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Effect of aspect ratio, initial temperature, and air
speed on the heat transfer coefficient of a hanging
vertical plate
Submitted by:
Cuddly Wombats
Team Members:
Eric EllisRobert Martin
Tom McCrocklin
Jose Villanueva
Team Leader:
Tom McCrocklin
Instructor:
Josh Strodtbeck, [email protected]
Dr. Mohamed Hassan Ali, [email protected]
University of Kentucky

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Dept. of Mechanical Engineering
ME 311002 Experimentation II
Experiment Conducted on:
February 23, 2010
Report Submitted on:
March 9, 2010

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Table of Contents
Nomenclatures
7
1. Abstract8
2. Background &
Theory
8
3. Experimental
Arrangement
12
3.1 Facilities...
................................12
3.2 Diagnostics and Sensor
Calibration........................13
3.2.1 Small Plate
Thermocouple/DMM
14
3.2.2 Large Plate
Thermocouple/DMM
14
3.2.3 Air Flow
Rate
..14
3.3 Experimental Set
up.............................
.14
3.4 Experimental
Procedure
..16
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1. Results and
Analysis
.16
5.1Test
Matrix..........
........................16
5.2 Experimental
Calculations
..18
5.3 Response
Plots...................
..............20
5.4 Regression Model and
Residuals........................22
5.5 Contour
Plots................
................23
1. Discussion and
Conclusions
..24
2. References
27
3. Appendices
28
8.1 Appendix A: Thermocouple/DMM
Calibrations.28
8.2 Appendix B: Converting Response
Values.30
8.3 Appendix C: Decision Limit and Effect Calculations..
.32
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8.4 Appendix D: Response Plot Calculations...
.33
8.5 Appendix E: Residual Model
Calculations34
8.6 Appendix F: Contour Plot
Calculations..35
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List of Tables
Table 1: List of Equipment and Serial
Numbers.12Table 2: Experimental
Factors.
17
Table 3: Test matrix with the eight treatments
defined..17
Table 4: Test matrix with heat transfer coefficients, averages, and
variance..19
Table 5: Temperatures for large plate thermocouple
calibration.27
Table 6: Temperatures for small plate thermocouple
calibration.28
Table 7: Heat Transfer Coefficient
Calculations30
Table 8: Results of Heat Transfer Coefficient calculations with
levels..31
Table 9: Results of Statistical
Analysis.32
Table 10: Effect
Calculations
..32
Table 11: Error
Calculations
33
Table 13: Residual Error
Calculations..3
4
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Table 14: Contour Plot Calculations for Large
Plate..35
Table 15: Contour Plot Calculations for Small
Plate36
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List of Figures
Figure 1: Forced Convection (2)...9
Figure 2: Natural Convection (2)
..9
Fig. 3: Large and Small Aluminum Plate
Dimensions..10
Fig. 4: Biot Number
Variables
11
Figure 5: Large Aluminum
Plate...12
Figure 6: Small Aluminum
Plate..13
Figure 7:
Furnace
....13
Figure 8: Experimental
Schematic..
15
Figure 9: Experimental
Photo..
15
Figure 10: Three dimensional depiction of the test matrix..
..18
Figure 11: Pareto Chart..
..20
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Figure 12: Factor A Response
Plot....20
Figure 13: Factor C Response
Plot....21
Figure 14: Interaction of AB Response
Plot.21
Figure 15: 3 dimensional test matrix with response
values...22
Figure 16: Residual
Plot
....23
Figure 17: Large Plate Contour
Plot..24
Figure 18: Small Plate Contour
Plot...24
Figure 19: Large Plate Thermocouple Calibration
Curve....28
Figure 20: Small Plate Thermocouple Calibration
Curve....29
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1. Nomenclature
A Plate Surface Area FactorB Initial Temperature Factor
C Air Flow Rate Factor
h Heat Transfer Coefficient
Se Standard Deviation
n Replicates
df Degrees of Freedom
DL Decision Limit
T Temperature at time t
T Air temperature
Ti Initial Temperature
t Time (in seconds)
As Surface Area
Density
V Volume
c Specific heat
Bi Biot number
Ts Surface temperature
RcondThermal resistance due to conduction
RconvThermal resistance due to condvection
DMM Digital Multimeter
k Thermal Conductivity
Rex Reynolds Number
Pr Prandtl Numberu Fluid velocity
Viscosity
S2 VarianceSe Standard deviation of errorSeff Standard deviation of effect
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temperature variations in the fluid [1]. As can be seen in Figure 2, with
a hot object and a cold fluid, the fluid is warmer near the surface of the
object, so the fluid rises due to a decrease in density. Depending on
the situation, it is possible to consider on type of convection negligible,
or it may be necessary to analyze both types of convection.
Fig. 1: Forced Convection (2)
Fig. 2: Natural Convection (2)
The general equation for convective heat transfer is:
q=hAs(TsT) (1)
In this experiment, it was assumed that forced convection was
significant and free convection was insignificant. This is a safe
assumption because for this experiment, a fan was moving air past
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both sides of an aluminum plate. Certainly free convection existed in
this experiment, however it can be assumed to be insignificant based
on the experimental setup.
To calculate the heat transfer coefficient in this experiment, the
lumped capacitance method was used. The lumped capacitance
method simplifies much more complicated analysis methods by
assuming that the thermal resistance due to conduction within the
solid is small compared with the thermal resistance between the solid
and its surroundings [1]. This assumes a relatively uniform
temperature throughout the solid and performs an energy balance
using a single temperature for the solid, rather than a temperature
gradient within the solid. In order to make this assumption, the Biot
number must be considered.
Bi=Ts,1Ts,2Ts,2T=RcondRconv=hLk (2)
To justify the use of the lumped capacitance method:
Bi

