1. 1
ME 421
Mechanical Engineering Lab
Dr. Sanders
Fall 2015–2016
Determination of the Thermal Conductivity for Various Insulated Can Holders
11/13/2015
Patrick Fonda
Matt Kelsay
Nicholas Wilkowski
Joseph Woodley
Rose-Hulman Institute of Technology
Terre Haute, IN 47803

2. 2
Abstract:
One of the main causes of displeasure among cold beverage drinkers is a result of an ineffective
method of keeping the beverage container cold. The most popular means of keeping an
aluminum can cold is by using an insulated can holder—commonly known as a ‘koozie’ or
‘huggie.’ Insulated can holders come in many different materials, all of which have a different
value of thermal conductivity, 𝑘. In order to determine the ideal method for insulating a
beverage in an aluminum can, the thermal conductivity of multiple insulated can holders—each
made of dissimilar materials—was investigated and determined experimentally. Along with
this, the usefulness of using the thermal conductivity of a koozie to determine effectiveness was
also looked at.
For this experiment, four different koozie materials were tested. The first was made of
inexpensive polyurethane foam, the second from neoprene, the third form molded EVA foam,
and the fourth was a Yeti Colster (vacuum insulated koozie). Measurements of each koozie
were taken before trials were run. Three trial experiments were run with each trial containing
all koozies for a total of three data points for each koozie. Temperature readings were taken
every 10 minutes during the trials. The raw data for these trials are contained in Appendix A.
From the raw data, the thermal conductivity of each koozie was determined. The table below
contains the average thermal conductivities found during the trials.
Averaged thermal conductivities of the four tested koozies.
In completing the experiment, we found that although the thermal conductivity is an adequate
indication of an effective koozie, it may not be the only factor that should be taken into
consideration.

3. 3
Table of Contents
Introduction Page 4
Experimental Facilities and Instrumentation Page 4
Data Reduction Page 5
Uncertainty Analysis Page 8
Results Page 10
Conclusion & Recommendations Page 11
Appendix A: Raw Data Page 12
Appendix B: Thermal Conductivity for Each Trial Page 15
Appendix C: Bibliography Page 16

4. 4
Introduction:
The objective of this experiment is to quantitatively determine the thermal conductivity of four
different types of insulated can holders: one being made from inexpensive polyurethane foam,
another made from molded EVA foam, another from neoprene, and the final being the vacuum
insulated YETI Colster. As the cold can of fluid within an insulated can holder sits in a room,
the fluid temperature inside the can will increase with time due to convective heat transfer
between the fluid and surrounding air. The change in temperature of the fluid is then
proportional to the thermal conductivity of the insulated can holder around the can, with a
lower thermal conductivity resulting in a more effective insulated can holder—meaning that the
can and its contents will remain colder for a longer period of time. The expectation of this
experiment is to determine the thermal conductivity of each insulated can holder with less than
± 30% uncertainty, as well as determine if thermal conductivity is the best indication of koozie
performance.
Experimental Facilities and Instrumentation:
In order to acquire the data needed to obtain the thermal conductivity, k, of the different
koozies, the apparatus shown in Figure 1 below is used. A can inside of an insulating koozie
sits on a ring stand. A clamp is used to support a thermometer probe that reads the
temperature of the water in the can, T(t). The thermometer is also used to measure the ambient
temperature, Tamb. cp is the specific heat of water, and m is the mass of the water and can. ro
represents the distance from the center of the can to the outside of the koozie while ri is the
distance from the center of the can to the inside of the koozie. L represents the height of the
insulating koozie.
Figure 1. Apparatus used to collect temperature readings of water over time.
T(t)
Tamb
Ring stand to hold
temperature probe
ri
ro
m,cp
L

5. 5
In total, four koozies will be tested, each composed of a different material. The first is made
from inexpensive polyurethane foam, the second is made from neoprene, the third from molded
EVA foam, and the fourth is a Yeti Colster.
The aim of this experiment is to gain the data and measurements necessary to determine the
thermal conductivity, k, of the four insulating koozies. Prior to running the experiment, the
outer radius, ro, inner radius, ri, and the insulating koozie height, L, should be measured for
each insulating koozie. In addition, all cans should be emptied of their original contents and
filled with water in order to use the known properties of water for data analysis. Once filled,
the cans are placed in a refrigerator overnight so that the temperature of the water in the cans
has time to equilibrate. In order to ensure that all koozies are tested in the same ambient
environment, all four koozies are tested at the same time. Each koozie-can pair has its own
thermometer probe in order to prevent discontinuities from pair to pair. The cans are removed
from the refrigerator and each mass is recorded. They are then placed in their corresponding
insulating koozie. Once all cans are in their insulating koozie, the initial water temperature for
each can is recorded and the timer is started. The water temperature is recorded every 10
minutes. Once the time has reached 60 minutes, the final water temperature for each can is
recorded. This procedure is repeated three times in order to obtain consistent data. It is
important to leave enough time in-between trials to allow the koozies to return to ambient
temperature.
Data Reduction:
The concepts behind the process of analyzing the data stems from fundamental heat transfer
analysis methods for thermal resistance. The thermal resistance of a material is a measurement
of a temperature difference by which the material resists heat flow. The system consists of a
series of thermal resistors: the ambient air, the koozie, the aluminum can, and the liquid inside
the can. This can be seen in Figure 2 on the next page, along with the derivation of the data
reduction equation.

