ANALYSIS OF INSULATION OF MATERIAL and Effect Diagram – Fishbone Diagram EXECUTIVE SUMMARY 3 Preparation 3.1 Material and Measuring Equipment 3.1.1 Material We select two clothing

ANALYSIS OF INSULATION OF MATERIAL

Group Member:

Wang Deyu, Li Dejun, Zhong Haoyuan

Xu Shanshan, Li Yaqiong, Yan Li

—— PROJECT OF DESIGN OF EXPERIMENT

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

CATALOG

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.

LITERATURE REVIE

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 = hi e

e = i g e i i =

e i = igh = hi e

e i = igh e i i =

= hi e e i i =

e = i g e i i =

Cause and Effect Diagram – Fishbone Diagram

EXECUTIVE SUMMARY

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:

PREPARATION

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

Flax, Black

Flax, White

Cotton, Black

Cotton, White

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:

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:

Beaker,150ml

Figure 3 Thermometer

3.3 Experiment Location

This experiment is done in C Builiding, Room 300, Tshinghua University. The

room temperature is 26 centigrade.

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

CHOICE OF EXPERIMENTAL DESIGN

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 Black Multiple Yes

- Light White Singular 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.

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.

PREFORMING THE EXPERIMENT

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

ELIMINATING NOISE

.

Appendix

StdOrder RunOrder CenterPt Blocks Material Color Layer Ventilation

1 1 1 1 Light White Singular No

2 2 1 1 Heavy White Singular No

3 3 1 1 Light Black Singular No

4 4 1 1 Heavy Black Singular No

5 5 1 1 Light White Multiple No

6 6 1 1 Heavy White Multiple No

7 7 1 1 Light Black Multiple No

8 8 1 1 Heavy Black Multiple No

9 9 1 1 Light White Singular Yes

10 10 1 1 Heavy White Singular Yes

11 11 1 1 Light Black Singular Yes

12 12 1 1 Heavy Black Singular Yes

13 13 1 1 Light White Multiple Yes

14 14 1 1 Heavy White Multiple Yes

15 15 1 1 Light Black Multiple Yes

16 16 1 1 Heavy Black Multiple Yes

17 17 1 2 Light White Singular No

18 18 1 2 Heavy White Singular No

19 19 1 2 Light Black Singular No

20 20 1 2 Heavy Black Singular No

21 21 1 2 Light White Multiple No

22 22 1 2 Heavy White Multiple No

23 23 1 2 Light Black Multiple No

24 24 1 2 Heavy Black Multiple No

25 25 1 2 Light White Singular Yes

26 26 1 2 Heavy White Singular Yes

27 27 1 2 Light Black Singular Yes

28 28 1 2 Heavy Black Singular Yes

29 29 1 2 Light White Multiple Yes

30 30 1 2 Heavy White Multiple Yes

31 31 1 2 Light Black Multiple Yes

32 32 1 2 Heavy Black Multiple Yes

Appendix 1 The design of experiment

Figure 4 The experiment equipment

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

来源自由度 Seq SS Adj SS Adj MS F P

Material 1 6.570 6.570 6.570 22.73 0.000

Color 1 3.445 3.445 3.445 11.92

0.003

Layer 1 2.820 2.820 2.820 9.76

0.007

Ventilation 1 122.853 122.853 122.853 425.00 0.000

Material*Color 1 5.200 5.200 5.200 17.99 0.001

Material*Layer 1 0.263 0.263 0.263 0.91 0.355

DATA ANALYSIS

Material*Ventilation 1 3.063 3.063 3.063 10.60 0.005

Color*Layer 1 0.015 0.015 0.015 0.05

0.821

Color*Ventilation 1 5.040 5.040 5.040 17.44 0.001

Layer*Ventilation 1 5.200 5.200 5.200 17.99 0.001

Material*Color*Layer 1 0.578 0.578 0.578 2.00 0.177

Material*Color*Ventilation 1 0.000 0.000 0.000 0.00 0.974

Material*Layer*Ventilation 1 0.008 0.008 0.008 0.03 0.871

Color*Layer*Ventilation 1 0.383 0.383 0.383 1.32 0.267

Material*Color*Layer*Ventilation 1 0.015 0.015 0.015 0.05 0.821

误差 16 4.625 4.625 0.289

合计 31 160.080

We delete Material*Color*Layer*Ventilation, and then recalculate the coefficients.


