermometer were added to the cup and a stop watch was used to time the
16
measurements. The thermometer was resting on the bottom and side of the cup during
the measurement gathering.
The measured results data is available in Appendix 1. A graph of the measured
temperature versus time can be seen in Figure 12.
Water Temperature vs. Time
380,00
370,00
Temperature (K)
360,00
350,00
340,00
Water Temperature
330,00
320,00
310,00
300,00
0
500
1000
1500
2000
Time (s)
Figure 12: Measured temperature of boiled water versus time in the Kiran Tea Glass
The double walled thermal model was updated to replicate the measured data by
changing the ambient and initial temperatures to match the values at the time the
measured data was captured. The results are presented in Figure 13.
17
Figure 13: Graph of the temperature of boiled water in the Kiran Tea Glass
The behavior between the test study and the thermal model is similar. The spike of
energy transfer at the beginning of the studies can be noted in both the measured data
and the thermal model. The shape of the curve after the initial spike is also similar
between the measured data and the thermal model. However, the heat lost rate and
ending temperatures between the measured data and the thermal model differ greatly.
Some reasons for the greater heat loss in the measured data than the thermal model may
include: the convection coefficients used in the thermal model are lower than reality,
significant amounts of energy are lost to the surface the cup rests on even though the cup
was resting on an insulating material, the thermometer conducts away extra heat, and the
effect of natural convection in the bulk of the water. The biggest driver would be the
natural convection coefficients used in the thermal models.
18
4. Conclusions
In conclusion, double walled cups are demonstrated to be more effective at keeping hot
liquids hot for longer periods of time than single walled cups. The layer of air between
two walls of glass allow the double walled cups to perform in a similar fashion to double
pane windows where the transfer of heat energy through the cup wall is significantly
slowed by the lower thermal conductivity of the air trapped within.
The studies themselves are considered successful. The model geometry closely
represents the real model from which they were based on, the appropriate boundary
conditions for the purpose of this initial study were applied, and the models were not
influenced by the mesh size used. The models created are a strong foundation for refined
boundary conditions, inputs, and thermal modeling techniques.
The water in the double walled cup thermal model exhibited a lower rate of thermal
energy loss to the surrounding environment than the single walled cup thermal model.
The non-wetted surfaces of the double walled cup gained thermal energy slower than the
single walled cup for the duration of the analysis due to the layer of air that significantly
slowed the transfer of heat energy from the water to the outside wall of the cup.
The measured data verified that the thermal models are well behaved and can be a first
step to developing a true representation of what takes places in physical rigs. At this
point in time, the thermal models cannot be used to accurately predict the thermal energy
loss rate and the temperature of the water at any given time without refinement. Refining
of the thermal model would include, simulating the circulation that occurs due to natural
convection and converging on the true convection coefficients of the water, air, and
glass. The thermal loss through the thermometer and through the bottom of the glass
should also be taken into account.
19
5. References
1. R. G. (1999, Feb 22). Starbucks plans to test a paper cup that insulates hands from
hot coffee. Wall Street Journal. Retrieved from
http://search.proquest.com/docview/398688536?accountid=37764
2. S. K. (1998, Mar 24). These people search for a cup that suits the coffee it holds --the current models can burn fingers, come unglued; mr. sadlier hawks `Insulair'. Wall
Street Journal. Retrieved from
http://search.proquest.com/docview/398614978?accountid=37764
3. Janninck, W.L. (1969). U.S. Patent No. 3456860. Washington, DC: US Patent and
Trademark Office. Retrieved from
http://www.google.com/patents?id=qJ9ZAAAAEBAJ&printsec=abstract&zoom=4#
v=onepage&q&f=false
4. Singaporean inventors develop double-walled cup. (2009, Sep 18). Indian Patents
News. Retrieved from
http://search.proquest.com/docview/443239946?accountid=37764
5. 11 oz stoneware coffee mug – white. Retrieved from http://splendids.com/11-ozstoneware-mugs-c-1_130/11-oz-stoneware-coffee-mug-white-p-1013
6. Bodum Bistro 15 oz. Mug & Reviews | Wayfair. Retrieved from
http://www.wayfair.com/Bodum-Bistro-15-oz.-Mug-10606-10-BMO1043.html
7. Nave, R. Heat Transfer. Retrieved from http://hyperphysics.phyastr.gsu.edu/hbase/thermo/heatra.html#c1
8. Kiran Tea Glasses at Teavana | Teavana. Retrieved from
http://www.teavana.com/tea-products/tea-cups-mugs/glass-tea-cups/p/kiran-teaglasses-8oz
9. Amazon CDN DTC450 Digital Candy Thermometer Retrieved from
http://www.amazon.com/gp/product/B00279OPDU
20
6. Appendices
6.1 Appendix 1: Measured temperature data from boiled water in the double walled cup
Time (s)
0
60
120
180
240
300
360
420
480
540
600
660
720
780
840
900
960
1020
1080
1140
1200
1260
1320
1380
1440
1500
1560
1620
1680
1740
1800
Temperature
Water
(F)
Temperature
210
372.04
195
363.71
189
360.37
183
357.04
178
354.26
174
352.04
169
349.26
166
347.59
163
345.93
159
343.71
157
342.59
154
340.93
151
339.26
149
338.15
147
337.04
144
335.37
142
334.26
140
333.15
138
332.04
137
331.48
135
330.37
133
329.26
132
328.71
130
327.59
129
327.04
127
325.93
126
325.37
124
324.26
123
323.71
122
323.15
121
322.59
21