6. 6
Figure 2. The experimental system can be modeled as a series of thermal resistors: the resistance
of the ambient air, the koozie, the aluminum can, and the liquid inside the can.
Equation 1 comes from a series of thermal resistors.
𝑅 𝑇𝑜𝑡𝑎𝑙 = 𝑅 𝑐𝑜𝑛𝑣,1 + 𝑅𝑖𝑛𝑠𝑢𝑙 + 𝑅 𝑎𝑙 + 𝑅 𝑐𝑜𝑛𝑣,2 Eq. (1)
Several assumptions can be made in order to simplify our overall data reduction equation. The
first of which is the only mode of heat transfer by the fluid inside the aluminum can is
conduction, and thus 𝑅 𝑐𝑜𝑛𝑣,1= 0.
𝑅 𝑐𝑜𝑛𝑣,1 =
1
2𝜋𝑟1ℎ1 𝐿
= 0 Eq. (2)
The next assumption involves the relative difference between the radius from the center of the
system to the inside of the can and the radius from the center to the outside of the can. That is,
since the thickness of the aluminum can is so low—that is 𝑟2≈ 𝑟1—the thermal resistance of the
aluminum is negligible. We can also say that since the thermal conductivity (𝑘 𝑎𝑙) is so large—
usually in the range of 205-250
𝑊
𝑚𝐾
—the value of 𝑅 𝑎𝑙 will approach zero relatively quickly.
𝑅 𝑎𝑙 =
ln
𝑟2
𝑟1
2𝜋𝑘 𝑎𝑙 𝐿
= 0 Eq. (3)

7. 7
Below is the thermal resistance of the koozie—or insulator— 𝑅𝑖𝑛𝑠𝑢𝑙.
𝑅𝑖𝑛𝑠𝑢𝑙 =
ln
𝑟3
𝑟1
2𝜋𝑘 𝑖𝑛𝑠𝑢𝑙 𝐿
Eq. (4)
The final assumption addresses the fact that since the ambient temperature will be measured as
close as possible to the outside of the insulated can holder, the resistance of the ambient air is
negligible. We can also assume that this value is zero since there exists relatively no airflow over
the outside surface of the koozie or can.
𝑅 𝑐𝑜𝑛𝑣,2 =
1
2𝜋𝑟3ℎ2 𝐿
= 0 Eq. (5)
The total amount of heat transfer through the system can be modeled by the equation:
𝑄̇ =
𝑇𝑖− 𝑇 𝑎𝑚𝑏
𝑅 𝑇𝑜𝑡𝑎𝑙
, Eq. (6)
where the total thermal resistance is just that of the thermal resistance of the insulated can
holder, due to the assumptions made for Equations 2, 3, & 5.
𝑅 𝑇𝑜𝑡𝑎𝑙 =
ln
𝑟3
𝑟1
2𝜋𝑘 𝑖𝑛𝑠𝑢𝑙 𝐿
Eq. (7)
Substituting Eq. (7) into Eq. (6) yields:
𝑄̇ =
𝑇𝑖− 𝑇∞,2
ln
𝑟3
𝑟1
2𝜋𝑘 𝑖𝑛𝑠𝑢𝑙 𝐿
Eq. (8)
Also, the maximum amount of heat transfer that will be present in the system can be modeled
by the equation:
𝑄 𝑚𝑎𝑥 = 𝑚𝐶 𝑝(𝑇𝑓 − 𝑇𝑖) Eq. (9)
The equation for transient heat transfer in a system will allow us to build an equation using the
maximum amount of heat transfer in the system from Eq. (9).
𝑄̇ =
𝑄 𝑚𝑎𝑥
∆𝑡
Eq. (10)

