ANALYSIS OF INSULATION OF MATERIAL
—— PROJECT OF DESIGN OF EXPERIMENT
Group Member:
Wang Deyu,
Li Dejun,
Zhong Haoyuan
Xu Shanshan, Li Yaqiong, Yan Li
CATALOG
1
Literature Review ................................................ 3
2
Executive Summary............................................. 4
3
Preparation ......................................................... 5
4
Choice of Experimental Design ............................ 8
5
Performing the Experiment ............................... 10
6
Eliminating Noise .............................................. 11
7
Data analysis..................................................... 14
8
Reference ......................................................... 27
LITERATURE REVIE
1
Literature Review
The problem of interest in our project is about how a specific insulation material, the cloth,
could affect the cooling rate of water. We first need to define how various factors would
accelerate or decelerate the cooling rate.
We searched for several periodicals and find two articles discussing insulation materials [1]
and cooling rates of water [2], in Chinese and English respectively.
In the article, we could learn that the most important factors that affect the rate of heat emission
of an object are contact areas of the heat source, the properties of the object, either physical or
chemical, and the heat conduction rate in the object itself. From our daily experience and some
fundamental physics knowledge, we expected that the color of the object may also contribute to
the heat emission of the object.
As for the insulation material, an article about garments suggests that the thermal
conductivity and evaporative resistance are more important among others in affecting the
comfortableness of garments. As this article discusses in particular about the garment design,
which involve more about the direct contact of the body, the conclusion should be for reference
only.
In summary, we would expect the cooling rate of the water in our project to be affected
mainly by: properties of the liquid, physical properties of insulation material, size of the container,
heat conduction property of the container, contact of the air, color of the material, and thickness
of the material.
We first propose a brief model to define the cooling rate of the water. It should be like this:
Δ𝑇 = 𝑓(𝐿𝑃, 𝑆, 𝑀, 𝐶, 𝑇, 𝐻𝐶, 𝐶𝐴)
where LP=liquid properties, S=size of the container, M=material, C=color of the material,
T=thickness of the material, HC=heat conduction, CA=contact of the air.
EXECUTIVE SUMMARY
2
Executive Summary
2.1
Problem Statement
The experiment is aimed to compare the performance of different kinds of heat
insulation materials under normal conditions. The results of the experiment would be
quantified into the details including the texture, thickness, exterior color and
ventilation.
2.2
Regression Model
Temp Diff
=
e i = igh
e = i g
e i
e i = igh
e i = igh
= hi e
e = i g
= hi e
e i
e i
i
i
e i
Cause and Effect Diagram – Fishbone Diagram
=
=
i
=
= hi e
i
=
PREPARATION
3
Preparation
3.1
Material and Measuring Equipment
3.1.1 Material
We select two clothing type with different texture, one is cotton which is
more tightened weaved, and the other is flax. For each type of material, we
choose two articles of different color, one is black and the other is white. Our
material is show as follows:
Cotton, Black
Flax, Black
Flax, White
Figure 1 Material
3.2
Container: Beaker
We use beaker to hold water. Each beaker is 150ml. In order to reduce the
impact of cool beaker, in each experiment, the beaker is warmed-up. To reduce
Cott
noise caused by desk, we put a paper bowl under the beaker. The paper bowl has
low specific heat capacity, so it absorbs heat at a low speed, which will favor our
experiment. The beaker is show as follows:
Beake
Figure 2 Beaker
3.2.1 Kerosene thermometer
To measure the temperature before and after experiment, we use two piece
of Kerosene thermometer. The scales of thermometers used in this experiment are
different, one is 1 centigrade and the other is 2 centigrade. The Kerosene
thermometer is shown as follows:
Figure 3 Thermometer
3.3
Experiment Location
This experiment is done in C Builiding, Room 300, Tshinghua University. The
room temperature is 26 centigrade.
CHOICE OF EXPERIMENTAL DESIGN
4
Choice of Experimental Design
4.1
Design of Experiment
4.1.1 Variable Selection
In the second chapter, the cause and effect diagram shows various factors that
could affect the response variable, the change of temperature. To perform the
experiment in a more efficient and more accurate way, we need to carefully select
the critical variables and the way to distinguish the levels of these variables.
