Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Design and research of three-dimensional thermal cloak with arbitrary shape based on the transformation thermodynamics

Xia Ge Yang Li Kou Wei Du Yong-Cheng

Citation:

Design and research of three-dimensional thermal cloak with arbitrary shape based on the transformation thermodynamics

Xia Ge, Yang Li, Kou Wei, Du Yong-Cheng
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • Based on the form-invariance of the thermal conduction equation different from wave equation, transformation thermodynamics has opened up a new area for the arbitrarily manipulating of heat fluxes at discretion by using thermal metamaterials. Moreover, it can help researchers to design different kinds of thermal devices with many unique properties that cannot be simply realized by natural materials, such as thermal cloaking, thermal concentrating, thermal rotating and thermal illusion. Among these devices, the conventional thermal cloak enabling heat fluxes to travel around the inner region, has attracted the most significant attention so far. At the present time, the studies of the thermal cloak mainly focus on two-dimensional space with arbitrary shape and three-dimensional space with regular shape, which appear to be far from enough to meet the engineering requirements. In this paper, we derive the general expression of the thermal conductivity for three-dimensional thermal cloak with arbitrary shape according to the transformation thermodynamics. In this paper, the thermal conductivity in the polar coordinate system is transformed into that in the Cartesian coordinate system by means of coordinate transformation. On the basis of the expression of the thermal conductivity, we adopt full-wave simulation by using the software COMSOL Multiphysics to analyze the cloaking performances of five designed thermal cloaks, i.e., spherical thermal cloak, ellipsoidal thermal cloak, three-dimensional conformal thermal cloak with arbitrary shapes, non-conformal thermal cloak with the sphere outside the ellipsoid, and three-dimensional non-conformal thermal cloak with arbitrary shapes. The results show that the heat fluxes travel around the protection area, and eventually return to their original paths. The temperature profile inside the thermal cloak keeps unchanged, and the temperature field outside the thermal cloak is not distorted, which proves that the cloak has a perfect thermal invisible effect. Both the conformal and non-conformal thermal cloak have perfect thermal protection and invisible function. In this paper, the transformation thermodynamics is extended from two-dimensional thermal cloak to three-dimensional thermal cloak with better universality. At the same time, this technology provides more flexibility in controlling heat flow and target temperature field, which will have potential applications in designing microchip, motor protection and target thermal stealth. It is believed that the method presented here can be applied to other branches of physics, such as acoustics, matter waves and elastic waves.
      Corresponding author: Yang Li, yangli123123@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11504426) and the National Defense Foundation of China (Grant No. 1010502020202).
    [1]

    Pendry J B, Schurig D, Smith D R 2006 Science 312 1780

    [2]

    Leonhardt U 2006 Science 312 1777

    [3]

    Pendry J B, Schurig D, Smith D R 2006 Opt. Express 14 9794

    [4]

    Pendry J B, Schurig D, Smith D R 2007 Opt. Express 15 14772

    [5]

    Liu Y, Zentgraf T, Bartal G, Zhang X 2010 Nano Lett. 10 1991

    [6]

    Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R 2006 Science 314 977

    [7]

    Cummer S A, Popa B, Schurig D, Smith D R, Pendry J B 2006 Phys. Rev. E 74 036621

    [8]

    Rahm M, Schurig D, Roberts D A, Cummer S A, Smith D R, Pendry J B 2008 Photon. Nanostruct. Fundam. Appl. 6 87

    [9]

    Aubry A, Lei D Y, Fernándezdomínguez A I, Sonnefraud Y, Maier S A, Pendry J B 2010 Nano Lett. 10 2574

    [10]

    Xu H X, Wang G M, Qi M Q, Li L, Cui T J 2013 Adv. Opt. Mater. 1 495

    [11]

    Chen H, Chan C T 2007 Appl. Phys. Lett. 90 241105

    [12]

    Enoch S, Tayeb G, Sabouroux P, Guérin N, Vincent P 2002 Phys. Rev. Lett. 89 213902

    [13]

    Chen Y, Yang F, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 151913

    [14]

    Wei Q, Chen Y, Liu X J 2012 Appl. Phys. A 109 913

    [15]

    Zhang S, Genov D A, Sun C, Zhang X 2008 Phys. Rev. Lett. 100 123002

    [16]

    Farhat M, Guenneau S, Enoch S 2009 Phys. Rev. Lett. 103 024301

    [17]

    Hu R, Wei X L, Hu J Y, Luo X B 2014 Sci. Rep. 4 3600

    [18]

    Li T H, Zhu D L, Mao F C, Huang M, Yang J J, Li S B 2016 Front. Phys. 11 1

    [19]

    Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907

    [20]

    Guenneau S, Amra C, Veynante D 2012 Opt. Express 20 8207

    [21]

    Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901

    [22]

    Mao F C, Li T H, Huang M, Yang J J, Chen J C 2014 Acta Phys. Sin. 63 014401 (in Chinese) [毛春福, 李廷华, 黄铭, 杨晶晶, 陈俊昌 2014 物理学报 63 014401]

