ANALYSIS OF INSULATION OF MATERIAL PROJECT OF DESIGN OF EXPERIMENT

Transcription

1 ANALYSIS OF INSULATION OF MATERIAL PROJECT OF DESIGN OF EXPERIMENT Group Member: Wang Deyu, Li Dejun, Zhong Haoyuan Xu Shanshan, Li Yaqiong, Yan Li

2 CATALOG 1 Literature Review Executive Summary Preparation Choice of Experimental Design Performing the Experiment Eliminating Noise Data analysis Reference... 27

3 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.

4 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 = 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

5 PREPARATION 3 Preparation 3.1 Material and Measuring Equipment 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:

6 Flax, Black Flax, White Cotton, Black Cott 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

7 Beake 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 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:

8 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 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

9 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 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 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 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.

10 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.

11 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

12 . Appendix StdOrder RunOrder CenterPt Blocks Material Color Layer Ventilation Light White Singular No Heavy White Singular No Light Black Singular No Heavy Black Singular No Light White Multiple No Heavy White Multiple No Light Black Multiple No Heavy Black Multiple No Light White Singular Yes Heavy White Singular Yes Light Black Singular Yes Heavy Black Singular Yes Light White Multiple Yes Heavy White Multiple Yes Light Black Multiple Yes Heavy Black Multiple Yes Light White Singular No Heavy White Singular No Light Black Singular No Heavy Black Singular No Light White Multiple No

13 Heavy White Multiple No Light Black Multiple No Heavy Black Multiple No Light White Singular Yes Heavy White Singular Yes Light Black Singular Yes Heavy Black Singular Yes Light White Multiple Yes Heavy White Multiple Yes Light Black Multiple Yes Heavy Black Multiple Yes Appendix 1 The design of experiment Figure 4 The experiment equipment

14 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 自由度 Seq SS Adj SS Adj MS F P Material Color Layer Ventilation Material*Color Material*Layer

15 Material*Ventilation Color*Layer Color*Ventilation Layer*Ventilation Material*Color*Layer Material*Color*Ventilation Material*Layer*Ventilation Color*Layer*Ventilation Material*Color*Layer*Ventilation 误差 合计 We delete Material*Color*Layer*Ventilation, and then recalculate the coefficients. 来源 自由度 Seq SS Adj SS Adj MS F P 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 We delete Material*Color*Layer, and then recalculate the coefficients.

16 来源 自由度 Seq SS Adj SS Adj MS F P 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 We delete Material* Layer*Ventilation, and then recalculate the coefficients. 来源 自由度 Seq SS Adj SS Adj MS F P 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 We delete Color*Layer*Ventilation, and then recalculate the coefficients. 来源自由度 Seq SS Adj SS Adj MS F P Material Color

17 Layer Ventilation Material*Color Material*Layer Material*Ventilation Color*Layer Color*Ventilation Layer*Ventilation Material*Color*Layer 误差 合计 We delete Material*Color*Layer, and then recalculate the coefficients. 来源 自由度 Seq SS Adj SS Adj MS F P Material Color Layer Ventilation Material*Color Material*Layer Material*Ventilation Color*Layer Color*Ventilation Layer*Ventilation 误差 合计 We delete Color*Layer, and then recalculate the coefficients. 来源 自由度 Seq SS Adj SS Adj MS F P Material Color Layer Ventilation Material*Color

18 Material*Layer Material*Ventilation Color*Ventilation Layer*Ventilation 误差 合计 We delete Material*Layer, and then recalculate the coefficients. 来源 自由度 Seq SS Adj SS Adj MS F P Material Color Layer Ventilation Material*Color Material*Ventilation Color*Ventilation Layer*Ventilation 误差 合计 Also we get S = R-Sq = 96.32% R-Sq( 调整 ) = 95.04% 项 系数系数标准误 T P 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 We also draw some plot in function DOE in Minitab to show the effect of left factors.

