CHE 342 Fall 13 Group Project
Vials, Bubbles, ‘n ‘Beams
(An analysis of heat transfer in insulated 1-D systems)
James Brogan
Eric Giuffrida
Rob Matthews
Stephanie Cohen
Justin Krauss
Group 12
December 4, 2013
1
Introduction
This experiment will demonstrate the effects of insulation as heat flows from an area of higher
temperature to an area of lower temperature. There are three types of heat transfer methods;
conduction, convection and radiation. Our experiment will focus on conduction and convection
methods only. The experiment is designed to be used for high school students and cost fewer
than twenty five dollars for the school to reproduce.
Conduction is the transfer of energy from more energetic molecules to less energetic molecules.
It is accomplished by collision between the particles. Since molecules behave differently, the
rate of heat transfer depends on the type of molecule. Therefore different materials allow for
conduction to occur at a different rate. Specifically the rate of heat transfer is proportional to the
number of free pair electrons. In general metals allow for the highest rate of conduction transfer
because they have the largest amount of free electrons per molecule. Mathematically
conduction follows Fourier’s Law q/A = −k𝛁T where q is the rate of heat transfer, A is area
proportional to flow of heat transfer, 𝛁T is the gradient of heat transfer, and k is called thermal
conductivity coefficient. The negative sign signifies that heat flows from high temperatures to
low temperatures, which is the opposite direction of the temperature gradient. K, or thermal
conductivity coefficient, is a property of the material through which conduction is occurring. A
large k value means that the material allows conduction to occur at a higher rate. A lower k
value means the material allows conduction to occur at a lower rate. In the temperature region
of our experiment (around 70°C) the conductive coefficient for bubble wrap is constant at
k = 0.185
W
. For vial glass in this temperature regime, the conductive resistance is also
mK
constant at k= 1.13
W
.
mK
Convection is the transfer of energy between a surface and an adjacent fluid. Mathematically it
is described by q/A = h △ T. The new variables introduced here are temperature difference (△
T) between the bulk fluid and the surface, and the convective heat transfer coefficient (h). The
convective heat transfer coefficient is a constant that depends on the fluid. For air at room
temperature, h = 10.45
𝑊
𝑚2 𝐾
.
Summary
In our experiment we will wrap glass vials with bubble wrap, which will act as an insulator.
There will be several vials all of the same size with a different thickness of bubble wrap around
each vial. This includes a vial with no bubble wrap around it. The vials will be filled with hot
water. Heat will proceed to flow from the hot water to the surrounding air through the sides of
the vials. The predominant methods of heat transfer in this process are conduction through the
glass, conduction through the bubble wrap, and convection between the outer surface of the
bubble wrap to the surrounding air. The amount of heat transferred from each vial, and the
temperature of the outermost surface of bubble wrap, will be compared by measuring the
temperature of the outermost layer of insulation with a laser temperature gun.
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Our experiment will show the effects of an insulator. By varying the thickness of the insulator
we will show how adding insulation affects the temperature profile of our system. In particular
we will show how temperature of the outermost layer is affected. We will also show how adding
insulation changes the amount of heat loss. This includes heat loss with no insulator, heat loss
with insulation thickness below the critical radius, and heat loss when above the critical radius.
Bubble wrap is a good insulator because it is made out of plastic and air, both of which have low
heat transfer coefficients.
Student
Materials
● Water
● Bubble Wrap
● 5 Glass Vials with a small radius (all of the same size)
● Hot Plate
● Thermometer
● Stopwatch/Clock
● Ruler
● Temperature Laser Gun
● Black sharpie
● Styrofoam board
Experiment/procedure
1. Heat water until the water reaches a temperature of 70°C
2. Record how thick one layer of bubble wrap is (in meters)
3. Measure the following: height of vial (in meters), radius to inner wall of vial (in m),
thickness of vial (in m)
4. Line the 5 vials up in a row. Adds layers of bubble wrap to the vials. The first vial will
have no bubble wrap, the second will have one layer, the third two layers, and so on.