The four major factors we choose are: Material, Color, Layer, and Ventilation.
For each of the variables, we choose to have two levels, and these two levels
should be distinguishable. For material, we find two kinds of cloth, one of which
has dense threads and is slightly thicker, the other one has relatively loose threads
and is lighter. To achieve larger difference between the two levels, we choose
black and white cloth of each kind in the experiment as the two levels in of the
color variable. Another factor that may significantly affect the cooling rate of the
water is the thickness of the insulation material. We decide to wrap 3 layers of
cloth as the high level and single layer as the low level.
Finally, whether to use
a covering for the beaker during cooling of the water determine the level of
ventilation in the experiment.
4.1.2 Setting Variables
The four variables and the corresponding settings to their levels are
determined. To be more explicit, we list them in Table 1.
Factor
Material
Color
Layer
Ventilation
+
-
Heavy
Light
Black
White
Multiple
Singular
Yes
No
Table 1 Variables in the insulation experiment
The experiment could then be designed on these four variables.
4.1.3 Blocking
In the experiment, we use two thermometers to measure the temperature of the
cooling water. Though the two thermometers are both kerosene thermometer,
they have different calibration. Thus, to mitigate the influence of the
measurement itself, we should develop two blocks to apply the two thermometers.
For each treatment of the experiment, there will be two replications, each of
which is in one block.
4.1.4 Experiment Design
The experiment has the following properties:
4 variables;
2 levels per variable;
2 replications per treatment;
2 blocks;
Full factorial.
Use Minitab 15 to generate an experiment design, we would have 32 runs, as
has been shown in
Appendix 1.
PREFORMING THE EXPERIMENT
5
Performing the Experiment
According to the design, we could start the experiment. We boil tap water to
approximately 100 degrees Celsius, and then quickly pour 200 ml boiling water into the two
beakers and two experimenters would use the thermometer to read the temperature of the
water. To ensure that the temperature is accurately measured, we begin reading when we first
see the temperature is steady and begin to drop. At a certain temperature, the experimenter
would write down the reading on the meter and count 3 minutes before a second reading is
acquired. Using the two readings with 3-minute interval, the drop of temperature within the
timespan could be calculated.
The two experimenters read the meter individually. The difference between the two
meter and between the readings by the two experimenters would be mitigated through
blocking.
In the treatment with no ventilation, a paper plate is used to cover the beaker. In the
center of the plate, a hole is left for the thermometer to be placed right in the beaker. Paper is
a kind of poor heat conductor. Thus, the noise could be minimized.
ELIMINATING NOISE
6
Eliminating Noise
6.1
Warm up of the beakers and the thermometers
To ensure that the boiling water will not lose its heat through channels we are not
interested in, the beakers and the thermometers themselves are to be preheated before
data is sampled.
6.2
Wrap the cloth tightly to the beaker
The clothes are wrapped around the beaker, no matter one-layer or three-layer is
applied, the clothes are fixed by using a hair clip. The slim clip would also ensure that
the least width is overlapped.
6.3
Pad the cup with a paper dish underneath
The bottom of the beaker should not directly contact the table, which is a good heat
conductor. We put another paper plate beneath the beaker to minimize the heat
conducted through the bottom.
The experiment is conducted under a condition as shown in
.
Appendix
StdOrder
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
RunOrder
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
CenterPt
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Blocks
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
Material
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Color
White
White
Black
Black
White
White
Black
Black
White
White
Black
Black
White
White
Black
Black
White
White
Black
Black
White
Layer
Singular
Singular
Singular
Singular
Multiple
Multiple
Multiple
Multiple
Singular
Singular
Singular
Singular
Multiple
Multiple
Multiple
Multiple
Singular
Singular
Singular
Singular
Multiple
Ventilation
No
No
No
No
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
22
23
24
25
26
27
28
29
30
31
32
22
23
24
25
26
27
28
29
30
31
32
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
Light
Heavy
White
Black
Black
White
White
Black
Black
White
White
Black
Black
Appendix 1 The design of experiment
Figure 4 The experiment equipment
Multiple
Multiple
Multiple
Singular
Singular
Singular
Singular
Multiple
Multiple
Multiple
Multiple
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
DATA ANALYSIS
7
Data analysis
7.1
Regression model
In this chapter, we will generate a model and solve it in Minitab.
