基于拉普拉斯方程的任意形状热斗篷研究与设计

秦春雷; 杨晶晶; 黄铭; 胡艺耀

doi:10.7498/aps.63.194402

摘要

如何灵活地控制和操纵热流是目前研究的热点. 本文基于拉普拉斯方程提出了一种设计任意形状热斗篷的方法. 对于形状规则的热斗篷，在特定边界条件下求解拉普拉斯方程得到了斗篷区域材料的热导率分布解析表达式；对于不规则形状的热斗篷，通过数值求解拉普拉斯方程得到了斗篷区域材料的热导率参数分布. 全波仿真结果表明，所设计的二维和三维任意形状热斗篷内部隐身区域的热通量为零，从而具有热保护功能；同时，热流绕过斗篷后温度场恢复原来的分布，实现了完美隐身功能. 这项研究为解决热斗篷内外边界非共形问题提供了一种可行的方法，对热保护器件的设计和制备有指导意义.

关键词:

Abstract

How to control and manipulate the heat flow in a flexible way is a hotspot of current research. Based on Laplace's equation, we propose a method to design thermal cloak of arbitrary shape. For a thermal cloak of regular shape, the thermal conductivity expression is derived by analytically solving the Laplace's equation under certain boundary conditions; for a thermal cloak of irregular shape, the distribution of thermal conductivity can also be obtained based on the numerical solution of Laplace's equation. Results of full wave simulation show that no heat fluxes emerge in the internal stealth area both for two-dimensional and three-dimensional thermal cloak of arbitrary shape. Meanwhile, the heat fluxes return to their original pathways, resulting in a perfect thermal invisible effect. This research provides a feasible method to design a thermal cloak of non-conformal cross section and has a guiding significance for the design and manufacturing of thermal cloak.

Keywords:

作者及机构信息

1.
云南大学无线创新实验室, 信息学院, 昆明 650091;

2.
电子科技大学电子工程学院, 成都 611731

基金项目: 国家自然科学基金（批准号：61161007，61261002）、云南省自然科学基金重点项目（批准号：2013FA006）、教育部博士点基金（批准号：20135301110003，20125301120009）和中国博士后基金（批准号：2013M531989）资助的课题.

Authors and contacts

1.
Wireless Innovation Lab, School of Information Science and Engineering of Yunnan University, Kunming 650091, China;

2.
School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61161007, 61261002), the Key Program of Natural Science of Yunnan Province, China (Grant No. 2013FA006), the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant Nos. 20135301110003, 20125301120009), and the China Postdoctoral Science Foundation (Grant No. 2013M531989).

参考文献

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[11]	Yu G X, Cui T J, Jiang W 2009 J. Infrared. Millim. W. 30 633
[12]	Chen H Y, Chan C T, Sheng P 2010 Nature materials 9 387
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施引文献

[1]	Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2]	Pendry J B 2000 Phy. Rev. Lett. 85 3966
[3]	Yang J J, Huang M, Yang C F, Xiao Z, Peng J H 2009 Optics Express 17 19656
[4]	Wu Q, Zhang K, Meng F Y, Li L W 2010 Acta Phys. Sin. 59 6071(in Chinese) [吴群, 张狂, 孟繁义, 李乐伟 2010 物理学报 59 6071]
[5]	Zheludev N I, Kivshar Y S 2012 Nature Materials 11 917
[6]	Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[7]	Hu J, Zhou X M, Hu G K 2009 Optics Express 17 1308
[8]	Luo X Y, Liu D Y, Liu J J, Dong J F 2014 Chin. Phys. B 23 054101
[9]	Yan M, Yan W, Qiu M 2008 Phys. Rev. B 78 125113
[10]	Li C, Meng X K, Liu X, Li F, Fang G Y, Chen H Y, Chan C T 2010 Phys. Rev. Lett. 105 233906
[11]	Yu G X, Cui T J, Jiang W 2009 J. Infrared. Millim. W. 30 633
[12]	Chen H Y, Chan C T, Sheng P 2010 Nature materials 9 387
[13]	Wang Z, Dong J F, Liu J J, Luo X Y 2012 Acta Phys. Sin. 61 204101(in Chinese) [王战, 董建峰, 刘锦景, 罗孝阳 2012 物理学报 61 204101]
[14]	Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907
[15]	Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[16]	Guenneau S, Amra C, Veynante D 2012 Optics Express 20 8207
[17]	Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102
[18]	Han T C, Yuan T, Li B W, Qiu C W 2013 Scientific Reports 3 1593
[19]	Mao F C, Li T H, Huang M, Yang J J, Chen J C 2014 Acta Phys. Sin. 63 014401(in Chinese) [毛福春, 李廷华, 黄铭, 杨晶晶, 陈俊昌 2014 物理学报 63 014401]
[20]	Courant R, Hilbert D 1991 Methods of Mathematical Physics (Weinheim: Wiley-VCH) pp110-112
[21]	Hu J, Zhou X M, Hu G K 2009 Comput. Mater. Sci. 46 708

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