mcm1994A Concrete Slab Floors 住宅的保温美国数学建模 - matlab数学建模

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标题：mcm1994A Concrete Slab Floors 住宅的保温美国数学建模
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所属分类: 数学建模资源类型：文档文件大小: 5.67 KB 上传时间: 2019-08-19 21:09:40 下载次数: 24 资源积分：1分提供者: jiqiren 20190819091150363

内容：
(MCM 1994A)

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.

Through special construction techniques, HUD engineers can build dwellings that do not need to rely on convection- that is, there is no need to rely on opening doors or windows to assist in temperature variation. The dwellings will be single-story, with concrete slab floors as the only foundation. You have been hired as a consultant to analyze the temperature variation in the concrete slab floor to determine if the temperature averaged over the floor surface can be maintained within a prescribed comfort zone throughout the year. If so, what size/shape of slabs will permit this?

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 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 3, Cost of Construction: Suggest a design that considers HUD's objective of reducing or eliminating heating and cooling costs, considering construction restrictions and costs.

表94A-1

周围温度舒适范围

最高85F 最高76F

最低60F 最低65F

住宅的保温(美国竞赛1994年A题)

HUP公司正在考虑建造从单幢住宅到公寓楼大小不同的住宅。公司主要关心的是房主定期支付的费用--特别是暖气和冷气的费用最少。建房地区位于全年温度变化不大的温带地区。

通过特殊的建筑技术HUP公司能不依靠对流--即不需要依靠开门开窗--来帮助调节住宅的温度。这些住宅都是只有混凝土厚板地板为仅有基础的单层住宅。你们被雇用为顾问来分析凝土厚板地板小的温度变化，由此决定地板表面的平均温度能否全年保持在指定的舒适范围内。如果可能的话，什么样的尺寸和形状能做到这点？

第一部分地板温度

由表94A-1给G66每天温度的变化范围，试研究混凝土厚板中温度的变化。假定最高温度在中午达到，最低温度在午夜达到。试决定能否在只考虑幅射的条件下设计厚板使其表面的平均温度保持在指定的舒适范围内。一开始，先假定热是通过暴露在外的厚板的周边传入住宅的，而厚板的上、下表面是绝热的。就这些假设是否恰当、假设的敏感性作山评论。如果你们不能找到满足表94A-1条件的解，你们能作出满足你们提出的表94A-1的厚板的设计吗?

第二部分建筑物温度

试分析一开始所作假设的实用性，并将其推广到分析单层住宅内温度的变化。住宅内温度能否保持在舒适范围内。

第三部分建筑费用

考虑到建筑的各种限制及费用，试提出一种考虑HUP公司关于降低甚至免去暖气和冷气费用这一目标的设计。

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mcm1994A Concrete Slab Floors 住宅的保温 .doc

关键词： mcm1994A Concrete Slab Floors 住宅的保温 美国数学建模

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