First, we formulate a model with combination of all the four major factors, namely
Material, Color, Layer, Ventilation, Material*Color, Material*Layer,
Material*Ventilation, Color*Layer, Color* ventilation, Layer*Ventilation,
Material*Color*Layer, Material*Color*Ventilation, Material*Layer*Ventilation,
Color*Layer*Ventilation, Material*Color*Layer*Ventilation
We use these 15 factors in a GLM and calculate the coefficients in Minitab
来源
Material
Color
0.003
Layer
0.007
Ventilation
Material*Color
Material*Layer
自由度
1
1
1
Seq SS
6.570
3.445
Adj SS
6.570
3.445
2.820
2.820
Adj MS
F P
6.570 22.73 0.000
3.445 11.92
2.820
9.76
1 122.853 122.853 122.853 425.00 0.000
1
5.200
5.200
5.200 17.99 0.001
1
0.263
0.263
0.263
0.91 0.355
Material*Ventilation
Color*Layer
0.821
Color*Ventilation
Layer*Ventilation
Material*Color*Layer
Material*Color*Ventilation
Material*Layer*Ventilation
Color*Layer*Ventilation
Material*Color*Layer*Ventilation
误差
合计
1
3.063
3.063
3.063 10.60 0.005
1
0.015
0.015
0.015
0.05
1
1
1
5.040
5.040
5.040 17.44
5.200
5.200
5.200 17.99
0.578
0.578
0.578
2.00
1
0.000
0.000
0.000
0.00
1
0.008
0.008
0.008
0.03
1
0.383
0.383
0.383
1.32
1
0.015
0.015
0.015
0.05
16
4.625
4.625
0.289
31 160.080
0.001
0.001
0.177
0.974
0.871
0.267
0.821
We delete Material*Color*Layer*Ventilation, and then recalculate the coefficients.
来源
Material
Color
Layer
Ventilation
Material*Color
Material*Layer
Material*Ventilation
Color*Layer
Color*Ventilation
Layer*Ventilation
Material*Color*Layer
Material*Color*Ventilation
Material*Layer*Ventilation
Color*Layer*Ventilation
误差
合计
自由度 Seq SS Adj SS Adj MS
F
P
1
6.570
6.570
6.570 24.07 0.000
1
3.445
3.445
3.445 12.62 0.002
1
2.820
2.820
2.820 10.33 0.005
1 122.853 122.853 122.853 450.08 0.000
1
5.200
5.200
5.200 19.05 0.000
1
0.263
0.263
0.263
0.96 0.340
1
3.063
3.063
3.063 11.22 0.004
1
0.015
0.015
0.015
0.06 0.816
1
5.040
5.040
5.040 18.47 0.000
1
5.200
5.200
5.200 19.05 0.000
1
0.578
0.578
0.578
2.12 0.164
1
0.000
0.000
0.000
0.00 0.973
1
0.008
0.008
0.008
0.03 0.868
1
0.383
0.383
0.383
1.40 0.253
17
4.640
4.640
0.273
31 160.080
We delete Material*Color*Layer, and then recalculate the coefficients.
来源
Material
Color
Layer
Ventilation
Material*Color
Material*Layer
Material*Ventilation
Color*Layer
Color*Ventilation
Layer*Ventilation
Material*Color*Layer
Material*Layer*Ventilation
Color*Layer*Ventilation
误差
合计
自由度 Seq SS Adj SS Adj MS
F
P
1
6.570
6.570
6.570 25.48 0.000
1
3.445
3.445
3.445 13.36 0.002
1
2.820
2.820
2.820 10.94 0.004
1 122.853 122.853 122.853 476.52 0.000
1
5.200
5.200
5.200 20.17 0.000
1
0.263
0.263
0.263
1.02 0.326
1
3.063
3.063
3.063 11.88 0.003
1
0.015
0.015
0.015
0.06 0.810
1
5.040
5.040
5.040 19.55 0.000
1
5.200
5.200
5.200 20.17 0.000
1
0.578
0.578
0.578
2.24 0.152
1
0.008
0.008
0.008
0.03 0.864
1
0.383
0.383
0.383
1.48 0.239
18
4.641
4.641
0.258
31 160.080
We delete Material* Layer*Ventilation, and then recalculate the coefficients.