When adding bubble wrap, wrap with the bubbles facing inward toward the vial.
5. Using the Sharpie, draw a black dot at the center of the layer of bubble wrap in each of
the 5 vials. In the case of the first vial, draw a black dot on the glass. Be sure that the
dot is at the same spot on every trial.
6. Cover the top and bottom of each vial with Styrofoam.
7. Pour 50 mL of hot water into each vial
8. After 30 seconds measure the temperature of the black dot on each vial by pointing the
temperature laser gun at the black dot. Angle the laser gun perpendicular to the surface
of the vial to ensure the laser only hits the black dot.
9. Record the temperature of the outermost surface (temperature of the black dot)
10. Calculate the heat transfer rate by using the following equation:
𝑇𝑤 − 𝑇𝑠
𝑞=
𝑟2
𝑟
ln (𝑟 ) ln (𝑟3 )
1
2
+
2ᴨ𝑘𝑔 𝐿 2ᴨ𝑘𝑏 𝐿
3
where Tw = temperature of the water = 70°C
kg = conductivity coefficient of glass = 1.13
W
mK
kb = conductivity coefficient of bubble wrap = 0.185
W
mK
hair = convective heat transfer coefficient of air = 10.45
𝑊
𝑚2 𝐾
r1 = distance from the center to the inner wall of vial
r2 = r1 + thickness of vial
r3 = r2 + thickness of bubble wrap
L = height of vial
TS = measured temperature of the outermost surface in °C
q = calculated heat loss transfer rate in J/s
(use the units listed above)
4
r1
r2
r3
L
Vial #
Total Thickness of insulation
Temperature (TS)
Heat loss transfer rate (q)
1
2
3
4
5
Questions
1. How does the thickness of bubble wrap affect the temperature at the outer layer of the
bubble wrap?
Answer: As the thickness of insulation increases, it will take more time for the
outer layer to heat to a higher temperature, making the more insulated trials result in
lower temperatures after the allotted 30 seconds.
2. How would the experimental results change if water at a different temperature was
used? Why?
Answer: If a significantly greater temperature of water is used, the outside layer
of bubble wrap would have a higher temperature. The opposite is true for a lower temperature.
This occurs because, according to the principles of conduction, heat transfer is caused by the
motion of higher energy particles from an area of high heat to an area of lower energy. The
higher temperature would cause higher energy particles to contact the low energy particles in
the insulation and transfer energy at a faster rate than the lower temperature (and therefore
lower energy) particles.
3. Would using a different type of insulator change the outcome?
Answer: Yes. For example, if aluminum foil was used as an insulator, many
layers would be required to achieve the same time as bubble wrap because aluminum is very
conductive.
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Teacher
Considerations
In order to achieve proper results, students should heat the water to 70°C, making sure it is a
consistent temperature for all. Student should be sure to wrap uniform strips of bubble wrap
layered around the vial. If you are short of wrapping the entire vial or have excess bubble wrap
around the vial you will not get the same results.
When wrapping the vials with an insulator, there will be air trapped between the layers of bubble
wrap. However since bubble wrap is made of plastic with air trapped between it, the air trapped
when wrapping layers is negligible. This may not be true if other fabrics besides bubble wrap
are used.
The purpose of the Styrofoam is to make this experiment effectively one dimensional.
Styrofoam can be considered adiabatic, meaning no heat is transferred through the Styrofoam.
The radial direction is the only direction heat transfer occurs. The vials may be assumed to be
perfectly cylindrical. Since water has a high specific heat, the water temperature can be
assumed to be constant. Radiation is ignored in this experiment because it is negligible. Thus
this experiment may be described mathematically by one dimensional (radial) heat transfer
through perfect cylinders.
