# 烤盘形状优化问题建模分析Modulation of the Shape Optimization of Ovenware

Abstract:
When baking in a rectangular pan, heat is concentrated in the four corners and the product gets overcooked at the corners. For this, Single Rod Heat Conduction Model is set up. In Single Rod Heat Conduction Model, cakes are regarded as numerous single rods through which heat transfer from the edge to the center under the assumption that heat fluxes have no influence on each other. To simplify the model, we just analyze symmetrical regular polygon. The heat transfer law is used to calculate temperature at a certain point and then the heat flux from various directions is synthesized at the point. After composing and analyzing, we find that the greater the marginal angle is, the smaller the total heat flow is. Moreover, the heat flux leads to a sharp increase of the temperature at the point. That is the explanation for heat concentration in the four corners which results in overcooked cake.

[1] 叶启晓 (1997) 微分、微分方程建模、数学建模竞赛资源材料(第二版). 湖南大学出版社, 长沙, 231-243.

[2] 张荆州 (2009) 先进的热传递. 北京科学出版社, 北京, 140-157.

[3] 杨史敏, 道温泉 (2006) 传热学(第八版). 北京高等教育出版社, 北京, 115-298.

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