19 百分比 项 标准化效应的 Pareto 图 ( 响应为 TempDiff,Alpha =.05) 2.07 D A 因子 A B C D 名称 Material Color Layer Ventilation CD AB BD B AD C 标准化效应 Figure 5 The pareto plot 标准化效应的正态图 ( 响应为 TempDiff,Alpha =.05) B AD C A CD D 因子 A B C D 效应类型不显著显著 名称 Material Color Layer Ventilation 20 BD 10 5 AB 标准化效应

20 百分比 频率 残差 百分比 残差 TempDiff 残差图 99 正态概率图 与拟合值 残差 拟合值 直方图 与顺序 残差 观测值顺序 Figure 6 The residual plot 残差 1 的概率图正态 - 95% 置信区间 均值 E-16 标准差 N 32 AD P 值 残差 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.

21 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 Material Color Layer Ventilation Material*Color Material*Ventilation Color*Ventilation Layer*Ventilation S = PRESS = 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 ) 来源 自由度 Seq SS Adj SS Adj MS F P 主效应 因子交互作用 残差误差 失拟 纯误差 合计 TempDiff 的系数估计, 使用未编码单位的数据 项 系数 常量 Material Color Layer Ventilation Material*Color Material*Ventilation Color*Ventilation Layer*Ventilation

22 百分比 项 标准化效应的 Pareto 图 ( 响应为 TempDiff,Alpha =.05) 2.08 D A 因子 A B C D 名称 Material Color Layer Ventilation BD AB C CD B AD 标准化效应 Figure 8 The pareto plot 标准化效应的正态图 ( 响应为 TempDiff,Alpha =.05) B AD C CD A D 因子 A B C D 效应类型不显著显著 名称 Material Color Layer Ventilation 20 AB 10 5 BD 标准化效应 30 40

23 频率 残差 百分比 残差 TempDiff 残差图 正态概率图 与拟合值 残差 拟合值 直方图 与顺序 残差 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 = 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 =

24 平均值 Interaction Plot for TempDiff Data Means Material White Black Singular Multiple No Yes Material Light Heavy Color Color White Black Layer Layer Singular Multiple 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 9 Material Color Light Heavy White Black 9 Layer Ventilation 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.

25 频率 残差 百分比 残差 We transform TempDiff into Exponential form, and get the residual plot as below Exp(Diff) 残差图 99 正态概率图 与拟合值 残差 拟合值 直方图 与顺序 残差 观测值顺序 Figure 12 The residual plot We see some obvious patterns, we don t recommend to transform the data in this way. 7.2 Results explanations No ventilation can remarkably maintain the high level of heat preservation From the main effects graph, D has the most significance, which means the ventilation-absence condition nearly plays the determinant role of heat preservation Any two-order interactions containing D, that is A*D, B*D, C*D, are also significant, indicating D indeed have main effect 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 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 Materials have main effect of heat preservation as well From the main effects graph, A has relatively large significance, which means the materials have effects on maintaining heat Some two-order interactions containing A, that is A*D, A*B, are also significant, indicating A indeed has main effect The negative coefficient of material=light means heavy material does better in maintaining heat Colors of material have main effect of heat preservation as well From the main effects graph, B has relatively large significance, which

26 means the different colors have different abilities to avoid heat loss Some two-order interactions containing B, that is B*D, A*B, are also significant, indicating B indeed have main effect The positive coefficient of color=white means white material has prior ability in maintaining heat, which may be contrary to our concept Thickness of material has less but also main effect of heat preservation as well From the main effects graph, C has relatively large significance, which means the different layers have different abilities to avoid heat loss 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 The negative coefficient of layer=singular means thicker material has prior ability in maintaining heat, consistent with our common sense Interaction explanation: Colors have less effect than materials do, and these two have interaction 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 Interactions containing ventilation are evident, which means when ventilation condition changes, the result changes much. 7.3 Possible causes 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 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 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: Inequity of preliminary heating results the different original conditions of materials such as cloth and the cups Two thermometers have different abilities of measuring such as sensitivity to temperature changes and measurement resolution.

27 7.4.3 System errors from two experimenters reading the thermometers such as view angular Water incrustation or impurities in later treatments because of repetitive uses Impurities in water may affect the temperature decrease rates 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.