Abstract

We propose a fundamental latent function of control heat transfer and heat flux density vectors at random positions on thermal materials by applying transformation optics. The expressions for heat flux bending are obtained, and the factors influencing them are investigated in both 2D and 3D cloaking schemes. Under certain conditions, more than one degree of freedom of heat flux bending exists corresponding to the temperature gradients of the 3D domain. The heat flux path can be controlled in random space based on the geometrical azimuths, radial positions, and thermal conductivity ratios of the selected materials.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  30. S. Guenneau and C. Amra, “Anisotropic conductivity rotates heat fluxes in transient regimes,” Opt. Express 21(5), 6578–6583 (2013).
    [Crossref] [PubMed]
  31. Y. Liu, F. Sun, and S. He, “Novel thermal lens for remote heating/cooling designed with transformation optics,” Opt. Express 24(6), 5683–5692 (2016).
    [Crossref] [PubMed]

2016 (4)

T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

G. Q. Xu and H. C. Zhang, “A concept of heat dissipation coefficient for thermal cloak based on entropy generation approach,” AIP Adv. 6(9), 095107 (2016).
[Crossref]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

Y. Liu, F. Sun, and S. He, “Novel thermal lens for remote heating/cooling designed with transformation optics,” Opt. Express 24(6), 5683–5692 (2016).
[Crossref] [PubMed]

2015 (6)

C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015).
[Crossref] [PubMed]

C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015).
[Crossref] [PubMed]

L. Wu, “Cylindrical thermal cloak based on the path design of heat flux,” ASME J. Heat Trans. 137(2), 021301 (2015).
[Crossref]

F. M. Canbazoglu, K. P. Vemuri, and P. R. Bandaru, “Estimating interfacial thermal conductivity in metamaterials through heat flux mapping,” Appl. Phys. Lett. 106(14), 143904 (2015).
[Crossref]

T. Chen, C. N. Weng, and Y. L. Tsai, “Materials with constant anisotropic conductivity as a thermal cloak or concentrator,” J. Appl. Phys. 117(5), 054904 (2015).
[Crossref]

M. N. Dang, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 016623 (2015).

2014 (6)

X. Y. Shen and J. P. Huang, “Thermally hiding an object inside a cloak with feeling,” Int. J. Heat Mass Tran. 78(7), 1–6 (2014).
[Crossref]

T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C. W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112(5), 054302 (2014).
[Crossref] [PubMed]

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Q. Li and J. S. Vipperman, “Two-dimensional acoustic cloaks of arbitrary shape with layered structure based on transformation acoustics,” Appl. Phys. Lett. 105(10), 101906 (2014).
[Crossref]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

T. Yang, K. P. Vemuri, and P. R. Bandaru, “Experimental evidence for the bending of heat flux in a thermal metamaterial,” Appl. Phys. Lett. 105(8), 083908 (2014).
[Crossref]

2013 (7)

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Reducing physical appearance of electromagnetic sources,” Opt. Express 21(4), 5053–5062 (2013).
[Crossref] [PubMed]

S. Guenneau and C. Amra, “Anisotropic conductivity rotates heat fluxes in transient regimes,” Opt. Express 21(5), 6578–6583 (2013).
[Crossref] [PubMed]

K. P. Vemuri and P. R. Bandaru, “Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials,” Appl. Phys. Lett. 103(13), 133111 (2013).
[Crossref]

S. Narayana, S. Savo, and Y. Sato, “Transient heat flux shielding using thermal metamaterials,” Appl. Phys. Lett. 102(20), 201904 (2013).
[Crossref]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

T. Yang, L. Huang, F. Chen, and W. Xu, “Heat flux and temperature field cloaks for arbitrarily shaped objects,” J. Phys. D Appl. Phys. 46(30), 305102 (2013).
[Crossref]

Y. Gao and J. P. Huang, “Unconventional thermal cloak hiding an object outside the cloak,” Europhys. Lett. 104(4), 468–477 (2013).
[Crossref]