8. 8
Substituting Eq. (8) into Eq. (10) yields:
𝑄 𝑚𝑎𝑥
∆𝑡
=
𝑇𝑖− 𝑇 𝑎𝑚𝑏
ln
𝑟3
𝑟1
2𝜋𝑘 𝑖𝑛𝑠𝑢𝑙 𝐿
Eq. (11)
Solving Eq. (11) for the thermal conductivity of the insulated can holder allows us to arrive at
the final form of our data reduction equation.
𝑘𝑖𝑛𝑠𝑢𝑙 =
1
2𝜋𝐿
(ln(
𝑟 𝑜
𝑟 𝑖
))
𝑇 𝑖− 𝑇 𝑎𝑚𝑏
𝑚𝐶 𝑝(𝑇𝑓− 𝑇 𝑖)/∆𝑡
Eq. (12)
Uncertainty Analysis:
Because of the nature of the Data Reduction Equation, Eq. (12), the shortcut form of the UMF
uncertainty equation could not be used. The uncertainty in the thermal conductivity is given by
𝑤 𝑘
2
= (
𝜕𝑘
𝜕𝑇𝑖
)
2
(𝑤 𝑇𝑖)2
+ (
𝜕𝑘
𝜕𝑇 𝑓
)
2
(𝑤 𝑇𝑓)2
+ (
𝜕𝑘
𝜕𝑇 𝑎𝑚𝑏
)
2
(𝑤 𝑇𝑎𝑚𝑏)2
+ (
𝜕𝑘
𝜕𝑚
)
2
(𝑤 𝑚)2
+
(
𝜕𝑘
𝜕𝑟𝑖
)
2
(𝑤𝑟𝑖
)2
+ (
𝜕𝑘
𝜕𝑟𝑜
)
2
(𝑤𝑟𝑜
)2
+ (
𝜕𝑘
𝜕𝐿
)
2
(𝑤 𝐿)2
+ 𝑤 𝑘,𝑟𝑎𝑛𝑑
2
.
Eq. (13)
The partial derivatives are given by the following:
𝜕𝑘
𝜕𝑇𝑖
= −
1
2
𝑚𝐶 𝑝 ln (
𝑟𝑜
𝑟𝑖
)
∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)𝜋𝐿
, Eq. (14)
𝜕𝑘
𝜕𝑇𝑓
=
1
2
𝑚𝐶 𝑝ln(
𝑟𝑜
𝑟𝑖
)
∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)𝜋𝐿
−
1
2
𝑚𝐶 𝑝 ln (
𝑟𝑜
𝑟𝑖
)
∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)
2
𝜋𝐿
,
Eq. (15)
𝜕𝑘
𝜕𝑇𝑎𝑚𝑏
=
1
2
𝑚(𝑇𝑓 − 𝑇𝑖)𝐶 𝑝ln(
𝑟𝑜
𝑟𝑖
)
∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)2 𝜋𝐿
, Eq. (16)
𝜕𝑘
𝜕𝑚
=
1
2
𝐶 𝑝(𝑇𝑓 − 𝑇𝑖) ln (
𝑟𝑜
𝑟𝑖
)
∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)𝜋𝐿
, Eq. (17)
𝜕𝑘
𝜕𝑟𝑖
= −
1
2
𝑚(𝑇𝑓 − 𝑇𝑖)𝐶 𝑝
𝑟𝑖∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)𝜋𝐿
,
Eq. (18)

