圆柱形热集中器理论、仿真和实现

毛福春; 李廷华; 黄铭; 杨晶晶; 贾邦婕

doi:10.7498/aps.63.170507

摘要

作为一种高效的热能收集与俘获技术，热集中器最近引起了研究者的关注. 本文从热传导方程和坐标变换关系出发，导出了圆柱形热集中器温度分布的解析表达式，并通过与COMSOL数值仿真结果比较证实了表达式的正确性. 分析了热集中器性能与材料各向异性和器件几何结构二者之间的联系，结果表明，包层热超材料的各向异性越大，集中器的热集中性能越好；包层与内核的半径比越大，集中器的热聚焦能力越强. 利用包层与背景媒质之间的温度关系，进一步研究了用常规材料实现热集中器的方法，通过将两种常见的天然材料沿角向按周期交替排列并调整各自面积的大小，可观察到不同程度热集中现象.

关键词:

Abstract

As a kind of ultra-efficient thermal energy harvesting cell, thermal concentrator has recently attracted great attention from researchers. An analytical expression which describes the temperature distribution in the concentrator is deduced from the heat conduction equation and coordinate transformation relations. The expression is validated by numerical experiments based on COMSOL. Influence of the anisotropy due to cladding and device geometry on the performance of the thermal concentrator is analyzed. It is demonstrated that the greater the anisotropy, the better the thermal concentration effect. Besides, increasing the aspect ratio between the cladding and the core radius also gives rise to a better performance. Based on the temperature distribution relations between the core and the background region, we further explore a method to practically realize such a thermal concentrator by using naturally available materials. It is suggested that different levels of thermal concentration can be achieved by arranging alternately two isotropic conductivities along the azimuth direction and tuning their thermal localizations respectively.

Keywords:

作者及机构信息

1.
云南大学无线创新实验室, 昆明 650091;

2.
昆明市谱传感与无线电监测重点实验室, 昆明 650091

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）和云南省自然科学基金（批准号：2011FB018）资助的课题.

Authors and contacts

1.
Wireless Innovation Lab of Yunnan University, Kunming 650091, China;

2.
Kunming Key Lab of Spectrum Sensing and Radio Monitoring, Kunming 650091, 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), and the Natural Science Foundation of Yunnan Province, China (Grant No. 2011FB018).

参考文献

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施引文献

[1]	Li N B, Ren J, Wang L, Zhang G, Hnggi P, Li B W 2012 Rev. Mod. Phys. 84 1045
[2]
[3]	Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102
[4]
[5]	Chang C W, Okawa D, Majumdar A, Zettl A 2006 Science 314 1121
[6]	Komatsu T S, Ito N 2011 Phys. Rev. E 83 012104
[7]
[8]
[9]	Wang L, Li B 2007 Phys. Rev. Lett. 99 177208
[10]
[11]	Wang L, Li B 2008 Phys. Rev. Lett. 101 267203
[12]
[13]	Li T H, Mao F C, Huang M, Yang J J, Chen J C 2014 Acta Phys. Sin. 63 054401 (in Chinese)[李廷华, 毛福春, 黄铭, 杨晶晶, 陈俊昌 2014 63 054401]
[14]	Hu R, Wei X, Hu J, Luo X 2014 Scientific reports 4
[15]
[16]	Chen T, Weng C N, Chen J S 2008 Appl. Phys. Lett. 93 114103
[17]
[18]	He X, Wu L 2013 Appl. Phys. Lett. 102 211912
[19]
[20]
[21]	Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907
[22]
[23]	Li J Y, Gao Y, Huang J P 2010 J. Appl. Phys. 108 074504
[24]	Guenneau S, Amra C, Veynante D 2012 Opt. Express 20 8207
[25]
[26]
[27]	Narayana S and Sato Y 2012 Phys. Rev. Lett. 108 214303
[28]	Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[29]
[30]	Guenneau S, Amra C 2013 Opt. Express 21 6578
[31]
[32]
[33]	Han T C, Zhao J J, Yuan T, Lei D Y, Li B W, Qiu C W 2013 Energy Environ. Sci. 2013
[34]	Han T, Yuan T, Li B W, Qiu C W 2013 Scientific Reports 3 1593
[35]
[36]
[37]	Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[38]
[39]	Wang Z, Luo X Y, Liu J J, Dong J F 2013 Acta Phys. Sin. 62 024101 (in Chinese)[王战, 罗孝阳, 刘锦景, 董建峰 2013 62 024101]
[40]	Gu C, Qu S B, Pei Z B, Xu Z, Liu J, Gu W 2011 Acta Phys. Sin. 60 027801 (in Chinese)[顾超, 屈绍波, 裴志斌, 徐卓, 刘嘉, 顾巍 2011 60 027801]
[41]
[42]
[43]	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 59 6071]
[44]
[45]	Leonhardt U 2006 Science 312 1777

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