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Fig. 3: Large and Small Aluminum Plate Dimensions
Fig. 4: Biot Number Variables
Using the lumped capacitance method, the heat transfer
coefficient can be calculated.
TTTiT=exphAsVct (4)
Controlled FactorsPlate surface areaInitial temperature
Air flow rateResponse VariableHeat transfer coefficient
Uncontrollable FactorsEnvironmental factors (ambient pressure, air temperature, etc.)ConductionRadiation
Factors Not Considered
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Free convectionPlates hanging at an angle
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3.Experimental Arrangement
3.1 FacilitiesThe experiment was conducted in room 303 of the Ralph G.
Anderson building, part of the University of Kentuckys College of
Engineering. The room was equipped with a furnace, aluminum plates,
hangers to hold the plates, fans, and measurement equipment. The
large aluminum plate can be seen in Figure 5, the small aluminum
plate can be seen in Figure 6, and the furnace can be seen in Figure 7.
Table 1 lists the complete set of equipment.
Table 1: List of Equipment and Serial Numbers
EquipmentSerial Number (if
applicable)
1 DMMsCCL030910976
CCL0202612195
2Large Aluminum
PlateN/A
3Small Aluminum
PlateN/A
4 Fans N/A
5Type K
ThermocouplesN/A
6 Stand/hangers N/A
7 Anemometer 9416193
Stopwatch N/A
Furnace N/A
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Fig. 5: Large Aluminum Plate
Fig. 6: Small Aluminum Plate
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Fig. 7: Furnace
3.2 Diagnostics & Sensor Calibration
Two thermocouples were used during this experiment. They
were embedded into the aluminum plates at used to measure the
temperature. As was discussed in the Background and Theory (section
2), the plates were assumed to have a uniform temperature, so only
one thermocouple was needed in each plate. Further calibration
details can be found in Appendix A.
3.2.1 Small Plate Thermocouple/DMM
One Type K thermocouple was connected to a DMM to measure
the temperature of the small aluminum plate. Using this system,
temperatures were recorded for boiling water and for an ice bath. A
linear calibration curve was created using these two reference points.
All measurements in the experiment were between these two
reference temperatures. More calibration details can be found inAppendix A. The DMM/thermocouple calibration curve is equation 7
below. The variable x is the true temperature and y is the measured
temperature in degrees Fahrenheit.
y=1.0588x34.24 (7)
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3.2.2 Large Plate Thermocouple/DMM
Similarly, a Type K thermocouple was connected to a DMM to
measure the temperature of the large aluminum plate. Again,
temperatures were recorded for boiling water and for an ice bath.
Using these two reference points, a linear calibration curve was
created. All measurements in the experiment were between these two
reference temperatures. More details can be found in Appendix A.
The DMM/thermocouple calibration curve is seen in equation 8 below.
The variable x is the true temperature and y is the measured
temperature in degrees Fahrenheit.
y=1.0651x38.41 (8)
3.2.3 Air Flow Rate
To measure the air flow rate, a digital anemometer was used.
The plates and fan were arranged such that air flowed past both sides
of the plate at equal velocities. This was verified by measuring the air
speed on both sides of the hanging aluminum plate directly prior to
taking measurements.
3.3 Experimental Setup
A diagram of out experimental setup can be seen in Figure 8
below. The stand was placed in front of the fan such that the air flow
hit the thin edge of the plate, then passed along the broad sides of the
plate. It was set up such that the air passed at equal velocities on both
sides of the plate. The thermocouple was embedded into a small hole
that was drilled through the middle of the plate and secured there to
ensure that the measured temperature was the temperature of the
plate, not the passing air. Two entire setups were constructed so that
the fans would not have to be moved to change the high flow rate and
low flow rate treatments, therefore reducing variability.
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Fig. 8: Experimental Schematic
Fig. 9: Experimental Photo