2012 (3)

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref] [PubMed]

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

2009 (2)

J. Yang, M. Huang, C. Yang, Z. Xiao, and J. Peng, “Metamaterial electromagnetic concentrators with arbitrary geometries,” Opt. Express 17(22), 19656–19661 (2009).
[Crossref] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

2008 (1)

C. Z. Fan, Y. Gao, and J. P. Huang, “Shaped graded materials with an apparent negative thermal conductivity,” Appl. Phys. Lett. 92(25), 251907 (2008).
[Crossref]

2006 (2)

Amra, C.

Bai, X.

T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C. W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112(5), 054302 (2014).
[Crossref] [PubMed]

Bandaru, P. R.

F. M. Canbazoglu, K. P. Vemuri, and P. R. Bandaru, “Estimating interfacial thermal conductivity in metamaterials through heat flux mapping,” Appl. Phys. Lett. 106(14), 143904 (2015).
[Crossref]

T. Yang, K. P. Vemuri, and P. R. Bandaru, “Experimental evidence for the bending of heat flux in a thermal metamaterial,” Appl. Phys. Lett. 105(8), 083908 (2014).
[Crossref]

K. P. Vemuri and P. R. Bandaru, “Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials,” Appl. Phys. Lett. 103(13), 133111 (2013).
[Crossref]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Bückmann, T.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Burokur, S. N.

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Reducing physical appearance of electromagnetic sources,” Opt. Express 21(4), 5053–5062 (2013).
[Crossref] [PubMed]

Canbazoglu, F. M.

F. M. Canbazoglu, K. P. Vemuri, and P. R. Bandaru, “Estimating interfacial thermal conductivity in metamaterials through heat flux mapping,” Appl. Phys. Lett. 106(14), 143904 (2015).
[Crossref]

Chen, F.

T. Yang, L. Huang, F. Chen, and W. Xu, “Heat flux and temperature field cloaks for arbitrarily shaped objects,” J. Phys. D Appl. Phys. 46(30), 305102 (2013).
[Crossref]

Chen, T.

T. Chen, C. N. Weng, and Y. L. Tsai, “Materials with constant anisotropic conductivity as a thermal cloak or concentrator,” J. Appl. Phys. 117(5), 054904 (2015).
[Crossref]

Danckaert, J.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

Dang, M. N.

M. N. Dang, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 016623 (2015).

de Lustrac, A.

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Reducing physical appearance of electromagnetic sources,” Opt. Express 21(4), 5053–5062 (2013).
[Crossref] [PubMed]

Fan, C. Z.

C. Z. Fan, Y. Gao, and J. P. Huang, “Shaped graded materials with an apparent negative thermal conductivity,” Appl. Phys. Lett. 92(25), 251907 (2008).
[Crossref]

Gao, D.

T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C. W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112(5), 054302 (2014).
[Crossref] [PubMed]

Gao, F.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Gao, Y.

Y. Gao and J. P. Huang, “Unconventional thermal cloak hiding an object outside the cloak,” Europhys. Lett. 104(4), 468–477 (2013).
[Crossref]

C. Z. Fan, Y. Gao, and J. P. Huang, “Shaped graded materials with an apparent negative thermal conductivity,” Appl. Phys. Lett. 92(25), 251907 (2008).
[Crossref]

Ginis, V.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

Guenneau, S.

Han, T.

T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C. W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112(5), 054302 (2014).
[Crossref] [PubMed]

He, S.

Huang, J. P.

X. Y. Shen and J. P. Huang, “Thermally hiding an object inside a cloak with feeling,” Int. J. Heat Mass Tran. 78(7), 1–6 (2014).
[Crossref]

Y. Gao and J. P. Huang, “Unconventional thermal cloak hiding an object outside the cloak,” Europhys. Lett. 104(4), 468–477 (2013).
[Crossref]

C. Z. Fan, Y. Gao, and J. P. Huang, “Shaped graded materials with an apparent negative thermal conductivity,” Appl. Phys. Lett. 92(25), 251907 (2008).
[Crossref]

Huang, L.