9. 9
𝜕𝑘
𝜕𝑟𝑜
=
1
2
𝑚(𝑇𝑓 − 𝑇𝑖)𝐶 𝑝
𝑟𝑜∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)𝜋𝐿
,
Eq. (19)
𝜕𝑘
𝜕𝐿
= −
1
2
𝑚(𝑇𝑓 − 𝑇𝑖)𝐶 𝑝 ln (
𝑟𝑜
𝑟𝑖
)
∆𝑡(𝑇𝑓 − 𝑇𝑎𝑚𝑏)𝜋𝐿2
. Eq. (20)
Substituting Eq. (14) – Eq. (20) into Eq. (13) and dividing each term by 𝑘2
yields the following:
(
𝑤 𝑘
𝑘
)2
=
(
−
1
2
𝑚𝐶 𝑝 ln(
𝑟 𝑜
𝑟 𝑖
)
∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)𝜋𝐿
𝑘
)
2
(𝑤 𝑇𝑖)2
+
(
1
2
𝑚𝐶 𝑝ln(
𝑟 𝑜
𝑟 𝑖
)
∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)𝜋𝐿
−
1
2
𝑚𝐶 𝑝 ln(
𝑟 𝑜
𝑟 𝑖
)
∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)
2
𝜋𝐿
𝑘
)
2
(𝑤 𝑇𝑓)2
+
(
1
2
𝑚(𝑇 𝑓−𝑇 𝑖)𝐶 𝑝ln(
𝑟 𝑜
𝑟 𝑖
)
∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)2 𝜋𝐿
𝑘
)
2
(𝑤 𝑇𝑎𝑚𝑏)2
+ (
1
2
𝐶 𝑝(𝑇 𝑓−𝑇 𝑖) ln(
𝑟 𝑜
𝑟 𝑖
)
∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)𝜋𝐿
𝑘
)
2
(𝑤 𝑚)2
+
(
−
1
2
𝑚(𝑇 𝑓−𝑇 𝑖)𝐶 𝑝
𝑟 𝑖∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)𝜋𝐿
𝑘
)
2
(𝑤𝑟𝑖
)2
+ (
1
2
𝑚(𝑇 𝑓−𝑇 𝑖)𝐶 𝑝
𝑟 𝑜∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)𝜋𝐿
𝑘
)
2
(𝑤𝑟𝑜
)2
+
(
−
1
2
𝑚(𝑇 𝑓−𝑇 𝑖)𝐶 𝑝 ln(
𝑟 𝑜
𝑟 𝑖
)
∆𝑡(𝑇 𝑓−𝑇 𝑎𝑚𝑏)𝜋𝐿2
𝑘
)
2
(𝑤 𝐿)2
+ (
𝑤 𝑘,𝑟𝑎𝑛𝑑
𝑘
)2
.
Eq. (21)
Eq. (21) can then be simplified to
(
𝑤 𝑘
𝑘
)2
= (−
1
𝑇 𝑓−𝑇𝑖
)
2
(𝑤 𝑇𝑖)2
+ (−
𝑇 𝑎𝑚𝑏−𝑇𝑖
(−𝑇 𝑓+𝑇 𝑎𝑚𝑏)(−𝑇 𝑓+𝑇𝑖)
)
2
(𝑤 𝑇𝑓)2
+ (
1
𝑇 𝑓−𝑇 𝑎𝑚𝑏
)
2
(𝑤 𝑇𝑎𝑚𝑏)2
+
(
1
𝑚
)
2
(𝑤 𝑚)2
+ (−
1
𝑟𝑖 ln(
𝑟 𝑜
𝑟 𝑖
)
)
2
(𝑤𝑟𝑖
)2
+ (
1
𝑟𝑜 ln(
𝑟 𝑜
𝑟 𝑖
)
)
2
(𝑤𝑟𝑜
)2
+ (−
1
𝐿
)
2
(𝑤 𝐿)2
+ (
𝑤 𝑟𝑎𝑛𝑑
𝑘
)2
.
Eq. (22)

10. 10
Table 1 shows the sample uncertainty calculations for Trial 1 using the polyurethane insulated
can holder.
Parameter
Representative
Value
Uncertainty
Relative
Uncertainty (%)
UMF
RSSC
(%)
UPC
(%)
Tf
11.5 °C 8.92e-3 °C 6.2 2.84 17.6 59
Ti
5.5 °C 5.97e-3 °C 12.9 0.92 11.8 26
Random - - 6.8 1.0 6.8 9
Tamb
24.0 °C 2.94e-3 °C 3.0 1.92 5.8 6
ri
0.02204 m 2.92e-4 m 0.094 6.15 0.58 <1
L 0.10252 m 1.02e-5 m 0.020 1.0 0.020 <1
ro
0.02593 m 2.48e-4 m 0.080 6.15 0.49 <1
m 0.36036 kg 1.41e-5 kg 0.028 1.0 0.028 <1
k 0.0342 W/m-K 0.00787 W/m-K 23.0 - 23.0 100
Table 1. Sample of uncertainty analysis obtained from data during Trial 1
Results:
From the raw data, the thermal conductivity of each koozie was determined. Table 2 below
contains the average thermal conductivities found over the three trials. In conjunction with our
expected results, the koozie with the lowest value of thermal conductivity was the Yeti Colster,
with a k-value of 0.0152 (W/mK). It is important to note that the relative uncertainty associated
with the Yeti Colster is abnormally high when compared to the relative uncertainty values of
the other koozies. We believe that this is a product of the low temperature change of the liquid
in the can held by the Yeti Colster over the duration of our experiment.
Table 2. Average thermal conductivities of the four tested insulated can holders.