3.4 Experimental Procedure1. Locate all necessary equipment identified in Section 3.1
Facilities.
2. Calibrate the thermocouples as described in Section 3.2
Diagnostics and Sensor Calibration.
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3. Align fans with plate hangers. Measure flow rates on both
sides of each plate to ensure accuracy.
4. Embed the thermocouples into the aluminum plates.
5. Heat aluminum plates to a temperature hotter than 150F or
120F depending on which treatment is being conducted. Use
caution when handling hot plates and working with furnace.
6. Place hot aluminum plate on hanger and turn on fan. Wait
until the temperature of the plate reaches 150F or 120F
(depending on which treatment is being conducted).
7. Record temperature measurements every 10 seconds until the
plate temperature has dropped to 120F for the high
temperature treatments, or 85F for the low temperature
treatments.
8. Repeat steps 57 for all treatments defined by the test matrix.
9. Turn off furnace and allow aluminum plates to cool
completely.
10. Conduct statistical analysis and draw conclusions.
4. Results and Analysis
5.1 Test Matrix
The following tables outline the factorial design approach for the
experiment. The first table identifies the experimental factors and
defines the high and low levels of each one. The second table shows
the eight different treatments that were executed in the experiment.
Table 2: Experimental Factors
Experimental Factors
ASurface Area 0.0758m2 +
0.0291m2 
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B
Initial
Temperature 150F +
120F 
C Air Flow Rate 2.5 m/s +
1.5 m/s 
Table 3: Test matrix with the eight treatments defined.
Test MatrixTreatme
nt Factors Interactions
A B C AB AC BC ABC
1    + + + 
2 +     + +
3  +   +  +
4 + +  +   5   + +   +
6 +  +  +  
7  + +   + 
8 + + + + + + +
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Figure 10: Three dimensional depiction of the test matrix
5.2 Experimental Calculations
In this experiment, significant factors were identified by
calculating the effect and comparing it to the decision limit. For any
factor or interaction, if the effect is greater than the decision limit, that
factor or interaction is considered significant. In this experiment, the
decision limit is 1.89 and factors A and C, as well as interaction AB are
significant. Appendix B and Appendix C show the details of converting
the response temperatures to heat transfer coefficients.
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Table 4: Test matrix with heat transfer coefficients, averages, and variance.
Test Matrix
Factors Interactions Replicate
Varian
ce
A B C AB AC BC ABC I II III
Avera
ge S2
1    + + + 
31.4
1
36.5
2
31.4
1 33.11 8.72
2 +     + +
33.9
4
28.7
8
31.3
2 31.35 6.65
3  +   +  +
31.0
0
35.6
1
34.0
4 33.55 5.49
4 + +  +   
27.0
9
27.0
9
28.5
9 27.59 0.74
5   + +   +
28.9
8
28.9
8
28.9
8 28.98 0.00
6 +  +  +  
28.7
8
26.3
3
31.3
2 28.81 6.23
7  + +   + 
29.5
3
34.0
4
28.0
8 30.55 9.64
8 + + + + + + +
27.0
9
27.0
9
25.6
3 26.60 0.71
Se 2.18
Y+
114.
36
118.
29
114.
95
116.
28
122.
07
121.
61
120.
48 Seff 0.89
Y
126.
19
122.
25
125.
60
124.
26
118.
47
118.
93
120.
06 DL 1.89Y+)
av
28.5
9
29.5
7
28.7
4
29.0
7
30.5
2
30.4
0
30.1
2 alpha 0.05Y)a
v
31.5
5
30.5
6
31.4
0
31.0
6
29.6
2
29.7
3
30.0
2 n 3Effe
ct 2.96 0.99 2.66 1.99 0.90 0.67 0.10 df 16
t
alpha 2.12
TR 8
N 24
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Figure 11: Pareto Chart
5.3 Response Plots
For all factors and interactions, mean responses were calculated.
These mean responses can be seen in the table above. Using these
values, response plots were created. Details for the calculations used
to generate these plots can be found in Appendix D.
Figure 12: Factor A Response Plot
Figure 13: Factor C Response Plot
Figure 14: Interaction of AB Response Plot
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Figure 15: 3 dimensional test matrix with response values
5.4 Regression Model and Residuals
A regression model was generated for the responses from this
experiment. Using Microsoft Excel, a plot was generated based on
Equation 9, which can be seen below. This regression plot can be seen
in Figure 15. Appendix E shows the table used to generate the residual
plot.
Y=30.071.48A1.33C1.00AB (9)
Figure 16: Residual Plot
