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1994_年美国大学生数学建模竞赛_mcm_试题 [2008/02/08 16:19]
amao 创建 		1994_年美国大学生数学建模竞赛_mcm_试题 [2014/12/30 22:36] (当前版本)
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 ====== 1994 年美国大学生数学建模竞赛 MCM 试题 ====== ====== 1994 年美国大学生数学建模竞赛 MCM 试题 ======
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 ===== 1994 MCM A: Concrete Slab Floors ===== ===== 1994 MCM A: Concrete Slab Floors =====
 The U.S. Dept. of Housing and Urban Development (HUD) is considering constructing dwellings of various sizes, ranging from individual houses to large apartment complexes. A principal concern is to minimize recurring costs to occupants, especially the costs of heating and cooling. The region in which the construction is to take place is temperate, with a moderate variation in temperature throughout the year.  The U.S. Dept. of Housing and Urban Development (HUD) is considering constructing dwellings of various sizes, ranging from individual houses to large apartment complexes. A principal concern is to minimize recurring costs to occupants, especially the costs of heating and cooling. The region in which the construction is to take place is temperate, with a moderate variation in temperature throughout the year. 
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 Part 1, Floor Temperature: Consider the temperature variation in a concrete slab given that the ambient temperature varies daily within the ranges given Table 1. Assume that the high occurs at noon and the low at midnight. Determine if slabs can be designed to maintain a temperature averaged over the floor surface within the prescribed comfort zone considering radiation only. Initially, assume that the heat transfer into the dwelling is through the exposed perimeter of the slab and that the top and bottom of the slabs are insulated. Comment on the appropriateness and sensitivity of these assumptions. If you cannot find a solution that satisfies Table 1, can you find designs that satisfy a Table 1 that you propose?  Part 1, Floor Temperature: Consider the temperature variation in a concrete slab given that the ambient temperature varies daily within the ranges given Table 1. Assume that the high occurs at noon and the low at midnight. Determine if slabs can be designed to maintain a temperature averaged over the floor surface within the prescribed comfort zone considering radiation only. Initially, assume that the heat transfer into the dwelling is through the exposed perimeter of the slab and that the top and bottom of the slabs are insulated. Comment on the appropriateness and sensitivity of these assumptions. If you cannot find a solution that satisfies Table 1, can you find designs that satisfy a Table 1 that you propose? 
  
- Ambient Temperature  Comfort Zone   +^ Ambient ^ Temperature  ^ Comfort Zone  ^ 
-High  85  76   +| High | 85 | 76  | 
-Low  60  65  +| Low | 60 | 65  |
  
 Part 2, Building Temperature: Analyze the practicality of the initial assumptions and extend the analysis to temperature variation within the single-story dwelling. Can the house be kept within the comfort zone?  Part 2, Building Temperature: Analyze the practicality of the initial assumptions and extend the analysis to temperature variation within the single-story dwelling. Can the house be kept within the comfort zone? 
1994_年美国大学生数学建模竞赛_mcm_试题.1202458769.txt.gz · 最后更改: 2014/12/30 22:35 (外部编辑)

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