均匀热流作用下考虑表面效应的非圆形纳米孔的级数解

张雨; 赵婕燕; 杨海兵

doi:10.21656/1000-0887.450308

均匀热流作用下考虑表面效应的非圆形纳米孔的级数解

doi: 10.21656/1000-0887.450308

张雨^1,,
赵婕燕²,
杨海兵^3, ,

1.
华南理工大学土木与交通学院，广州 510640
2.
南京航空航天大学航空学院，南京 210016
3.
河海大学力学与工程科学学院，南京 211100

基金项目:

国家自然科学基金 11902116

广东省自然科学基金 2022A1515011773

详细信息

作者简介:
张雨(2001—)，男，硕士生(E-mail: gorain2526@163.com)

通讯作者:
杨海兵(1988—)，男，副教授，博士(通信作者. E-mail: yanghb@hhu.edu.cn)

中图分类号: O39
计量
- 文章访问数: 88
- HTML全文浏览量: 40
- PDF下载量: 15
- 被引次数: 0
出版历程
- 收稿日期: 2024-11-18
- 修回日期: 2025-02-26
- 刊出日期: 2026-01-01

Series Solutions for Non-Circular Nanoholes With Surface Effects Under Uniform Heat Flux

1.
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, P. R. China
2.
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China
3.
College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, P. R. China

摘要

摘要: 该文研究了均匀远场热流作用下单个非圆形纳米孔的二维平面问题.为考察微观尺度下表面声子散射对热传导的影响，该文引入了考虑温度跳跃的弱热传导模型，并利用完整的Gurtin-Murdoch低阶表面能模型来表征表面效应的影响.基于复变函数理论和级数展开，通过保角映射技术定义了纳米孔的几何形状，从而得到了不同孔型对应的温度场和热应力场的级数解.通过对一些非圆形纳米孔的数值算例进行分析，研究了表面效应对热应力场的影响.结果表明：考虑表面效应将显著增加纳米孔附近的热应力，并且表面弹性和表面张力的共同作用在决定热应力大小中起到了关键作用.
- 均匀热流 /
- Gurtin-Murdoch模型 /
- 弱热传导模型 /
- 表面效应
Abstract: The 2D plane problem of non-circular nanoholes under uniform far-field heat flow was investigated. To examine the effects of surface phonon scattering on heat conduction at the microscale, a weakly thermal conductivity model considering temperature jump was introduced, and the complete Gurtin-Murdoch lower-order surface energy model was employed to characterize the surface effects. Based on the theory of complex functions and series expansion, the series solutions for the temperature field and the thermal stress field were obtained corresponding to different hole shapes defined with the conformal mapping techniques. Several numerical examples of non-circular nanoholes were presented to analyze the surface effects on thermal stress fields. The results indicate that, surface effects significantly increase the thermal stresses around the nanohole, and the combined action of surface elasticity and surface tension plays a key role in determining the magnitude of the thermal stress.
- uniform heat flux /
- Gurtin-Murdoch model /
- weakly thermal conductivity model /
- surface effect

HTML全文

图 1 含非圆形纳米孔洞的无限基体

Figure 1. An infinite matrix containing a non-circular nanohole

下载: 全尺寸图片幻灯片

图 2 本篇工作与前人工作的对比

Figure 2. Comparison of this work with previous work

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图 3 表面张力和表面弹性对不同非圆形状孔洞的影响

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 3. Influences of surface tension and surface elasticity on different non-circular nanoholes

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图 4 表面效应对非圆形纳米孔热应力分布的影响

Figure 4. Effects of surface properties on thermal stress distributions around non-circular nanoholes

下载: 全尺寸图片幻灯片

图 5 热流单独作用下非圆形纳米孔的热应力分布

Figure 5. Thermal stress distributions in non-circular nanoholes under heat flux

下载: 全尺寸图片幻灯片

图 6 表面张力和表面弹性之和恒定时不同非圆孔洞的应力的变化

Figure 6. Variations in different non-circular holes under the same sum of surface tension and surface elasticity

下载: 全尺寸图片幻灯片

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