5.6 Contour Plots
The contour plots below were created using the regression model
equation. For these plots, the factors were changed from (1) to (1) at
intervals of (0.2). Due to the discrete sizes of the plates, plots were
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created that show the variation in the initial temperature and the air
flow rate at each plate size. The results were used to generate Table
14 and Table 15 in Appendix F, which were in turn used to generate
the contour plots seen below as Figure 17 and Figure 18, respectively.
Figure 17: Large Plate Contour Plot
Figure 18: Small Plate Contour Plot
5.Discussion and Conclusions
The objective of this experiment was to determine the effects
that surface area, initial temperature, and air flow rate have on the
heat transfer coefficient of a vertical aluminum plate. As can be seen
in Figure 11, the surface area and the air flow rate were determined to
be significant factors. Additionally, the interaction between surface
area and initial temperature was also determined to have a significant
impact on the heat transfer coefficient of the plate.
The most significant factor was determined to be the surfacearea. As can be seen in the response plot for factor A, the smaller
plate yielded the highest heat transfer coefficients. This result is
consistent with the base equation (Equations 4) used to calculate the
heat transfer coefficient. The equation for heat transfer coefficient,
found by manipulating Equation 4, can be seen here.
h=lnTTiTTVcAst (10)
It is apparent that surface area is inversely related to the heat transfer
coefficient. The experimental results support this.
The next significant factor is the air flow rate past the plate. The
results show that as the air flow rate increases, the heat transfer
coefficient decreases. This result was an unexpected result. Air
velocity is not a direct factor in the equation used for heat transfer
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coefficient. However, it can be studied another way. According to
Incropera et. al., for a flat plate in parallel flow, the heat transfer
coefficient is
h=kx0.664Rex1/2Pr1/3 (11)
Also, it is known that
Rex=ux (12)
Equation 12 shows that the Reynolds number is directly proportional to
the velocity of the fluid, u. Furthermore, equation 8 shows that the
heat transfer coefficient is directly related to the heat transfer
coefficient. Based on these equations, the heat transfer coefficient
was expected to be directly proportional to the velocity. However, the
experimental results showed the opposite correlation. More
experiments should be conducted to explore this phenomenon. The
experimental setup and equipment is a strong possibility for this error.
The air speed was measured on both sides of the plate prior to each
series of temperature readings. However, the low air flow rate was 1.7
m/s and the high air flow rate was 2.5 m/s. This was limited by the
capabilities of the fans in the lab. It is possible while the
measurements were being taken, other environmental factors had a
great impact on the heat transfer coefficient than the slight variation in
air speed. If conducted again, we would have a much greater
difference between the high and low air flow rates.
This experiment also showed that the initial temperature of the
plate was not a significant factor in the heat transfer coefficient. The
results show that temperature dropped with time at approximately the
same linear rate across all of the temperatures that were used in this
experiment. This factor could be investigated further by using
temperatures that had a more significant difference. However, for the
temperatures used in this experiment, the initial temperature of the
plate is an insignificant factor.
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There are a few major potential sources of error in this
experiment. Slight variations in the setup could have a significant
effect on the air flow around the plate. In order to create parallel flow
across both sides of a vertical plate, the fan and plate had to be
oriented very precisely, and this had to be repeated for all trials in the
experiment. Due to heating and moving the plates and turning the fan
on and off, there is strong potential for misaligning the plate and fan
