Tuesday Cuddly Wombats Ellis Report2

8/8/2019 Tuesday Cuddly Wombats Ellis Report2

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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 311-002 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

5


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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

6


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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

10


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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(Ts-T) (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,1-Ts,2Ts,2-T=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.

T-TTi-T=exp-hAsVct (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=1.0588x-34.24 (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=1.0651x-38.41 (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 Set-up

A diagram of out experimental set-up 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 5-7 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

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=30.07-1.48A-1.33C-1.00AB (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=lnT-TiT-TVcAst (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 6-9)

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(yi-y)2n-1 (13)

Se=s2/TR (14)

Seff=Se4/N (15)

DF=n-1TR (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=Model-Response (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


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

Tuesday Cuddly Wombats Ellis Report2

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