Material 1 6.570 6.570 6.570 24.07 0.000

Color 1 3.445 3.445 3.445 12.62 0.002

Layer 1 2.820 2.820 2.820 10.33 0.005

Ventilation 1 122.853 122.853 122.853 450.08 0.000

Material*Color 1 5.200 5.200 5.200 19.05 0.000

Material*Layer 1 0.263 0.263 0.263 0.96 0.340


Color*Layer 1 0.015 0.015 0.015 0.06 0.816




Material*Color*Ventilation 1 0.000 0.000 0.000 0.00 0.973



误差 17 4.640 4.640 0.273

合计 31 160.080

We delete Material*Color*Layer, and then recalculate the coefficients.


Material 1 6.570 6.570 6.570 25.48 0.000

Color 1 3.445 3.445 3.445 13.36 0.002

Layer 1 2.820 2.820 2.820 10.94 0.004

Ventilation 1 122.853 122.853 122.853 476.52 0.000

Material*Color 1 5.200 5.200 5.200 20.17 0.000

Material*Layer 1 0.263 0.263 0.263 1.02 0.326


Color*Layer 1 0.015 0.015 0.015 0.06 0.810






误差 18 4.641 4.641 0.258

合计 31 160.080

We delete Material* Layer*Ventilation, and then recalculate the coefficients.


Material 1 6.570 6.570 6.570 26.86 0.000

Color 1 3.445 3.445 3.445 14.08 0.001

Layer 1 2.820 2.820 2.820 11.53 0.003

Ventilation 1 122.853 122.853 122.853 502.15 0.000

Material*Color 1 5.200 5.200 5.200 21.26 0.000

Material*Layer 1 0.263 0.263 0.263 1.07 0.313


Color*Layer 1 0.015 0.015 0.015 0.06 0.805





误差 19 4.648 4.648 0.245

合计 31 160.080

We delete Color*Layer*Ventilation, and then recalculate the coefficients.


Material 1 6.570 6.570 6.570 26.12 0.000

Color 1 3.445 3.445 3.445 13.70 0.001

Layer 1 2.820 2.820 2.820 11.21 0.003

Ventilation 1 122.853 122.853 122.853 488.36 0.000

Material*Color 1 5.200 5.200 5.200 20.67 0.000

Material*Layer 1 0.263 0.263 0.263 1.04 0.319


Color*Layer 1 0.015 0.015 0.015 0.06 0.808




误差 20 5.031 5.031 0.252

合计 31 160.080

We delete Material*Color*Layer, and then recalculate the coefficients.


Material 1 6.570 6.570 6.570 24.60 0.000

Color 1 3.445 3.445 3.445 12.90 0.002

Layer 1 2.820 2.820 2.820 10.56 0.004

Ventilation 1 122.853 122.853 122.853 459.95 0.000

Material*Color 1 5.200 5.200 5.200 19.47 0.000

Material*Layer 1 0.263 0.263 0.263 0.98 0.333


Color*Layer 1 0.015 0.015 0.015 0.06 0.813



误差 21 5.609 5.609 0.267

合计 31 160.080

We delete Color*Layer, and then recalculate the coefficients.


Material 1 6.570 6.570 6.570 25.70 0.000

Color 1 3.445 3.445 3.445 13.48 0.001

Layer 1 2.820 2.820 2.820 11.03 0.003

Ventilation 1 122.853 122.853 122.853 480.54 0.000

Material*Color 1 5.200 5.200 5.200 20.34 0.000

Material*Layer 1 0.263 0.263 0.263 1.03 0.322




误差 22 5.624 5.624 0.256

合计 31 160.080

We delete Material*Layer, and then recalculate the coefficients.


