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Recently, thermal metamaterials have attracted more and more attention, and they have been used to manipulate the flow of heat flux. As a typical case, the thermal cloak can conceal the heat signature of an object. To the best of our knowledge, most of researches on cloak have focused on the case in which the background is a single homogeneous medium. However, cloaking in the layered and gradually changing backgrounds is very common in our real life such as hiding the buried mines in several soil backgrounds. In this paper, on the basis of transformation thermodynamics, a general expression of the thermal conductivity for two-dimensional thermal cloak with arbitrary shape in the layered and gradually changing backgrounds is derived by the coordinate transformation method. According to the expression, we design the thermal cloak in different inhomogeneous backgrounds. Results of full wave simulation show that heat flux can travel around the protection area and eventually return to their original path. 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 thermal protection and thermal stealth function. In the end, we propose a useful method of utilizing homogeneous isotropic materials to construct a thermal device according to the equivalent medium theory. The method is closer to the practical application of the project because of considering the complex backgrounds. At the same time, this technology provides a feasible method to control heat transfer in the future and has great significance for thermal stealth and thermal protection.
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Keywords:
- transformation thermodynamics /
- inhomogeneous background /
- thermal conductivity /
- temperature control
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[2] Chen H Y, Chan C T 2007 Appl. Phys. Lett. 91 183518
[3] Zhang S, Genov D A, Sun C, Zhang X 2008 Phys. Rev. Lett. 100 123002
[4] Farhat M, Guenneau S, Enoch S 2009 Phys. Rev. Lett. 103 024301
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[6] Hu R, Wei X L, Hu J Y, Luo X B 2014 Sci. Rep. 4 3600
[7] Guenneau S, Amra C, Veynante D 2012 Opt. Express 20 8207
[8] Yang T Z, Huang L J, Chen F, Xu W K 2013 J.Phys.D:Appl.Phys. 46 305102
[9] 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 63 014401]
[10] Li T H, Zhu D L, Mao F C, Huang M, Yang J J, Li S B 2016 Front. Phys. 11 11503
[11] Narayana S, Sato Y 2012 Phys. Rev. Lett. 108 214303
[12] Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[13] Xu H Y, Shi X H, Gao F, Sun H D, Zhang B 2014 Phys. Rev. Lett. 112 054301
[14] Han T C, Bai X, Gao D L, Thong J T L, Li B W, Qiu C W 2014 Adv. Mater. 26 1731
[15] Ma Y G, Liu Y C, Raza M, Wang Y D, He S L 2014 Phys. Rev. Lett. 112 054301
[16] Ma Y G, Lan L, Jiang W, Sun F, He S L 2013 NPG Asia Mater. 5 e73
[17] Yu C M 1983 Heat Conduction (Beijing: Higher Education Press) p1 (in Chinese) [俞昌铭 1983 热传导 (北京: 高等教育出版社) 第1页]
[18] Yang S M, Tao W Q 2006 Heat Transfer (the Fourth Edition) (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]
[19] Sun L K, Yu Z F, Huang J 2015 Acta Phys. Sin. 64 084401 (in Chinese) [孙良奎, 于哲峰, 黄洁 2015 64 084401]
[20] Shen X Y, Huang J P 2016 Acta Phys. Sin. 65 178103 (in Chinese) [沈翔瀛, 黄吉平 2016 65 178103]
[21] Yuan X B, Lin G C, Wang Y S 2016 Mod. Phys. Lett. B 30 1650256
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[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[2] Chen H Y, Chan C T 2007 Appl. Phys. Lett. 91 183518
[3] Zhang S, Genov D A, Sun C, Zhang X 2008 Phys. Rev. Lett. 100 123002
[4] Farhat M, Guenneau S, Enoch S 2009 Phys. Rev. Lett. 103 024301
[5] Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907
[6] Hu R, Wei X L, Hu J Y, Luo X B 2014 Sci. Rep. 4 3600
[7] Guenneau S, Amra C, Veynante D 2012 Opt. Express 20 8207
[8] Yang T Z, Huang L J, Chen F, Xu W K 2013 J.Phys.D:Appl.Phys. 46 305102
[9] 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 63 014401]
[10] Li T H, Zhu D L, Mao F C, Huang M, Yang J J, Li S B 2016 Front. Phys. 11 11503
[11] Narayana S, Sato Y 2012 Phys. Rev. Lett. 108 214303
[12] Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[13] Xu H Y, Shi X H, Gao F, Sun H D, Zhang B 2014 Phys. Rev. Lett. 112 054301
[14] Han T C, Bai X, Gao D L, Thong J T L, Li B W, Qiu C W 2014 Adv. Mater. 26 1731
[15] Ma Y G, Liu Y C, Raza M, Wang Y D, He S L 2014 Phys. Rev. Lett. 112 054301
[16] Ma Y G, Lan L, Jiang W, Sun F, He S L 2013 NPG Asia Mater. 5 e73
[17] Yu C M 1983 Heat Conduction (Beijing: Higher Education Press) p1 (in Chinese) [俞昌铭 1983 热传导 (北京: 高等教育出版社) 第1页]
[18] Yang S M, Tao W Q 2006 Heat Transfer (the Fourth Edition) (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]
[19] Sun L K, Yu Z F, Huang J 2015 Acta Phys. Sin. 64 084401 (in Chinese) [孙良奎, 于哲峰, 黄洁 2015 64 084401]
[20] Shen X Y, Huang J P 2016 Acta Phys. Sin. 65 178103 (in Chinese) [沈翔瀛, 黄吉平 2016 65 178103]
[21] Yuan X B, Lin G C, Wang Y S 2016 Mod. Phys. Lett. B 30 1650256
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