T. Yang, L. Huang, F. Chen, and W. Xu, “Heat flux and temperature field cloaks for arbitrarily shaped objects,” J. Phys. D Appl. Phys. 46(30), 305102 (2013).
[Crossref]

Huang, M.

Kadic, M.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Lan, C.

Li, B.

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Li, Q.

Q. Li and J. S. Vipperman, “Two-dimensional acoustic cloaks of arbitrary shape with layered structure based on transformation acoustics,” Appl. Phys. Lett. 105(10), 101906 (2014).
[Crossref]

Liu, Y.

Narayana, S.

S. Narayana, S. Savo, and Y. Sato, “Transient heat flux shielding using thermal metamaterials,” Appl. Phys. Lett. 102(20), 201904 (2013).
[Crossref]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

Pendry, J. B.

Peng, J.

Piau, G. P.

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

Qiu, C. W.

T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C. W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112(5), 054302 (2014).
[Crossref] [PubMed]

Sato, Y.

S. Narayana, S. Savo, and Y. Sato, “Transient heat flux shielding using thermal metamaterials,” Appl. Phys. Lett. 102(20), 201904 (2013).
[Crossref]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

Savo, S.

S. Narayana, S. Savo, and Y. Sato, “Transient heat flux shielding using thermal metamaterials,” Appl. Phys. Lett. 102(20), 201904 (2013).
[Crossref]

Schittny, R.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Schurig, D.

Shen, X. Y.

X. Y. Shen and J. P. Huang, “Thermally hiding an object inside a cloak with feeling,” Int. J. Heat Mass Tran. 78(7), 1–6 (2014).
[Crossref]

Shi, X.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Smith, D. R.

Soukoulis, C. M.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

Sun, F.

Sun, H.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Tassin, P.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

Thiel, M.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Thong, J. T. L.

T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C. W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112(5), 054302 (2014).
[Crossref] [PubMed]

Tichit, P. H.

Tsai, Y. L.

T. Chen, C. N. Weng, and Y. L. Tsai, “Materials with constant anisotropic conductivity as a thermal cloak or concentrator,” J. Appl. Phys. 117(5), 054904 (2015).
[Crossref]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Vemuri, K. P.

F. M. Canbazoglu, K. P. Vemuri, and P. R. Bandaru, “Estimating interfacial thermal conductivity in metamaterials through heat flux mapping,” Appl. Phys. Lett. 106(14), 143904 (2015).
[Crossref]

T. Yang, K. P. Vemuri, and P. R. Bandaru, “Experimental evidence for the bending of heat flux in a thermal metamaterial,” Appl. Phys. Lett. 105(8), 083908 (2014).
[Crossref]

K. P. Vemuri and P. R. Bandaru, “Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials,” Appl. Phys. Lett. 103(13), 133111 (2013).
[Crossref]

Veretennicoff, I.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

Veynante, D.

Vipperman, J. S.

Q. Li and J. S. Vipperman, “Two-dimensional acoustic cloaks of arbitrary shape with layered structure based on transformation acoustics,” Appl. Phys. Lett. 105(10), 101906 (2014).
[Crossref]

Wegener, M.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Weng, C. N.

T. Chen, C. N. Weng, and Y. L. Tsai, “Materials with constant anisotropic conductivity as a thermal cloak or concentrator,” J. Appl. Phys. 117(5), 054904 (2015).
[Crossref]

Wu, L.

L. Wu, “Cylindrical thermal cloak based on the path design of heat flux,” ASME J. Heat Trans. 137(2), 021301 (2015).
[Crossref]

Xiao, Z.

Xu, G. Q.

G. Q. Xu and H. C. Zhang, “A concept of heat dissipation coefficient for thermal cloak based on entropy generation approach,” AIP Adv. 6(9), 095107 (2016).
[Crossref]

Xu, H.