Material 1 6.570 6.570 6.570 25.67 0.000

Color 1 3.445 3.445 3.445 13.46 0.001

Layer 1 2.820 2.820 2.820 11.02 0.003

Ventilation 1 122.853 122.853 122.853 479.96 0.000

Material*Color 1 5.200 5.200 5.200 20.32 0.000




误差 23 5.887 5.887 0.256

合计 31 160.080

Also we get

S = 0.505930 R-Sq = 96.32% R-Sq（调整） = 95.04%

项系数系数标准误 T P

常量 6.65313 0.08944 74.39 0.000

Material

Light -0.45313 0.08944 -5.07 0.000

Color

White 0.32813 0.08944 3.67 0.001

Layer

Singular -0.29688 0.08944 -3.32 0.003

Ventilation

No -1.95938 0.08944 -21.91 0.000

Material*Color

Light White -0.40312 0.08944 -4.51 0.000

Material*Ventilation

Light No 0.30938 0.08944 3.46 0.002

Color*Ventilation

White No -0.39687 0.08944 -4.44 0.000

Layer*Ventilation

Singular No 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.

Figure 5 The pareto plot

C

AD

B

BD

AB

CD

A

D

2520151050

项

标准化效应

2.07

A Material

B Color

C Layer

D Ventilation

因子名称

标准化效应的 Pareto 图（响应为 TempDiff，Alpha = .05)

2520151050-5

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百分

比

A Material

B Color

C Layer

D Ventilation

因子名称

不显著

显著

效应类型

CD

BD

AD

AB

D

C

B

A

标准化效应的正态图（响应为 TempDiff，Alpha = .05)

Figure 6 The residual plot

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.

10-1

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3230282624222018161412108642

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残差

正态概率图与拟合值

直方图与顺序

TempDiff 残差图

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残差1

百分

比

均值 -2.49800E-16

标准差 0.4358

N 32

AD 0.831

P 值 0.029

残差1 的概率图正态 - 95% 置信区间

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）

项效应系数系数标准误 T P

常量 6.7542 0.05487 123.08 0.000

Material 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

Material*Color -0.7727 -0.3864 0.05507 -7.02 0.000

Material*Ventilation 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

S = 0.298239 PRESS = 3.81306

R-Sq = 98.71% R-Sq（预测） = 97.38% R-Sq（调整） = 98.23%

对于 TempDiff 方差分析（已编码单位）


主效应 4 129.498 129.425 32.3564 363.77 0.000

2因子交互作用 4 13.964 13.964 3.4909 39.25 0.000

残差误差 21 1.868 1.868 0.0889

失拟 7 0.368 0.368 0.0526 0.49 0.826

纯误差 14 1.500 1.500 0.1071

合计 29 145.330

TempDiff 的系数估计，使用未编码单位的数据

项系数

常量 6.75417

Material 0.469886

Color -0.227083

Layer 0.313636

Ventilation 1.94261

Material*Color -0.386364

Material*Ventilation 0.208333

Color*Ventilation -0.413636

Layer*Ventilation 0.302083

Figure 8 The pareto plot

AD

B

CD

C

AB

BD

A

D

403020100

项

标准化效应

2.08

A Material

B Color

C Layer

D Ventilation

因子名称

标准化效应的 Pareto 图（响应为 TempDiff，Alpha = .05)

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百分

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B Color

C Layer

D Ventilation

因子名称

不显著

显著

效应类型

CD

BD

AD

AB

D

C

B

A

标准化效应的正态图（响应为 TempDiff，Alpha = .05)


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 = hi e

e = i g e i i =

e i = igh = hi e e i = igh e i i =

= hi e e i i = e = i g e i i =

0.500.250.00-0.25-0.50

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残差


直方图与顺序

TempDiff 残差图

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.

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.

BlackWhite MultipleSingular YesNo10.0

7.5

5.010.0

7.5

5.010.0

7.5

5.0

Material

Color

Layer

Ventilation

Light

Heavy

Material

White

Black

Color

Singular

Multiple

Layer

Interaction Plot for TempDiffData Means

HeavyLight

9

8

7

6

5

BlackWhite

MultipleSingular

9

8

7

6

5

YesNo

Material

平均

值

Color

Layer Ventilation

TempDiff 主效应图数据平均值

We transform TempDiff into Exponential form, and get the residual plot as below


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

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残差


直方图与顺序

Exp(Diff) 残差图

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.

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.

REFERENCE

Documents

ANALYSIS OF INSULATION OF MATERIAL and Effect Diagram – Fishbone Diagram EXECUTIVE SUMMARY 3 Preparation 3.1 Material and Measuring Equipment 3.1.1 Material We select two clothing