The thermal conductivity (k) and convective (h) coefficients can be found online or in a text
book. The k values for both glass and bubble wrap are relatively constant. They differ between
high and low temperatures, however since our experiment will always be in a high temperature
regime of around 70°C we can assume both of these k values are constant. We used Pyrex
glass to estimate the k value of the vial in this temperature regime. We took an average of the
thermal conductivity coefficient of air and low density polyethylene in this temperature regime to
find the conductivity coefficient of bubble wrap. We assumed the bubble was made of 50% air
and 50% low density polyethylene. The plastic in the bubble used in our experiment was made
of low density polyethylene however not all bubble wrap is made from this. If bubble wrap made
from another plastic material is used, than this bubble wrap will have a different k value. The
convective coefficient (h) of air changes with temperature. However for air at a constant
temperature, such room temperature, the convective coefficient is constant.
The critical radius is very small for bubble wrap. For our bubble wrap in air at room
temperature, the critical radius is r3, critical = 17.7 millimeters. For this reason vials or beakers
with a very small inner wall diameter must be used. For the glass vials in our experiment, r1 = 9
millimeters. The thickness of our bubble wrap was around 4 millimeters. This allowed us to
have data above and below the critical radius of insulation.
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Expected Outcome
When the experiment is run, there should be a noticeable difference in the temperature of the
outside layer, depending on the thickness of bubble wrap for each vial. Higher thicknesses of
bubble wrap will result in a lower temperature. The vial without bubble wrap should produce the
highest outer surface temperature. If you increase the thickness of insulation, the temperature
of the outermost surface will decrease.
When calculating the rate of heat loss, you should find that a critical radius is reached. When
the distance from the center to the outermost layer of insulation (r3) is below the critical radius,
increasing the thickness of insulation (r3) will result in an increase in the rate heat lost. When
above the critical radius, increasing r3 will result in a decrease in the rate heat lost. When r3 is
equal to the critical radius, the rate of heat lost is at a maximum.
Analysis
In general, the temperature profile depends on the amount of resistance. The temperature is
highest where the hot water is located. The temperature then decreases as heat flows through
the resistive layers. Increasing the thickness of the insulator increases the amount of
resistance, resulting in a lower outermost surface temperature.
There is a critical thickness below which adding insulation will increase heat loss. This is
represented by the equations and graph below.
In general 
𝑞=
∆𝑇
∑𝑅
For our system 
𝑞𝑟 =
𝑇𝑤 − 𝑇𝑠
𝑟2
𝑟
ln ( ) ln ( 3 )
𝑟1
𝑟2
1
+
+
2ᴨ𝑘𝑔 𝐿 2ᴨ𝑘𝑏 𝐿 2ᴨ𝑟3 𝐿ℎ𝑎𝑖𝑟
In the denominator from left to right, the resistances are from conductivity of the glass,
conductivity of the bubble wrap, and convection from the surrounding air. Increasing the
amount of insulation increases r3, causing the conductive resistance of bubble wrap to increase.
However increasing r3 also causes the convective resistance to decrease. This results in a
value of r3 where there is a maximum heat loss. This value of r3 is called the critical radius.
The value for the critical radius can be derived by taking the derivative of qr with respect to r3
and setting this equal to zero. For a cylindrical system like ours we find that
Where h0 = thermal convective coefficient of the surrounding fluid. In our case this would be the
convective coefficient of air at room temperature. Here is a graph that shows how qr varies with
r3.
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r3
Conclusion
This experiment illustrates the effects of using a material, such as bubble wrap, as an insulator
and the impact of the thickness of that insulator on the temperature at the outside of the system.
The system in this experiment demonstrates important chemical engineering concepts,
including: heat transfer, conduction, convection, and the critical radius all in a one-dimensional
system. As the amount of insulation in the system is increased, the resulting temperature on the
outer layer will decrease, revealing the effects of insulation on a one-dimensional cylindrical
system.
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