烤盘形状优化问题建模分析

Modulation of the Shape Optimization of Ovenware

摘要: 在探讨使用矩形烤盘烘烤蛋糕容易使蛋糕边角烤糊的原因时，本文建立了“单芯棒”传导模型。烘烤中的蛋糕被视为由众多单一“棒”组成，温度的传导看作是通过这一个个“棒”从烤盘边缘向蛋糕中心传导，并假设温度在棒中传导时互不影响。为了简化模型便于分析，本文着重探讨了烤盘是正多边形时温度的传导情况。对蛋糕确定点温度分析时，考虑该点四周热流的影响，对该点四周热流进行合成，进而分析该点一定时间内热量积聚情况。在分析后，我们发现边缘角度越小,在靠近边角处的总热量流越大。当时间一定时，总热流越大，会使该点在相同的时间内获得的热量较大，较小的蛋糕边角，热量积聚，使得在烘烤蛋糕时相比远离边角的地方吸收较多的热量，这是蛋糕被过度烘烤的主要原因。

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.