    [23]

    Qin C L, Yang J J, Huang M 2014 Acta Phys. Sin. 63 194402 (in Chinese) [秦春雷, 杨晶晶, 黄铭 2014 物理学报 63 194402]

    [24]

    Yang S M, Tao W Q 2006 Heat Transfer (4th Ed.) (Beijing: Higher Education Press) p43 (in Chinese) [杨世铭, 陶文铨 2006 传热学(第四版)(北京: 高等教育出版社) 第43页]

    [25]

    Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102

    [26]

    Chen T, Weng C N, Tsai Y L 2015 J. Appl. Phys. 117 054904

    [27]

    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]

  • [1]

    Pendry J B, Schurig D, Smith D R 2006 Science 312 1780

    [2]

    Leonhardt U 2006 Science 312 1777

    [3]

    Pendry J B, Schurig D, Smith D R 2006 Opt. Express 14 9794

    [4]

    Pendry J B, Schurig D, Smith D R 2007 Opt. Express 15 14772

    [5]

    Liu Y, Zentgraf T, Bartal G, Zhang X 2010 Nano Lett. 10 1991

    [6]

    Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R 2006 Science 314 977

    [7]

    Cummer S A, Popa B, Schurig D, Smith D R, Pendry J B 2006 Phys. Rev. E 74 036621

    [8]

    Rahm M, Schurig D, Roberts D A, Cummer S A, Smith D R, Pendry J B 2008 Photon. Nanostruct. Fundam. Appl. 6 87

    [9]

    Aubry A, Lei D Y, Fernándezdomínguez A I, Sonnefraud Y, Maier S A, Pendry J B 2010 Nano Lett. 10 2574

    [10]

    Xu H X, Wang G M, Qi M Q, Li L, Cui T J 2013 Adv. Opt. Mater. 1 495

    [11]

    Chen H, Chan C T 2007 Appl. Phys. Lett. 90 241105

    [12]

    Enoch S, Tayeb G, Sabouroux P, Guérin N, Vincent P 2002 Phys. Rev. Lett. 89 213902

    [13]

    Chen Y, Yang F, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 151913

    [14]

    Wei Q, Chen Y, Liu X J 2012 Appl. Phys. A 109 913

    [15]

    Zhang S, Genov D A, Sun C, Zhang X 2008 Phys. Rev. Lett. 100 123002

    [16]

    Farhat M, Guenneau S, Enoch S 2009 Phys. Rev. Lett. 103 024301

    [17]

    Hu R, Wei X L, Hu J Y, Luo X B 2014 Sci. Rep. 4 3600

    [18]

    Li T H, Zhu D L, Mao F C, Huang M, Yang J J, Li S B 2016 Front. Phys. 11 1

    [19]

    Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907

    [20]

    Guenneau S, Amra C, Veynante D 2012 Opt. Express 20 8207

    [21]

    Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901

    [22]

    Mao F C, Li T H, Huang M, Yang J J, Chen J C 2014 Acta Phys. Sin. 63 014401 (in Chinese) [毛春福, 李廷华, 黄铭, 杨晶晶, 陈俊昌 2014 物理学报 63 014401]

    [23]

    Qin C L, Yang J J, Huang M 2014 Acta Phys. Sin. 63 194402 (in Chinese) [秦春雷, 杨晶晶, 黄铭 2014 物理学报 63 194402]

    [24]

    Yang S M, Tao W Q 2006 Heat Transfer (4th Ed.) (Beijing: Higher Education Press) p43 (in Chinese) [杨世铭, 陶文铨 2006 传热学(第四版)(北京: 高等教育出版社) 第43页]

    [25]

    Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102

    [26]

    Chen T, Weng C N, Tsai Y L 2015 J. Appl. Phys. 117 054904

    [27]

    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]