setup. Although the air flow rates were monitored at the thermocouple
location on both sides of the plate prior to each reading, variation
could still exist and have a significant impact on the experimental
results.
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6. References
1) Incropera, F., DeWitt, D., Bergman, T., and Lavine, A.,Introduction to Heat Transfer, John Wiley and Sons, Inc, NewYork, 2007. (pages 69)
2) http://images.anandtech.com/old/cooling/heatsinkguide/convection.gif(forced convection image)
3) Montgomery, Douglas C. Design and Analysis of Experiments. 7th. Danvers:John Wiley & Sons, INC., 2008.
30
http://images.anandtech.com/old/cooling/heatsinkguide/convection.gifhttp://images.anandtech.com/old/cooling/heatsinkguide/convection.gifhttp://images.anandtech.com/old/cooling/heatsinkguide/convection.gifhttp://images.anandtech.com/old/cooling/heatsinkguide/convection.gifhttp://images.anandtech.com/old/cooling/heatsinkguide/convection.gif 
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Appendices
8.1 Appendix A: Thermocouple/DMM Calibration
Both thermocouples used in this experiment were calibrated inorder to be certain to yield accurate temperature readings throughout
the experiment. In order to calibrate the thermocouples, temperature
readings were taken at known temperatures (freezing and boiling), and
a calibration curve was constructed. The thermocouples were inserted
into boiling water and an ice bath. For both thermocouples, the
readings and calibration curves can be seen here. In the calibration
equations, Equation 7 and Equation 8, x is the actual temperature
and y is the measured temperature, measured in degrees Fahrenheit.
Large Plate TC
Table 5: Temperatures for large plate thermocouple calibration.
Ideal
(R)
Measured
(R)Freezi
ng 492 498
Boiling 672 667
Figure 19: Large Plate Thermocouple Calibration Curve
Small Plate TC
Table 6: Temperatures for small plate thermocouple calibration.
Ideal
(R)
Measured
(R)
Freezing 492 497
Boiling 672 667
Figure 20: Small Plate Thermocouple Calibration Curve
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Table 8: Results of Heat Transfer Coefficient calculations with levels.
Test MatrixFactor
s Interactions Replicate Variance
A B C
A
B
A
C
B
C ABC I II III Average S2
1    + + +  31.41 36.52 31.41 33.11 8.72
2 +     + + 33.94 28.78 31.32 31.35 6.65
3  +   +  + 31.00 35.61 34.04 33.55 5.49
4 + +  +    27.09 27.09 28.59 27.59 0.74
5   + +   + 28.98 28.98 28.98 28.98 0.00
6 +  +  +   28.78 26.33 31.32 28.81 6.23
7  + +   +  29.53 34.04 28.08 30.55 9.64
8 + + + + + + + 27.09 27.09 25.63 26.60 0.71
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8.3 Appendix C: Decision Limit and Effect calculations
S2=i=1n(yiy)2n1 (13)
Se=s2/TR (14)
Seff=Se4/N (15)
DF=n1TR (16)
DL=Sefft (17)
Table 9: Results of Statistical Analysis.
Se 2.18Seff 0.89
DL 1.89
alpha 0.05
n 3
df 16
t alpha 2.12
TR 8
N 24
Table 10: Effect Calculations
Y+ 114.36118.29 114.95116.28122.07 121.61120.48
Y 126.19122.25 125.60124.26118.47 118.93120.06
Y+)av 28.59 29.57 28.74 29.07 30.52 30.40 30.12
Y)av 31.55 30.56 31.40 31.06 29.62 29.73 30.02
Effect 2.96 0.99 2.66 1.99 0.90 0.67 0.10
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8.4 Appendix D: Response Plot Calculations
Standard error calculations were done using Microsoft Excel.The
response plots seen in section 5.3 were created using the numbersbelow. The calculation for Error Percent can be seen in equation 18.
Table 11: Error Calculations
Term Mean
Standard
Error Error Percent
All 30.07
A 1 31.55 2.3 7.29
1 28.59 2.3 8.04
B 1 30.56 0.06 0.201 29.57 0.06 0.20
C 1 31.40 1.2 3.82
1
125.6
0 1.2 0.96
AB 1 31.06 0.9 2.90
1 29.07 0.9 3.10
BC 1 29.62 0.2 0.68
1 30.52 0.2 0.66
AC 1 29.73 0.1 0.34
1 30.40 0.1 0.33ABC 1 30.02 0.07 0.23
1 30.12 0.07 0.23
Error Percent=100Standard ErrorMean (18)
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8.5 Appendix E: Residual Model Calculations
The regression equation, Equation 9 was used to generate theresidual plot. The equation was used to calculate the Model value in
the table below. The residual plot, Figure 16, was created using these
calculations.
Error=ModelResponse (19)
Table 13: Residual Error Calculations
Treatme
nt
Significant
factors/interactions Model Error
A C AB I II III
1 1 1 1 33.88
2.4748
83

