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On the basis of transformation thermodynamics, a thermal conductivity expression for cylindrical thermal cloak with arbitrary cross section is derived. Based on the expression, we design a thermal cloak with a non conformal section profile. Results of full wave simulation show that the cloak possesses heat protection function, since it is capable of guiding heat fluxes to travel around its inner domain, leaving the inner region untouched; meanwhile, the heat fluxes return to their original pathways, resulting in a perfect thermal invisible effect. Arbitrary shaped cylindrical thermal cloak with conformal or non-conformal cross section can be designed based on the derived thermal conductivity expression, and all of them have perfect thermal protection and invisibility functions. It is indicated that the derived conductivity expression is applicable to designing cylindrical thermal cloaks with an arbitrary cross section. The generality of this method has been confirmed, and it may have potential applications in the designing of thermal protection devices for computer chips and satellite, etc.
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Keywords:
- transformation thermodynamics /
- thermal cloak /
- arbitrary shape /
- non conformal
[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[2] Leonhardt U 2006 Science 312 1777
[3] Qu S B, Wang J F, Ma H, Xu Z, Zhang J Q 2013 Metamaterial Design and Applications in Stealth Technology (Beijing: Science Press) p174 (in Chinese) [屈绍波, 王甲富, 马华, 徐卓, 张介秋 2013超材料设计及其在隐身技术中的应用(北京: 科学出版社) 第174页]
[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 596071]
[5] 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]
[6] 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]
[7] Wang S Y, Liu S B 2012 Chin. Phys. B 21 044102
[8] Guo P F, Li D, Dai Q, Fu Y Q 2013 Chin. Phys. B 22 054101
[9] Yang J J, Huang M, Yang C F, Xiao Z, Peng J H 2009 Opt. Express 17 19661
[10] Li T H, Huang M, Yang J J, Yu J, Lan Y Z 2011 J. Phys. D: Appl. Phys. 44 325102
[11] Zheludev N I, Kivshar Y S 2012 Nat. Mater. 11 917
[12] Pendry J B, Aubry A, Smith D R, Maier S A 2012 Science 337 549
[13] Chen H Y, Chan C T 2010 J. Phys. D: Appl. Phys. 43 113001
[14] Richard V C, Sébastein G 2013 Acoustic Metamaterials (Netherlands: Springer) pp197–218
[15] Zhang S, Genov D A, Sun C, Zhang X 2008 Phys. Rev. Lett. 100 132002
[16] Greenleaf A, Kurylev Y, Lassas M, Uhlmann G 2008 Phys. Rev. Lett. 101 220404
[17] Yu Z Z, Feng Y J, Wang Z B, Zhao M J, Jiang T 2013 Chin. Phys. B 22 034102
[18] Milton G W, Briane M, Willis J R 2006 New J. Phys. 8 248
[19] Brun S, Guenneau, Movchan A B 2009 Appl. Phys. Lett. 94 061903
[20] Chen T, Weng C N, Chen J S 2008 Appl. Phys. Lett. 93 114103
[21] Narayana S, Sato Y 2012 Phys. Rev. Lett. 108 214303
[22] Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907
[23] Li J Y, Gao Y, Huang J P 2010 J. Appl. Phys. 108 074504
[24] Guenneau S, Amra C, Veynante D 2012 Optics Express 20 8207
[25] Guenneau S, Amra C 2013 Optics Express 21 6578
[26] Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[27] Han T C, Yuan T, Li B W, Qiu C W 2013 Scientific Reports 3 1593
[28] He X, Wu L 2013 Appl. Phys. Lett. 102 211912
[29] Guenneau S, Puvirajesinghe T M 2013 J. R. Soc. Interface 10 20130106
[30] Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102
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[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[2] Leonhardt U 2006 Science 312 1777
[3] Qu S B, Wang J F, Ma H, Xu Z, Zhang J Q 2013 Metamaterial Design and Applications in Stealth Technology (Beijing: Science Press) p174 (in Chinese) [屈绍波, 王甲富, 马华, 徐卓, 张介秋 2013超材料设计及其在隐身技术中的应用(北京: 科学出版社) 第174页]
[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 596071]
[5] 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]
[6] 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]
[7] Wang S Y, Liu S B 2012 Chin. Phys. B 21 044102
[8] Guo P F, Li D, Dai Q, Fu Y Q 2013 Chin. Phys. B 22 054101
[9] Yang J J, Huang M, Yang C F, Xiao Z, Peng J H 2009 Opt. Express 17 19661
[10] Li T H, Huang M, Yang J J, Yu J, Lan Y Z 2011 J. Phys. D: Appl. Phys. 44 325102
[11] Zheludev N I, Kivshar Y S 2012 Nat. Mater. 11 917
[12] Pendry J B, Aubry A, Smith D R, Maier S A 2012 Science 337 549
[13] Chen H Y, Chan C T 2010 J. Phys. D: Appl. Phys. 43 113001
[14] Richard V C, Sébastein G 2013 Acoustic Metamaterials (Netherlands: Springer) pp197–218
[15] Zhang S, Genov D A, Sun C, Zhang X 2008 Phys. Rev. Lett. 100 132002
[16] Greenleaf A, Kurylev Y, Lassas M, Uhlmann G 2008 Phys. Rev. Lett. 101 220404
[17] Yu Z Z, Feng Y J, Wang Z B, Zhao M J, Jiang T 2013 Chin. Phys. B 22 034102
[18] Milton G W, Briane M, Willis J R 2006 New J. Phys. 8 248
[19] Brun S, Guenneau, Movchan A B 2009 Appl. Phys. Lett. 94 061903
[20] Chen T, Weng C N, Chen J S 2008 Appl. Phys. Lett. 93 114103
[21] Narayana S, Sato Y 2012 Phys. Rev. Lett. 108 214303
[22] Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907
[23] Li J Y, Gao Y, Huang J P 2010 J. Appl. Phys. 108 074504
[24] Guenneau S, Amra C, Veynante D 2012 Optics Express 20 8207
[25] Guenneau S, Amra C 2013 Optics Express 21 6578
[26] Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[27] Han T C, Yuan T, Li B W, Qiu C W 2013 Scientific Reports 3 1593
[28] He X, Wu L 2013 Appl. Phys. Lett. 102 211912
[29] Guenneau S, Puvirajesinghe T M 2013 J. R. Soc. Interface 10 20130106
[30] Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102
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