  • [1] Zhu Hai-Long, Li Xue-Ying, Tong Hong-Hui. Three-dimensional numerical simulation of physical field distribution of radio frequency thermal plasma. Acta Physica Sinica, 2021, 70(15): 155202. doi: 10.7498/aps.70.20202135
    [2] Xia Ge, Yang Li, Kou Wei, Du Yong-Cheng. Design and research of columnar thermal cloak with arbitrary shape in inhomogeneous backgrounds. Acta Physica Sinica, 2017, 66(11): 114401. doi: 10.7498/aps.66.114401
    [3] Liu Chen, Sun Hong-Xiang, Yuan Shou-Qi, Xia Jian-Ping. Broadband acoustic focusing effect based on temperature gradient distribution. Acta Physica Sinica, 2016, 65(4): 044303. doi: 10.7498/aps.65.044303
    [4] Xue Ming-Xi, Chen Zhi-Bin, Wang Wei-Ming, Ouyang Hui-Quan, Liu Xian-Hong, Song Yan, Zhang Chao, Xiao Wen-Jian, Hou Zhang-Ya. Research on spectral peaks thermal-drifting in multi-wavelength infrared laser diode. Acta Physica Sinica, 2014, 63(15): 154206. doi: 10.7498/aps.63.154206
    [5] Wang Ping, Yin Yu-Zhen, Shen Sheng-Qiang. Numerical study of convection heat transfer in ordered three-dimensional porous media. Acta Physica Sinica, 2014, 63(21): 214401. doi: 10.7498/aps.63.214401
    [6] Qin Chun-Lei, Yang Jing-Jing, Huang Ming, Hu Yi-Yao. Research and design of thermal cloak with arbitrary shape based on Laplace’s equation. Acta Physica Sinica, 2014, 63(19): 194402. doi: 10.7498/aps.63.194402
    [7] Li Ting-Hua, Mao Fu-Chun, Huang Ming, Yang Jing-Jing, Chen Jun-Chang. Research and design of thermal concentrator with arbitrary shape based on transformation thermodynamics. Acta Physica Sinica, 2014, 63(5): 054401. doi: 10.7498/aps.63.054401
    [8] Mao Fu-Chun, Li Ting-Hua, Huang Ming, Yang Jing-Jing, Chen Jun-Chang. Research and design of thermal cloak in arbitary shape. Acta Physica Sinica, 2014, 63(1): 014401. doi: 10.7498/aps.63.014401
    [9] Wang Yu, Li Xiao-Dong, Yu Liang, Yan Jian-Hua. Numerical simulation study on characteristics of gliding arc discharge. Acta Physica Sinica, 2011, 60(3): 035203. doi: 10.7498/aps.60.035203
    [10] Zhi Rong, Gong Zhi-Qiang, Wang Qi-Guang, Xiong Kai-Guo. Influence of time delay on global temperature correlation. Acta Physica Sinica, 2011, 60(8): 089202. doi: 10.7498/aps.60.089202
    [11] Wang Qi-Guang, Feng Ai-Xia, Gong Zhi-Qiang, Huang Yan. Spatiotemporal analysis of information entropy of the global temperature. Acta Physica Sinica, 2011, 60(9): 099204. doi: 10.7498/aps.60.099204
    [12] Liu Dong, Yan Jian-Hua, Wang Fei, Huang Qun-Xing, Chi Yong, Cen Ke-Fa. Simultaneous experimental reconstruction of three-dimensional flame soot temperature and volume fraction distributions. Acta Physica Sinica, 2011, 60(6): 060701. doi: 10.7498/aps.60.060701
    [13] Chang Yan-Qin, Shen Tao, Andreev Y. M., Shaiduko A. V., Huang Jin-Zhe, Wang Hong. Simulation of the temperature-beam coupling in frequency doubling of BBO crystals. Acta Physica Sinica, 2010, 59(9): 6243-6249. doi: 10.7498/aps.59.6243
    [14] Han Qi-Gang, Ma Hong-An, Xiao Hong-Yu, Li Rui, Zhang Cong, Li Zhan-Chang, Tian Yu, Jia Xiao-Peng. Finite element method study on the temperature distribution in the cell of large single crystal diamond. Acta Physica Sinica, 2010, 59(3): 1923-1927. doi: 10.7498/aps.59.1923
    [15] Wu Di, Liu Jin-Yuan, Gong Ye, Wang Xiao-Gang, Liu Yue, Ma Teng-Cai, Lei Ming-Kai. Numerical study on the evolution of temperature of double-layer target irradiated by high power ion beam. Acta Physica Sinica, 2010, 59(7): 4826-4830. doi: 10.7498/aps.59.4826
    [16] Wang Qi-Guang, Hou Wei, Zheng Zhi-Hai, Gao Rong. The long range correlation of East Asia’s atmosphere. Acta Physica Sinica, 2009, 58(9): 6640-6650. doi: 10.7498/aps.58.6640
    [17] Zhi Rong, Gong Zhi-Qiang, Zheng Zhi-Hai, Zhou Lei. Scale analysis of global temperature based on correlation matrix theory. Acta Physica Sinica, 2009, 58(3): 2113-2120. doi: 10.7498/aps.58.2113
    [18] Yang Yong-Ming, Xu Qi-Ming, Guo Zhen. Cystal end temperature distribution under different pumping light in solid state laser. Acta Physica Sinica, 2008, 57(1): 223-229. doi: 10.7498/aps.57.223
    [19] Liu Ming-Qiang, Li Bin-Cheng. Analysis of temperature and deformation fields in an optical coating sample. Acta Physica Sinica, 2008, 57(6): 3402-3409. doi: 10.7498/aps.57.3402
    [20] Yan Chang-Chun, Xue Guo-Gang, Liu Cheng, Gao Shu-Mei. Study on the three-dimensional theory of super thin multi-layered films irradiated by the continuously modulated laser. Acta Physica Sinica, 2005, 54(7): 3058-3062. doi: 10.7498/aps.54.3058
Metrics
  • Abstract views:  5217
  • PDF Downloads:  209
  • Cited By: 0
Publishing process
  • Received Date:  22 November 2016
  • Accepted Date:  09 March 2017
  • Published Online:  05 May 2017

/

返回文章
返回