来源
Material
Color
Layer
Ventilation
Material*Color
Material*Layer
Material*Ventilation
Color*Layer
Color*Ventilation
Layer*Ventilation
Material*Color*Layer
Color*Layer*Ventilation
误差
合计
自由度 Seq SS Adj SS Adj MS
F
P
1
6.570
6.570
6.570 26.86 0.000
1
3.445
3.445
3.445 14.08 0.001
1
2.820
2.820
2.820 11.53 0.003
1 122.853 122.853 122.853 502.15 0.000
1
5.200
5.200
5.200 21.26 0.000
1
0.263
0.263
0.263
1.07 0.313
1
3.063
3.063
3.063 12.52 0.002
1
0.015
0.015
0.015
0.06 0.805
1
5.040
5.040
5.040 20.60 0.000
1
5.200
5.200
5.200 21.26 0.000
1
0.578
0.578
0.578
2.36 0.141
1
0.383
0.383
0.383
1.56 0.226
19
4.648
4.648
0.245
31 160.080
We delete Color*Layer*Ventilation, and then recalculate the coefficients.
来源
Material
Color
自由度
1
1
Seq SS
6.570
3.445
Adj SS
6.570
3.445
Adj MS
F
P
6.570 26.12 0.000
3.445 13.70 0.001
Layer
Ventilation
Material*Color
Material*Layer
Material*Ventilation
Color*Layer
Color*Ventilation
Layer*Ventilation
Material*Color*Layer
误差
合计
1
2.820
2.820
2.820 11.21 0.003
1 122.853 122.853 122.853 488.36 0.000
1
5.200
5.200
5.200 20.67 0.000
1
0.263
0.263
0.263
1.04 0.319
1
3.063
3.063
3.063 12.18 0.002
1
0.015
0.015
0.015
0.06 0.808
1
5.040
5.040
5.040 20.04 0.000
1
5.200
5.200
5.200 20.67 0.000
1
0.578
0.578
0.578
2.30 0.145
20
5.031
5.031
0.252
31 160.080
We delete Material*Color*Layer, and then recalculate the coefficients.
来源
Material
Color
Layer
Ventilation
Material*Color
Material*Layer
Material*Ventilation
Color*Layer
Color*Ventilation
Layer*Ventilation
误差
合计
自由度 Seq SS Adj SS Adj MS
F
P
1
6.570
6.570
6.570 24.60 0.000
1
3.445
3.445
3.445 12.90 0.002
1
2.820
2.820
2.820 10.56 0.004
1 122.853 122.853 122.853 459.95 0.000
1
5.200
5.200
5.200 19.47 0.000
1
0.263
0.263
0.263
0.98 0.333
1
3.063
3.063
3.063 11.47 0.003
1
0.015
0.015
0.015
0.06 0.813
1
5.040
5.040
5.040 18.87 0.000
1
5.200
5.200
5.200 19.47 0.000
21
5.609
5.609
0.267
31 160.080
We delete Color*Layer, and then recalculate the coefficients.
来源
Material
Color
Layer
Ventilation
Material*Color
自由度 Seq SS Adj SS Adj MS
F
P
1
6.570
6.570
6.570 25.70 0.000
1
3.445
3.445
3.445 13.48 0.001
1
2.820
2.820
2.820 11.03 0.003
1 122.853 122.853 122.853 480.54 0.000
1
5.200
5.200
5.200 20.34 0.000
Material*Layer
Material*Ventilation
Color*Ventilation
Layer*Ventilation
误差
合计
1
0.263
0.263
0.263
1.03 0.322
1
3.063
3.063
3.063 11.98 0.002
1
5.040
5.040
5.040 19.72 0.000
1
5.200
5.200
5.200 20.34 0.000
22
5.624
5.624
0.256
31 160.080
We delete Material*Layer, and then recalculate the coefficients.
