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For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number 42221 Problem Chosen A For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ 2016 MCM/ICM Summary Sheet Have a hot bath This paper establishes the heat transfer model and the optimizing model to provide the person in a simple water containment vessel with the best strategy to add water. Firstly, according to the Fourier's law, we simplify the hot water added in as a point heat source and develop a partial differential equation model of the temperature of the bathtub water in space and time. Applying ANSYS to solve the partial differential equation, we can get the change of the temperature distribution with the water inflow per unit time and the temperature of water added in. Secondly, making the water inflow per unit time and the temperature of water added in as design variables and setting the temperature even throughout the bathtub and as close as possible to the initial temperature while without wasting too much water as targets to establish a multi-objective optimization model. Then, we transform the multiple target into single target by using the weight methods. Next, we applying the Genetic Algorithm to solve the model, and getting the results that in the case of the certain size of the bathtub and the person. When the bathing time is 30min ,the temperature of the hot water added in is 322.71K , the water inflow per unit time is 1.2鸫10?4 m3 , the variance of the finial temperature of the water is 0.05513K2 and the difference between finial temperature and initial temperature is ?0.125K , the water wasted is 0.23m3 . Thirdly, we study how would our model’s results change with the shape and volume of the tub, the shape/volume/temperature of the person in the bathtub(Table 6,7,8 ,Figure 13,14,16), the motions made by the person(Figure 17,18) and the addition of the bubble additive initially(Table 9 Figure 19). When the shape of the tub change, in 30 min washing time the temperature of the hot water added in is 324.03K , the water inflow per unit time is 1.5鸫10?4 m3 (Table 5 Figure 12).When the volume of the tub is getter larger, the temperature of the hot water added increases and the water inflow per unit time is the same trend(Figure 7,8,9,10). Finally, we provide a one-page non-technical explanation for users of the bathtub to explain the strategy. Key words: heat transfer model, partial differential equation, multi-objective optimization model, Genetic Algorithm Contents 1 Introduction.................................................................................................................1 1.1 Background ..................................................................................................1 1.2 Our work.......................................................................................................1 2 Problem restatement................................................................................................2 3 Terminology............................................................................................................2 3.1 Terms ............................................................................................................2 3.2 Symbols ........................................................................................................3 4 General Assumptions ..............................................................................................3 5 The Heat Transfer Model ........................................................................................4 5.1 Local Assumption.........................................................................................4 5.2 Basic model ..................................................................................................4 5.3 Take people into consideration.....................................................................9 5.4 ANSYS simulation .....................................................................................10 6 Multi-objective optimization model ......................................................................... 11 6.1 The build of the multi-objective optimization model ..................................... 11 6.2 The strategy to add water ................................................................................13 7 Sensitivity Analysis...............................................................................................14 7.1 Change the characteristic of the bathtub.........................................................15 7.2 Change the characteristic of the person ..........................................................17 7.3 Add the motion of the person in the bathtub...................................................19 7.4 Add the bubble additive to the bathwater .......................................................19 8 Strengths and Weaknesses ....................................................................................20 8.1 Strengths .........................................................................................................20 8.2 Weaknesses .....................................................................................................20 9 Explanation for users ................................................................................................21 Reference .....................................................................................................................21 Team # 42221 Page 1 of 1 Introduction 1.1 Background The bathtub, which is a simple water containment vessel and uses ceramic or other adiabatic material is often used in our daily life. Taking people’s comfort into consideration, the bathtub is designed as a container with a water inlet and water outlet, and when the tub reaches its capacity, excess water escapes through the overflow drain. Aimed to get relaxed and cleansed, filling the bathtub with hot water before bathing is what we always do. With the time goes by, the temperature of the water will gradually drop. In order to maintain the suitable temperature, adding a constant trickle of hot water from the faucet to reheat the bathing water is necessary. Figure 1 The bathtub we use To have a comfortable hot bath is important for us to relax ourselves. However, there was no research on the model that can predict the temperature change of the water in the bathtub and guide people how to adjust, thus, our task is to build a model to provide a method for people to adjust the temperature of the water. 1.2 Our work Our work begins with a heat transfer model. In this model, the heat conduction equation which uses the Fourier’s law and the energy conservation law to describe the change of temperature of the water in the bathtub is established. Firstly, we only consider the circumstance that the bathtub whose shape is cuboid is filled with water and without people in Team # 42221 Page 2 of it. Besides, we put a person into the model and adds a boundary condition to the heat conduction equation to get the final heat transfer model. Based on this, we set targets keep the temperature even in the bathtub and as close as possible to the initial temperature while wasting as little as possible of the water when taking a bath to optimize the heat transfer model. Since our task is to provide people with the strategy to put the water into the bathtub, to test the model applicability in our daily life, we change the characteristic of the bathtub, the characteristic of the person in the bathtub and add the bubble additive to find how would the result change of the multi-objective optimization model. In this paper, the finite element analysis and ANSYS are applied to solve a fourdimensional differential heat conduction equation to get the temperature distribution of the water in the bathtub. 2 Problem restatement The problems that we need t 内容过长，仅展示头部和尾部部分文字预览，全文请查看图片预览。 Beijing: Higher Education Press,2012.7 [2] K.Deb.Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems. Evolutionary Computation .(1999) [3] XU Lei. Multi-objective optimization problem based on genetic algorithm research and application[D]. Central South University,(2007). [4] Finite Element Analysis and Optimal Design Based on ANSYS in a XH2408 Gantry Style NC Machining Center[J]. International Journal of Plant Engineering and Management,2010,03:188-192. [文章尾部最后500字内容到此结束,中间部分内容请查看底下的图片预览]请点击下方选择您需要的文档下载。

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