2.6401
8
2.4748
83
a 1 1 1 30.92

3.0237
9
2.1352
92

0.4006
3
b 1 1 1 31.22
0.2217
06

4.3860
2

2.8167
1
ab 1 1 1 28.26
1.1670
11
1.1670
11

0.3261
5
c 1 1 1 31.88
2.9007
56
2.9007
56
2.9007
56
ac 1 1 1 28.92
0.1352
92
2.5895
94

2.4006
3
bc 1 1 1 29.22

0.3064
2

4.8167
1
1.1356
06abc 1 1 1 26.26 
0.8329

0.8329
0.6314
96
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9 9
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8.6 Appendix F: Contour Plot Calculations
Using the regression model, Equation 9, the contour plots, Figure17 and Figure 18, were created. These plots vary the significant
factors from (1) to (1) in the regression model. These plots show
initial temperature vs air flow rate with either the large surface area or
the small surface area. In this experiment, the surface area was
discrete based on the size of the plates available, while the initial
temperature and air flow rate could be more precisely controlled.
Therefore, contour plots were generated comparing these two
variables. The tables used to make these plots are included here.
Table 14: Contour Plot Calculations for Large Plate
Factor C (Air Flow Rate)
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1Fac
tor
B
(Ini
tial
Te
mp
era
tur
e)
1
30.9
2
30.6
5
30.3
9
30.1
2
29.8
5
29.5
9
29.3
2
29.0
6
28.7
9
28.5
2
28.2
6
0.8
30.7
2
30.4
5
30.1
9
29.9
2
29.6
6
29.3
9
29.1
2
28.8
6
28.5
9
28.3
2
28.0
6