M. N. Dang, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 016623 (2015).

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Xu, W.

T. Yang, L. Huang, F. Chen, and W. Xu, “Heat flux and temperature field cloaks for arbitrarily shaped objects,” J. Phys. D Appl. Phys. 46(30), 305102 (2013).
[Crossref]

Yang, C.

Yang, J.

Yang, T.

T. Yang, K. P. Vemuri, and P. R. Bandaru, “Experimental evidence for the bending of heat flux in a thermal metamaterial,” Appl. Phys. Lett. 105(8), 083908 (2014).
[Crossref]

T. Yang, L. Huang, F. Chen, and W. Xu, “Heat flux and temperature field cloaks for arbitrarily shaped objects,” J. Phys. D Appl. Phys. 46(30), 305102 (2013).
[Crossref]

Yi, J.

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Zhang, B.

M. N. Dang, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 016623 (2015).

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Zhang, H. C.

G. Q. Xu and H. C. Zhang, “A concept of heat dissipation coefficient for thermal cloak based on entropy generation approach,” AIP Adv. 6(9), 095107 (2016).
[Crossref]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Zhang, Y.

M. N. Dang, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 016623 (2015).

Zhou, J.

AIP Adv. (1)

G. Q. Xu and H. C. Zhang, “A concept of heat dissipation coefficient for thermal cloak based on entropy generation approach,” AIP Adv. 6(9), 095107 (2016).
[Crossref]

Appl. Phys. Lett. (7)

K. P. Vemuri and P. R. Bandaru, “Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials,” Appl. Phys. Lett. 103(13), 133111 (2013).
[Crossref]

T. Yang, K. P. Vemuri, and P. R. Bandaru, “Experimental evidence for the bending of heat flux in a thermal metamaterial,” Appl. Phys. Lett. 105(8), 083908 (2014).
[Crossref]

F. M. Canbazoglu, K. P. Vemuri, and P. R. Bandaru, “Estimating interfacial thermal conductivity in metamaterials through heat flux mapping,” Appl. Phys. Lett. 106(14), 143904 (2015).
[Crossref]

Q. Li and J. S. Vipperman, “Two-dimensional acoustic cloaks of arbitrary shape with layered structure based on transformation acoustics,” Appl. Phys. Lett. 105(10), 101906 (2014).
[Crossref]

C. Z. Fan, Y. Gao, and J. P. Huang, “Shaped graded materials with an apparent negative thermal conductivity,” Appl. Phys. Lett. 92(25), 251907 (2008).
[Crossref]

S. Narayana, S. Savo, and Y. Sato, “Transient heat flux shielding using thermal metamaterials,” Appl. Phys. Lett. 102(20), 201904 (2013).
[Crossref]

M. N. Dang, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 016623 (2015).

ASME J. Heat Trans. (1)

L. Wu, “Cylindrical thermal cloak based on the path design of heat flux,” ASME J. Heat Trans. 137(2), 021301 (2015).
[Crossref]

Europhys. Lett. (1)

Y. Gao and J. P. Huang, “Unconventional thermal cloak hiding an object outside the cloak,” Europhys. Lett. 104(4), 468–477 (2013).
[Crossref]

Int. J. Heat Mass Tran. (1)

X. Y. Shen and J. P. Huang, “Thermally hiding an object inside a cloak with feeling,” Int. J. Heat Mass Tran. 78(7), 1–6 (2014).
[Crossref]

J. Appl. Phys. (1)

T. Chen, C. N. Weng, and Y. L. Tsai, “Materials with constant anisotropic conductivity as a thermal cloak or concentrator,” J. Appl. Phys. 117(5), 054904 (2015).
[Crossref]

J. Opt. (1)

T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

J. Phys. D Appl. Phys. (1)

T. Yang, L. Huang, F. Chen, and W. Xu, “Heat flux and temperature field cloaks for arbitrarily shaped objects,” J. Phys. D Appl. Phys. 46(30), 305102 (2013).
[Crossref]

Nat. Commun. (1)

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

New J. Phys. (1)

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys. 14(3), 033007 (2012).
[Crossref]

Opt. Express (8)

Phys. Rev. Lett. (4)

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

T. Han, X. Bai, D. Gao, J. T. L. Thong, B. Li, and C. W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112(5), 054302 (2014).
[Crossref] [PubMed]

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Sci. Rep. (1)

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

Science (1)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

The transport process. (a) Original domain Ω; (b) Transformation domain Ω’.