11. 11
Conclusion & Recommendations:
The results show that the Yeti Colster has the lowest value for thermal conductivity. During the
trials the Yeti Colster kept the can almost a constant temperature. The percent relative
uncertainty is high for the Yeti Colster, at 57.1%, which is not within our target of 30% relative
uncertainty. The percentage of relative uncertainty for the neoprene koozie of 19.8% is within
our target. With these relative uncertainty values, there exists an overlap of thermal
conductivity ranges between the Yeti Colster and the neoprene koozie, so further testing would
be required to make it clear that the k values deviate from each other. If the values of thermal
conductivity deviate further in successive experiments, it could be concluded that the Yeti
Colster is a more effective insulated can holder than the neoprene koozie.
In carrying out our experiment, we were also able to conclude that thermal conductivity may
not be the most indicative property of an effective koozie, as can be seen in Appendix A. Due to
its high thermal conductivity value it would appear from Table 2 that the molded EVA koozie
would perform the worst among the koozies tested; however, it was the second most effective
koozie because of its relatively high thickness.
In reproducing this experiment, several recommendations can be made in order to determine
the most effective koozie. The first of the recommendations involves a participant holding the
can/koozie system in order to develop an ideal real world model. This should yield similar
results of thermal conductivity for each of the four koozies; however, the data reduction
equation would have to be adjusted in order to account for the additional heat source and
thermal resistance of the participant’s hand. Another recommendation we believe would be
beneficial in determining an effective koozie is carrying out the experiment in various ambient
environments. This would possibly include a hotter environment than the one in which this
experiment was carried out in. A final recommendation involves starting the liquid at a higher
initial temperature and letting it cool in the ambient air. We believe that this will yield results
similar to those found in the current experiment.

12. 12
Appendix A: Raw Data
Trial 1:
Table 3 shows the mass of water used in each can for Trial 1.
Table 3. Mass measurements for first trial.
Table 4 shows the temperature at each time interval while Figure 3 is a plot of this data
Table 4. Temperature readings for each time interval.
Figure 3: Trial 1 plot of temperature change for each insulated can holder over a time of 60
minutes.
mass (g)
cheap 360.36
neoprene 339.85
EVA 364.06
YETI 367.34
Time Cheap Neoprene EVA YETI
0 5.5 6 5.4 5.3
10 6.7 7.3 6.3 5.7
20 7.9 8.9 7.3 6
30 9 10.2 8.3 6.5
40 10 11.5 9.3 6.7
50 10.7 12.4 10.1 7.1
60 11.5 13.5 10.8 7.5
Tamb 24

13. 13
Trial 2:
Table 5 shows the mass of water used in each can for Trial 2.
Table 5. Mass measurements for first trial.
Table 6 shows the temperature at each time interval while Figure 4 is a plot of this data
Table 6. Temperature readings for each time interval.
Figure 4: Trial 2 plot of temperature change for each insulated can holder over a time of 60
minutes.
mass (g)
cheap 337.74
neoprene 361.46
EVA 365.05
YETI 357.6
Time Cheap Neoprene EVA YETI
0 4.5 5 5 4.3
10 6.3 7 5.5 4.7
20 7.8 8.6 6.3 4.8
30 8.5 9.6 7.1 5.1
40 9.7 11 8 5.4
50 10 11.5 8.9 5.8
60 10.7 12.3 9.6 6.2
Tamb 24

14. 14
Trial 3:
Table 7 shows the mass of water used in each can for Trial 3.
Table 7. Mass measurements for first trial.
Table 8 shows the temperature at each time interval while Figure 5 is a plot of this data
Table 8. Temperature readings for each time interval.
Figure 5: Trial 3 plot of temperature change for each insulated can holder over a time of 60
minutes.
mass (g)
cheap 337.35
neoprene 360.67
EVA 364.55
YETI 357.11
Time Cheap Neoprene EVA YETI
0 5 4.7 4.4 4.7
10 6.3 6.3 5.6 5.2
20 7.3 7.4 6.5 5.4
30 8.5 8.9 7.5 5.6
40 9.4 9.9 8.1 5.9
50 10.6 11.4 9.3 6.3
60 11.4 12.2 10 6.6
Tamb 24

15. 15
Appendix B: Thermal Conductivity for Each Trail
Table 9 shows the thermal conductivity calculated for each koozie for each trial.
Table 9. Thermal conductivity of each koozie calculated for each trail.

16. 16
Appendix C: Bibliography
Cengel, Y.A., Ghajar, A.J. 2010 Heat and Mass Transfer, 4th Edition. New York City, NY: McGraw-Hill
Education
Flanagan, M.; Orear, C.; Johnson, K.; and Kitchens, C., "The Cooler Koozie, optimizing thermal
insulation for beverage consumption" (2014). Focus on Creative Inquiry. Paper 70.
http://tigerprints.clemson.edu/foci/70
Water—Thermal Properties. (n.d.). Retrieved November 12, 2015 from
http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html