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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temperature gradient is small, and with the corner side extension , showing uneven increase characteristics . And in relatively sharp lesser extent around the corner , the temperature gradient is relatively more evenly distributed , the difference is not very obvious corner and around corners .
Symmetrical octagon:
3-1 3-2
Figure 3 Temperature distribution function and the temperature gradient function
image on symmetrical octagon baking pan edge To some degree, the temperature distribution to the edges of the octagon bakeware is still uneven , the temperature of the corners is slightly higher than the temperature on both sides of the corner . And temperature gradient function images of the octagon shows , the temperature gradient at the corners both sides constituting the corner and the corner is not the same , so it can be drawn that temperature at octagon is relatively higher while the temperature gradient at octagon corner is relatively smaller , and therefore heat is relatively larger. When extending to the intermediate region from the outer space the heat is gradually reduced so is it from corner to its both sides . Contrasted with the rectangular and symmetrical octagon,from an overall point of view temperature function and temperature gradient function distribution more tends to be evenly distributed at the edge .Seeing the image of its function of temperature , temperature at the entire outer edge regardless the corner or the edge is essentially
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little changed , and the gradient change of the temperature gradient function in the corner and on both sides of the corner is not that obvious compared with a hexagon . Therefore , with respect to the rectangular and hexagonal , octagonal -shaped edge portion in the heat distribution is more uniform .
Circle:
4-1 4-2
Figure 4 Temperature distribution function and the temperature gradient function
image on circle baking pan edge
Figure 4-1 shows that the temperature of the circular edge pan gets increasingly low from the outer edge close to the center , and from an image point of view , the hotplate temperature distribution is relatively uniform in the circumferential direction close to the outer edge .
Figure 4-2 shows that in a circle hotplate,the temperature gradient along the outer edge of the hotplate to the near central region radially inwardly gradually decreases , and gradient distributes uniformly close to the outer edge along with the circumferential direction.That is, the distribution of the temperature and its gradient in the circumferential direction can be described as a uniform distribution .It’s to say that heat in the edge of the hotplate circular is a uniform distribution in the tangential direction and in radial direction from the outer edge to the inside center space the heat gradually decrease .
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2.4 Conclusions:
According to the function of the solution image we get by establishing a bakeware edge heat distribution model in specific two-dimensional case when the pan is in a specific shape , we can conclude :
? The heat distribution in a rectangular-edged pan:
The heat at the edge of the rectangle is larger than that of the intermediate region overall, and on one edge of the rectangle heat the heat gradually increases from the center of the edge to the ends of it, gradually decreases from the edge region of the pan to the intermediate region , and the distribution of heat is uneven throughout the baking pan edge.The heat distributes in the four corners area is higher than the other vicinal locations of the four sides and the heat gradually decreases from outside to inside .
? The heat distribution in polygon pan whose shapes are between rectangular and
circle :
Polygon shape baking pan between rectangular and circular the distribution of heat at edge is bigger than the middle area ,and the outside boundary is of uneven heat distribution , the corner and the near corner border are at the high heat value.But with the increase of the number of edges , heat distributes in the vicinity of the corners tends to be evenly distributed gradually . ? The heat distribution in circle-edged pan:
Near the outer edge ,the pan distributes higher heat than the internal central region , and the heat in the circumferential tangential direction is of a uniform distribution in vicinity of the pan’s outer edge .And in the radial direction heat is gradually decreasing from the inside outward .
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? During the heating process the influence of different heat distribution lead by
different shape of the pans :
Because of the rectangular-edge baking pan is uneven in the heat distribution , and the four corners concentrate more heat especially, as a consequence products in the four corners of the baking pan are easily baked overdone . In contrast, the heat distribution of the circular hotplate edge is uniform, so the heat distributing on the entire boundary of the hotplate is uniform .Then it does not appear that the product at edge of the pan is baked overdone because of excessive localized heat on rectangle bakeware edge .
2.5 Model extension:
The uniformity of bakeware heat distribution in the polygon degree conclusion: When the bakeware shape changes from a rectangle to a hexagonal , octagonal, and gradually into circular, there is increase in the number of its edges , the heat distribution of the edge is also increasingly uniform . Figure 5 An illustration of the shape transition