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| 热传导中的变分原理 | |
| 引用本文： | 程新广,李志信,过增元. 热传导中的变分原理[J]. 工程热物理学报, 2004, 25(3): 457-459 |
| 作者姓名： | 程新广 李志信 过增元 |
| 作者单位： | 清华大学工程力学系,传热强化与过程节能教育部重点实验室,北京,100084;清华大学工程力学系,传热强化与过程节能教育部重点实验室,北京,100084;清华大学工程力学系,传热强化与过程节能教育部重点实验室,北京,100084 |
| 基金项目： | 国家重大基础研究发展规划资助项目(No.G20000263) |
| 摘 要： | 采用力学中建立最小势能原理和最小余能原理的加权余量法,分别得到了热传导中势能型与余能型的变分原理。通过对势能型变分原理的分析发现,对于可逆的导热过程,“力”(热流)在“位移”(温度)上做的“功”完全转换为物体的“势能”,即热量传递势容。而在不可逆的稳态导热过程中,这个势能完全被耗散掉了,成为传递势容耗散。对于非稳态导热过程,则类似于粘弹性物体,热流在温度位移上做的“功”一部分转换为物体的传递势容,而另外一部分成为传递势容的耗散。 |
| 关 键 词： | 变分原理 热量传递势容 热量传递势容耗散 |
| 文章编号： | 0253-231X(2004)03-0457-03 |
| 修稿时间： | 2003-12-16 |
VARIATIONAL PRINCIPLES IN HEAT CONDUCTION |
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| CHENG Xin-Guang,LI Zhi-Xin,GUO Zeng-Yuan. VARIATIONAL PRINCIPLES IN HEAT CONDUCTION[J]. Journal of Engineering Thermophysics, 2004, 25(3): 457-459 | |
| Authors: | CHENG Xin-Guang LI Zhi-Xin GUO Zeng-Yuan |
| Affiliation: | CHENG Xin-Guang,LI Zhi-Xin,GUO Zeng-Yuan Department of Engineering Mechanics,Tsinghua University Beijing 100084,China |
| Abstract: | Analogue to variational principles in solid mechanics, variational principles in heat con-duction are developed by the method of weighted residuals in this paper. In steady heat conduction,the principle show that the "potential energy", which is transformed from the "work" done by the"force" of heat flux in the "displacement" of temperature, is entirely dissipated. The potential en-ergy is defined as the heat transport potential capacity. However, in unsteady heat conduction, some"potential energy" is stored in the material, and the else is dissipated. |
| Keywords: | variational principles heat transport potential capacity dissipation |
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