来源
Material
Color
Layer
Ventilation
Material*Color
Material*Ventilation
Color*Ventilation
Layer*Ventilation
误差
合计
Also we get
S = 0.505930
自由度 Seq SS Adj SS Adj MS
F
P
1
6.570
6.570
6.570 25.67 0.000
1
3.445
3.445
3.445 13.46 0.001
1
2.820
2.820
2.820 11.02 0.003
1 122.853 122.853 122.853 479.96 0.000
1
5.200
5.200
5.200 20.32 0.000
1
3.063
3.063
3.063 11.97 0.002
1
5.040
5.040
5.040 19.69 0.000
1
5.200
5.200
5.200 20.32 0.000
23
5.887
5.887
0.256
31 160.080
R-Sq = 96.32%
项
常量
Material
Light
Color
White
Layer
Singular
Ventilation
No
Material*Color
Light
White
Material*Ventilation
Light
No
Color*Ventilation
White No
Layer*Ventilation
Singular No
R-Sq（调整） = 95.04%
系数 系数标准误
T
P
6.65313
0.08944 74.39 0.000
-0.45313
0.32813
-0.29688
-1.95938
-0.40312
0.08944
0.08944
0.08944
-5.07 0.000
3.67 0.001
-3.32 0.003
0.08944 -21.91 0.000
0.08944
-4.51 0.000
0.30938
0.08944
3.46 0.002
-0.39687
0.08944
-4.44 0.000
0.40313
0.08944
4.51 0.000
We also draw some plot in function DOE in Minitab to show the effect of left factors.
标准化效应的 Pareto 图
（响应为 TempDiff，Alpha =
.05)
2.07
因子
A
B
C
D
D
A
名称
Material
Color
Layer
Ventilation
CD
项
AB
BD
B
AD
C
0
5
10
15
标准化效应
20
25
Figure 5 The pareto plot
标准化效应的正态图
（响应为 TempDiff，Alpha =
.05)
99
效应类型
不显著
显著
95
D
百分比
90
80
A
70
CD
60
50
40
30
因子
A
B
C
D
AD
C
B
BD
20
10
AB
5
1
-5
0
5
10
标准化效应
15
20
25
名称
Material
Color
Layer
Ventilation
TempDiff 残差图
正态概率图
与拟合值
99
0.5
残差
百分比
90
50
10
-0.5
-1.0
-1.5
1
-1
0
1
残差
4
8
拟合值
直方图
与顺序
8
0.5
6
0.0
残差
频率
0.0
4
10
12
-0.5
-1.0
2
0
6
-1.5
-1.5
-1.0
-0.5
残差
0.0
0.5
Figure 6
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
观测值顺序
The residual plot
残差1 的概率图
正态 - 95% 置信区间
99
均值
-2.49800E-16
标准差
0.4358
N
32
AD
0.831
P 值
0.029
95
90
80
百分比
70
60
50
40
30
20
10
5
1
-1.5
-1.0
-0.5
0.0
残差1
0.5
1.0
Figure 7 The probability plot for the residual
We find that most residual fit well yet some out liers occur.
We delete 2 points (11th run and 24th run) and redo the job.
And the result is shown below.
