2013美赛A题一等奖论文
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4.1 Model assumption .............................................................................................................. 14 4.2 Model requirement ............................................................................................................. 14 4.3 Model establishment .......................................................................................................... 14 4.4 Model solution and analysis...............................................................................................20 4.5 Sensitivity analysis.............................................................................................................21 5. Superiority and weakness........................................................................................................... 22 6. Further research..........................................................................................................................22 7. Practical suggestions .................................................................................................................. 23 8. References .................................................................................................................................. 23 9. ADS............................................................................................................................................24 10. Appendix ...................................................................................................... 错误!未定义书签。
Figure 1 A kind of brownie pan used in daily life
2. General assumption for all models
The oven is rectangular The heat distribute evenly in the oven, that is the temperature is constant everywhere The baking pan is heated evenly The thickness of the pan is constant Without consideration of the influence caused by various material of the pan
3.3 Sensitivity analysis............................................................................................................. 11 4. How to choose an optimal pan? ................................................................................................. 14
Ordinarily, chocolate and butter is the main ingredient. Thus, we are easy to find the brownie pan is a tool to bake the brownie. But the problem is when baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners. This will make the food bakes unevenly, which may lead to corners of baked paste case, and middle section has not been baked. While in a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.
3.1 Model establishment ............................................................................................................ 1 3.1.1 Model Ⅰ: Micro-point model ................................................................................. 1 3.1.2 Model Ⅱ:Thermodynamics conduction model ...................................................... 3
Therefore, we have proposed two models. One is to show the distribution of heat across the outer edge of a pan for pans of different shapes. The other is to select an optimal shape of the pan based on the length-width ratio of the oven to make our performance optimization.
3. What is the distribution of heat across the outer edge of a pan?
3.1 Model establishment 3.1.1 Model Ⅰ: Micro-point model We build a micro-point model to show the different distribution of heat in different position for different shapes of brownie pan. As isFra Baidu bibliotekmentioned in the problem, when baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges).
Team #17999
Page 1 of 26
1. Introduction
The brownie, one of America’s favorite baked treats, was born in the U.S.A. Even though it is a relatively recent entry to the food pantheon—the recipe first appeared in print in Boston, in the early 20th century—there’s no smoking gun. And it’s a sweet dessert that is like eating chocolate but not that sweet. So it’s easy to see that the brownie got its name from its dark brown color.
Team #17999
2013 美赛 A 题一等奖论文
哈尔滨工业大学
杨宜蒙 李春柳 姜子木
【注:此页非正式论文页】
Contest
1. Introduction .................................................................................................................................. 1 2. General assumption for all models...............................................................................................1 3. What is the distribution of heat across the outer edge of a pan?..................................................1
3.2 Model solution and analysis.................................................................................................5 3.2.1 Model Ⅰ: Micro-point model ................................................................................. 5 3.2.2 Model Ⅱ: Thermodynamics conduction model ..................................................... 6
Figure 1 A kind of brownie pan used in daily life
2. General assumption for all models
The oven is rectangular The heat distribute evenly in the oven, that is the temperature is constant everywhere The baking pan is heated evenly The thickness of the pan is constant Without consideration of the influence caused by various material of the pan
3.3 Sensitivity analysis............................................................................................................. 11 4. How to choose an optimal pan? ................................................................................................. 14
Ordinarily, chocolate and butter is the main ingredient. Thus, we are easy to find the brownie pan is a tool to bake the brownie. But the problem is when baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners. This will make the food bakes unevenly, which may lead to corners of baked paste case, and middle section has not been baked. While in a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.
3.1 Model establishment ............................................................................................................ 1 3.1.1 Model Ⅰ: Micro-point model ................................................................................. 1 3.1.2 Model Ⅱ:Thermodynamics conduction model ...................................................... 3
Therefore, we have proposed two models. One is to show the distribution of heat across the outer edge of a pan for pans of different shapes. The other is to select an optimal shape of the pan based on the length-width ratio of the oven to make our performance optimization.
3. What is the distribution of heat across the outer edge of a pan?
3.1 Model establishment 3.1.1 Model Ⅰ: Micro-point model We build a micro-point model to show the different distribution of heat in different position for different shapes of brownie pan. As isFra Baidu bibliotekmentioned in the problem, when baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges).
Team #17999
Page 1 of 26
1. Introduction
The brownie, one of America’s favorite baked treats, was born in the U.S.A. Even though it is a relatively recent entry to the food pantheon—the recipe first appeared in print in Boston, in the early 20th century—there’s no smoking gun. And it’s a sweet dessert that is like eating chocolate but not that sweet. So it’s easy to see that the brownie got its name from its dark brown color.
Team #17999
2013 美赛 A 题一等奖论文
哈尔滨工业大学
杨宜蒙 李春柳 姜子木
【注:此页非正式论文页】
Contest
1. Introduction .................................................................................................................................. 1 2. General assumption for all models...............................................................................................1 3. What is the distribution of heat across the outer edge of a pan?..................................................1
3.2 Model solution and analysis.................................................................................................5 3.2.1 Model Ⅰ: Micro-point model ................................................................................. 5 3.2.2 Model Ⅱ: Thermodynamics conduction model ..................................................... 6