Fig. 2
Fig. 2

Models of thermal cloaking schemes. (a) 2D scheme; (b) 3D scheme.

Fig. 3
Fig. 3

Heat flux line distribution for cloaking schemes and the upper-right illustrations show the temperature variation corresponding the heat flux line: (a) heat flux line for 2D cloaking scheme; (b) heat flux line for 3D cloaking scheme.

Fig. 4
Fig. 4

Variation of heat flux bending at interfaces (between layer 1 and 2, layer 5 and 6, layer 9 and 10, layer 10 and background, respectively) with different radios of thermal conductivities for 2D cloaking scheme.

Fig. 5
Fig. 5

Variation in heat flux bending on interface between layer 1 and 2 corresponding to the change of �� for 3D cloak scheme, (a) variation in ϕ1; (b) variation in ϕ2; (c) variation in ϕ3; (d) variation in ϕ4; (e) variation in ϕ5; (f) variation in ϕ6.

Fig. 6
Fig. 6

Variation in heat flux bending on interface between layer 5 and 6 corresponding to the change of �� for 3D cloak scheme, (a) variation in ϕ1; (b) variation in ϕ2; (c) variation in ϕ3; (d) variation in ϕ4; (e) variation in ϕ5; (f) variation in ϕ6.

Fig. 7
Fig. 7

Variation in heat flux bending upon the change in thermal material ratios without considering variation in radial positions, i.e. r r R 1 = 1, R1 = 0, when θ’ = −45° in 3D space, (a) variation in ϕ1; (b) variation in ϕ2; (c) variation in ϕ4; Variation in heat flux bending upon the change in radial positions when θ’ = −45° and thermal conductivity ratio is 1000 or 0.001 in 3D space, (d) variation in ϕ1; (e) variation in ϕ2; (f) variation in ϕ4.

Equations (25)