拟合因子: TempDiff 与 Material, Color, Layer, Ventilation
TempDiff 的效应和系数的估计（已编码单位）
项
效应
T
P
6.7542
0.05487 123.08
0.000
0.9398
0.4699
0.05507
8.53
0.000
Color
-0.4542
-0.2271
0.05487
-4.14
0.000
Layer
0.6273
0.3136
0.05507
5.70
0.000
Ventilation
3.8852
1.9426
0.05507
35.28
0.000
-0.7727
-0.3864
0.05507
-7.02
0.000
0.4167
0.2083
0.05487
3.80
0.001
Color*Ventilation
-0.8273
-0.4136
0.05507
-7.51
0.000
Layer*Ventilation
0.6042
0.3021
0.05487
5.50
0.000
常量
Material
Material*Color
Material*Ventilation
系数
S = 0.298239
PRESS = 3.81306
R-Sq = 98.71%
R-Sq（预测） = 97.38%
系数标准误
R-Sq（调整） = 98.23%
对于 TempDiff 方差分析（已编码单位）
来源
自由度
Seq SS
Adj SS
Adj MS
F
P
32.3564 363.77
0.000
主效应
4 129.498 129.425
2因子交互作用
4
13.964
13.964
3.4909
残差误差
21
1.868
1.868
0.0889
失拟
7
0.368
0.368
0.0526
14
1.500
1.500
0.1071
纯误差
合计
29 145.330
TempDiff 的系数估计，使用未编码单位的数据
项
常量
Material
系数
6.75417
0.469886
Color
-0.227083
Layer
0.313636
Ventilation
Material*Color
Material*Ventilation
1.94261
-0.386364
0.208333
Color*Ventilation
-0.413636
Layer*Ventilation
0.302083
39.25
0.000
0.49
0.826
标准化效应的 Pareto 图
（响应为 TempDiff，Alpha =
.05)
2.08
因子
A
B
C
D
D
A
名称
Material
Color
Layer
Ventilation
BD
项
AB
C
CD
B
AD
0
10
20
标准化效应
30
40
Figure 8 The pareto plot
标准化效应的正态图
（响应为 TempDiff，Alpha =
.05)
99
效应类型
不显著
显著
95
D
90
A
80
70
百分比
因子
A
B
C
D
C
60
50
40
30
CD
AD
B
AB
20
10
BD
5
1
-10
0
10
20
标准化效应
30
40
名称
Material
Color
Layer
Ventilation
TempDiff 残差图
正态概率图
与拟合值
99
0.50
0.25
残差
百分比
90
50
0.00
-0.25
10
-0.50
1
-0.50
-0.25
0.00
残差
0.25
0.50
4
6
直方图
10
12
与顺序
8
0.50
6
0.25
残差
频率
8
拟合值
4
0.00
-0.25
2
-0.50
0
-0.6
-0.3
0.0
残差
0.3
0.6
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
观测值顺序
Figure 9 The residual plot
At this time, the residuals fit fine in a normal distribution, and the main effects and all the 4
interactions are significant. We
Temp Diff =
e i = igh
e = i g
e i
e i = igh
= hi e
e i
= hi e
i
=
= hi e
e i = igh
i
e = i g
=
e i
e i
i
=
i
=
Interaction Plot for TempDiff
Data Means
White
Black
Singular
Multiple
No
Yes
10.0
Material
Light
Heavy
7.5
Material
5.0
10.0
Color
White
Black
7.5
Color
5.0
10.0
Layer
Singular
Multiple
7.5
Layer
5.0
Ventilation
Figure 10 The interaction plot for tempdiff
From this interaction plot we see only Material-Layer and Color-Layer have no obvious
interaction, which fits fine with the model.
TempDiff 主效应图
数据平均值
Material
9
Color
8
7
平均值
6
5
Light
Heavy
White
Layer
9
Black
Ventilation
8
7
6
5
Singular
Multiple
No
Yes
Figure 11 The effect plot proof the positive/negative of coefficients of each factor
.What’s more, we used to try to transform the response factor to look for better model.
We transform TempDiff into logarithm form, and we find it not any better.
We transform TempDiff into Exponential form, and get the residual plot as below
Exp(Diff) 残差图
与拟合值
30000
90
20000
残差
百分比
正态概率图
99
50
10
1
10000
0
-10000
-20000
-10000
0
残差
10000
20000
0
直方图
15000
30000
拟合值
45000
与顺序
30000
20000
6
残差
频率
8
4
0
2
0
10000
-10000
-10000
0
10000
20000
残差
Figure 12
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
观测值顺序
The residual plot
We see some obvious patterns, we don’t recommend to transform the data in this way.
7.2
Results explanations
7.2.1 No ventilation can remarkably maintain the high level of heat preservation
7.2.1.1 From the main effects graph, D has the most significance, which means the
ventilation-absence condition nearly plays the determinant role of heat
preservation.