0.6
30.5
2
30.2
5
29.9
9
29.7
2
29.4
6
29.1
9
28.9
2
28.6
6
28.3
9
28.1
2
27.8
6
0.4
30.3
2
30.0
6
29.7
9
29.5
2
29.2
6
28.9
9
28.7
2
28.4
6
28.1
9
27.9
2
27.6
6
0.2
30.1
2
29.8
6
29.5
9
29.3
2
29.0
6
28.7
9
28.5
2
28.2
6
27.9
9
27.7
3
27.4
6
0
29.9
2
29.6
6
29.3
9
29.1
2
28.8
6
28.5
9
28.3
3
28.0
6
27.7
9
27.5
3
27.2
6
0.2
29.7
2
29.4
6
29.1
9
28.9
2
28.6
6
28.3
9
28.1
3
27.8
6
27.5
9
27.3
3
27.0
6
0.4
29.5
2
29.2
6
28.9
9
28.7
3
28.4
6
28.1
9
27.9
3
27.6
6
27.3
9
27.1
3
26.8
6
0.6
29.3
3
29.0
6
28.7
9
28.5
3
28.2
6
27.9
9
27.7
3
27.4
6
27.1
9
26.9
3
26.6
60.8 29.1
3
28.8
6
28.5
9
28.3
3
28.0
6
27.7
9
27.5
3
27.2
6
27.0
0
26.7
3
26.4
6
38

8/8/2019 Tuesday Cuddly Wombats Ellis Report2
39/39
1
28.9
3
28.6
6
28.3
9
28.1
3
27.8
6
27.5
9
27.3
3
27.0
6
26.8
0
26.5
3
26.2
6
Table 15: Contour Plot Calculations for Small Plate
Factor C (Air Flow Rate)
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1
Fa
cto
r B
(Ini
tial
Te
mp
era
tur
e)
1 33.88
33.6
1
33.3
4
33.0
8
32.8
1
32.5
5
32.2
8
32.0
1
31.7
5
31.4
8
31.2
1
0.8 33.68
33.4
1
33.1
4
32.8
8
32.6
1
32.3
5
32.0
8
31.8
1
31.5
5
31.2
8
31.0
1
0.6 33.48
33.2
1
32.9
5
32.6
8
32.4
1
32.1
5
31.8
8
31.6
1
31.3
5
31.0
8
30.8
1
0.4 33.28
33.0
1
32.7
5
32.4
8
32.2
1
31.9
5
31.6
8
31.4
1
31.1
5
30.8
8
30.6
2
0.2 33.08
32.8
1
32.5
5
32.2
8
32.0
1
31.7
5
31.4
8
31.2
2
30.9
5
30.6
8
30.4
2
0 32.88
32.6
1
32.3
5
32.0
8
31.8
1
31.5
5
31.2
8
31.0
2
30.7
5
30.4
8
30.2
2
0.2 32.68
32.4
1
32.1
5
31.8
8
31.6
2
31.3
5
31.0
8
30.8
2
30.5
5
30.2
8
30.0
2
0.4 32.48
32.2
2
31.9
5
31.6
8
31.4
2
31.1
5
30.8
8
30.6
2
30.3
5
30.0
8
29.8
2
0.6 32.28
32.0
2
31.7
5
31.4
8
31.2
2
30.9
5
30.6
8
30.4
2
30.1
5
29.8
9
29.6
2
0.8 32.0831.8
231.5
531.2
831.0
230.7
530.4
830.2
229.9
529.6
929.4
2
1 31.88
31.6
2
31.3
5
31.0
8
30.8
2
30.5
5
30.2
9
30.0
2
29.7
5
29.4
9
29.2
2