发布时间 : 星期二 文章2013美赛论文更新完毕开始阅读
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We can guess through the process of model establishing:the heat distribution of polygon hotplate is related to size of the various angles of the polygon .Ignoring the other factors ,the greater the angle , the more uniform heat distribution .At the same time,a polygonal bakeware heat distribution also has a certain relationship with the number of sides of the polygon .the circle can be regarded as the graphics consists of a myriad of segments constituting .Obviously, is proportional to the degree of uniformity of the distribution of the number of sides of the polygon and heat .In addition,as for the rectangle baking type,the ratio of the width and the length can also have influence on its heat distribution.
We can apply a evaluation of the degree of uniformity in the model , we can qualify the degree of the heat distribution uniformity at the edge of the polygon so that we can establish a certain numerical relationship between the index and the angle of the polygon as well as the number of its edges .
Refer to the water distribution uniformity of sprinkler irrigation [4],we introduce the uniform coefficient proposed by Christiansen .
nCU?(1??h?hii?1?hi?1n)*100%iIn this formula : hi:The temperature of the i-th measurement point , k; h: The average temperature of each measuring point on the polygon edges , k; n:The total number of measurement points. At the edges of the polygon hotplate ,temperature distribution is similar to sprinkler water distribution, then we can verify the influence of the different shapes to the heat
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distribution of the bakeware edge .For example , when we consider the relationship between the heat distribution and the symmetry of a polygon shape ,we calculate the change of heat distribution uniformity with different aspect ratio rectangular bakeware and put the result in the following table.
Table 1 The changes of heat distribution uniformity with different aspect ratio
The data from the table reflects a rule that the greater the aspect ratio of the rectangle is ,the more uneven the heat distribution of the edge is . This conclusion is based on node temperature distribution via the pde [5]toolbox in the Matlab.We first check point after refinement node diagram , the principle is getting the same distance from the nearest edge of the point and at the same time make the point we choose distribute even on each side as possible as we can.Then, we calculate the temperature values at each point .Then through the temperature distribution of the above formula calculation pattern uniformity coefficient. Then through the above formula we calculate the pattern uniformity coefficient of temperature distribution. Because of the limited number of the nodes , The image may not reflect the true and reliable uniformity of temperature distribution to some degree . But we tried to make the access point data collection process homogenization , and we noted the accuracy of the data in the process calculation , which made our data has a certain credibility to some degree .
3. Model 2:Bakeware model
3.1 Problem Analysis:
We have shown the specific heat distribution on the edge of different shape baking
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pan in the process of using.Although the temperature distribution on the edge of the rectangular baking pan is not uniform, but for a rectangular oven , that meet certain length and width rectangular bakeware it can achieve 100% utilization of the space .Round baking pan’s temperature distribution on the edge is basic uniform , but its biggest drawback is the lower space utilization than the rectangular for a rectangular oven .
If the rectangular baking tray is applied to our current life,the food in the baking pan will not be even heating because of the temperature difference caused by the baking pan shape ,unable to make delicious food。By the same token , round baking pan is not being thought highly because of its own shortcomings . So we decided to design a model which can work out suitable baking pan shape that fit for different oven. This kind of bakeware can not only meet the the baking volume requirements ( oven rack space usage efficience) , but also take the degree of each baking pan heated evenly into full consideration.
According to the actual situation,we mainly take two conditions into consideration in the process of pans’ designing.Firstly,we can maximize the number of hotplates in the oven space ,that is.to maximum finite area the pans occupied in the rack which is in rectangular oven of which the ratio of the width and length isW/L.Secondly, as for the pan , we want to maximize uniform distribution of heat, which requires us to consider the case of the heat distribution of the edge of the different shapes of the hotplate in order to optimize the suitable shape .
On the basis of the consideration of the above conditions , and in order to achieve space optimization and temperature distribution optimized target,we thought of two different ways : one is to proceed from the angle of the polygon constantly by increasing the number of edges to optimize the temperature distribution ,and at the same time , analyze the problem of the size of the different polygon space , then through the comparative analysis we find the optimal model;The other one is starting from the optimization by sharping angle, use the rectangle as the prototype to replace
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the right angle through continuous arc of their point of view ( with different radius of the arc ) , and compare the space usage to identify the most optimistic model . Based on the full analysis of the advantages and disadvantages of the two approaches , the two approaches are quite feasible . However, on the one hand , taking the limitations of the simulation software into account , on the other hand , considering the practicality of the hotplate , we chose the second pathway .We take these two conditions into consideration,In quantitative analysis the two factors are attached weight , respectively, p and (1?p) , and we weigh the relationship between the two factors , which are limited space disc placed to maximize the number and the requirements of the heat distribution greatest .We think of a way to calculate the pan’s edge heat distribution uniformity to optimize the pan shape , through the establishment of a planning model for finding the optimal model .
3.2 Assumptions:
? Assuming that the temperature and other conditions are the same in the oven
liner . Under this condition , any position on the grill can be placed with hotplate , in which the idealized space utilization can be achieved is 100% .
? When the model being adjusted in order to make uniform heat distribution, for
the corner of a lot of heat we build up connection arc ,and in order not to form a new corner resulting in increased heat concentrated position , we assume the near corner of the arc and the original rectangular tangentially connected .
? Assuming the size of the available space of the oven liner is proportional to
oven external design size . That is, the ratio of the length and width of the grill is equal to that of the length and width of the oven .
? Assuming the side of the pan is mutually perpendicular to the bottom side of it.