7.2.1.2 Any two-order interactions containing D, that is A*D, B*D, C*D, are also
significant, indicating D indeed have main effect.
7.2.1.3 Moreover, from the original data we can find any combination of treatment
with no ventilation has the better heat preservation relatively to that with
ventilation, which in turn confirm the result.
7.2.1.4 The negative coefficient of ventilation=no means the rate of temperature
decreasing will accelerate. And the absolute value of the coefficient is the
largest, indicating the main effect of ventilation or not.
7.2.2 Materials have main effect of heat preservation as well
7.2.2.1 From the main effects graph, A has relatively large significance, which
means the materials have effects on maintaining heat.
7.2.2.2 Some two-order interactions containing A, that is A*D, A*B, are also
significant, indicating A indeed has main effect.
7.2.2.3 The negative coefficient of material=light means heavy material does
better in maintaining heat.
7.2.3 Colors of material have main effect of heat preservation as well
7.2.3.1 From the main effects graph, B has relatively large significance, which
means the different colors have different abilities to avoid heat loss.
7.2.3.2 Some two-order interactions containing B, that is B*D, A*B, are also
significant, indicating B indeed have main effect
7.2.3.3 The positive coefficient of color=white means white material has prior
ability in maintaining heat, which may be contrary to our concept.
7.2.4 Thickness of material has less but also main effect of heat preservation as well
7.2.4.1 From the main effects graph, C has relatively large significance, which
means the different layers have different abilities to avoid heat loss.
7.2.4.2 Only one two-order interaction containing C, that is C*D, has main effect,
indicating layers have the least effect among all the main effect on heat
loss rate.
7.2.4.3 The negative coefficient of layer=singular means thicker material has prior
ability in maintaining heat, consistent with our common sense.
7.2.5 Interaction explanation:
7.2.5.1 Colors have less effect than materials do, and these two have interaction.
7.2.5.2 The relatively parallel lines of interactions containing layers mean in the
combination of layer and color, and layer and material, layer has the same
effect with the other one and has no interaction.
7.2.5.3 Interactions containing ventilation are evident, which means when
ventilation condition changes, the result changes much.
7.3
Possible causes
7.3.1 Ventilation-absence condition has the best ability of maintaining heat may result
in that in this experiment condition the heat is lost mostly from the top of the cup,
more that from the wall of cup. Thus, if the top of the cup is covered, more heat
will be maintained inside, leading to less temperature difference.
7.3.2 White color surprisingly has better ability of maintaining heat can be explained as
this: although darker materials can absorb more heat radiation from the
surroundings such as when put in the sunlight, however, in room condition heat
radiation can be neglected and instead, darker materials absorb more heat from
the water inside. Thus, more heat from the water wrapped by black cloth is loss.
This indicates that not all the common senses are right.
7.3.3 Heavy cloth has better heat maintaining ability, which corresponds to our
intuition. However, layers have less effect. The results may be explained by our
design of “heavy or light” and “number of layers”, which means only attributes
are introduced, no quantity ensure the validity of appropriate number of layers to
have more effect on the results.
7.4
Error sources:
7.4.1 Inequity of preliminary heating results the different original conditions of
materials such as cloth and the cups.
7.4.2 Two thermometers have different abilities of measuring such as sensitivity to
temperature changes and measurement resolution.
7.4.3 System errors from two experimenters reading the thermometers such as view
angular.
7.4.4 Water incrustation or impurities in later treatments because of repetitive uses.
7.4.5 Impurities in water may affect the temperature decrease rates
7.4.6 Room temperature may change during the relatively long period time during the
experiment process.
REFERENCE
8
Reference
[1]. 水压机泵站工作液体降温问题分析, Ma Shaomin, Shenyang Heavy Machine Factory,
Forging Shop.
[2]. Fabric Selection for a Liquid Cooling Garment, Huantian Cao; Donna H Branson; Semra Peksoz;
Jinhee Nam; Cheryl A Farr, Textile Research Journal; Jul 2006; 76, 7; ProQuest Agriculture
Journals.