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ρ(α)c(α) T t =( κ(α)T ).
κ=( κ x 0 0 0 κ y 0 0 0 κ z )=( ( l n1 + l n ) κ n1 κ n l n1 κ n + l n κ n1 0 0 0 κ n1 l n1 + κ n l n l + n1 l n 0 0 0 κ n1 l n1 + κ n l n l + n1 l n ), (n2).
r'= R 1 (α)+ ( R 2 (α) R 1 (α)) R 2 (α) r,θ'=θ,φ'=φ.
J= ( x',y',z' ) (x,y,z) = ( x',y',z' ) ( r',θ',φ' ) ( r',θ',φ' ) (r,θ,φ) ( r,θ,φ ) (x,y,z) =( x' r' x' θ' x' φ' y' r' y' θ' y' φ' z' r' z' θ' x' φ' )diag(ω,1,1)( r x r y r z θ x θ y θ z φ x φ y φ z ).
κ'= JκJ' det(J) .
κ'=( κ rr κ rθ κ rφ κ θr κ θθ κ θφ κ φr κ φθ κ φφ ).
ρ'c' T t = 1 ( r' R 1 ) 2 ( r' ( κ r' ( r' R 1 ) 2 T r' )+ 1 sin 2 θ' φ' ( κ φ' T φ' ) + 1 sinθ' θ' ( κ θ' sinθ' T θ' ) ).
q r' = q T r' r' + q T θ' r' + q T φ' r' = (r R 1 ) 2 sinθ( κ x cos 2 φ sin 2 θ+ κ y sin 2 φ sin 2 θ+ κ z cos 2 θ) T r' , r(r R 1 ) sin 2 θcosθ( κ x cos 2 φ+ κ y sin 2 φ κ z ) T θ'
q θ' = q T r' θ' + q T θ' θ' + q T φ' θ' =r(r R 1 ) sin 2 θcosθ( κ x cos 2 φ+ κ y sin 2 φ κ z ) T r' , ( r ) 2 sinθ( κ x cos 2 φ cos 2 θ+ κ y sin 2 φ cos 2 θ+ κ z sin 2 θ) T θ'
q φ' = q T r' φ' + q T θ' φ' + q T φ' φ' =r(r R 1 ) sin 2 θsinφcosφ( κ y κ x ) T r' . ( r ) 2 cosθsinφcosφ( κ y κ x ) T θ'
ϕ 1 = tan 1 ( q T r' θ' q T r' r' )= tan 1 ( rsinθcosθ( κ x cos 2 φ+ κ y sin 2 φ κ z ) (r R 1 )( κ x cos 2 φ sin 2 θ+ κ y sin 2 φ sin 2 θ+ κ z cos 2 θ) ),
ϕ 2 = tan 1 ( q T r' φ' q T r' r' )= tan 1 ( rsinθsinφcosφ( κ y κ x ) (r R 1 )( κ x cos 2 φ sin 2 θ+ κ y sin 2 φ sin 2 θ+ κ z cos 2 θ) ),
ϕ 3 = tan 1 ( q T r' φ' q T r' θ' )= tan 1 ( sinφcosφ( κ y κ x ) cosθ( κ x cos 2 φ+ κ y sin 2 φ κ z ) ),
ϕ 4 = tan 1 ( q T θ' r' q T θ' θ' )= tan 1 ( (r R 1 )sinθcosθ( κ x cos 2 φ+ κ y sin 2 φ κ z ) r( κ x cos 2 φ cos 2 θ+ κ y sin 2 φ cos 2 θ+ κ z sin 2 θ ) ),
ϕ 5 = tan 1 ( q T θ' φ' q T θ' θ' )= tan 1 ( cotθsinφcosφ( κ y κ x ) κ x cos 2 φ cos 2 θ+ κ y sin 2 φ cos 2 θ+ κ z sin 2 θ ),
ϕ 6 = tan 1 ( q T θ' φ' q T θ' r' )= tan 1 ( r'sinφcosφ( κ y κ x ) ( r' R 1 ) sin 2 θ( κ x cos 2 φ+ κ y sin 2 φ κ z ) ).
κ y κ x = κ z κ x =1+ l n1 l n ( l n1 + l n ) 2 ( κ n1 κ n ) 2 κ n1 κ n , (n2).
ε= l n1 l n ( l n1 + l n ) 2 ( κ n1 κ n ) 2 κ n1 κ n , (n2).
ϕ 1 = tan 1 ( rεsinθcosθ cos 2 φ (r R 1 )(1+ε sin 2 φ sin 2 θ+ε cos 2 θ) ),
ϕ 2 = tan 1 ( rεsinθsinφcosφ (r R 1 )(1+ε sin 2 φ sin 2 θ+ε cos 2 θ) ),
ϕ 3 = tan 1 ( tanφ cosθ ),
ϕ 4 = tan 1 ( (r R 1 )εsinθcosθ cos 2 φ r( 1+ε sin 2 φ cos 2 θ+ε sin 2 θ ) ),
ϕ 5 = tan 1 ( εsinφcosφ tanθ(1+ε cos 2 φ sin 2 θ+ε sin 2 θ) ), (θ± aπ 2 ).
ϕ 6 = tan 1 ( rtanφ (r R 1 ) sin 2 θ ), (θ± aπ 2 ).
κ r = κ 0 R 2 R 2 R 1 ( r' R 1 r' ) 2 , κ θ = κ φ = κ 0 R 2 R 2 R 1 .

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