過往許多熱遮罩裝置設計成圓形或對稱形狀，本研究探討任意形狀熱遮罩同樣是否擁有熱遮罩的效果，也就是說被保護區域溫度梯度很小以及背景區域溫度分布未受裝置影響。本研究以模擬和實驗的方法來進行。首先以COMSOL模擬來觀察不同的熱傳導係數和不同的幾何尺寸會對遮罩造成甚麼影響，並提出等效面積的方法與文獻的理論值做比較。其中在不規則形狀方面模擬值與等效面積之理論值差距皆在5 %以內，而在橢圓形遮罩方面，模擬值與等效面積理論值差距最大達到57.6 %。利用模擬結果找尋最佳熱學材料搭配，發現外層遮罩寬度為16 mm的情況有較高的材料選擇自由度，因此以16 mm遮罩來進行實驗及後續討論。實驗部分以熱影像儀來量測溫度分布，水槽作為冷熱源，並盡量減少裝置與空氣的接觸，以盡量符合模擬的邊界條件。接著比較模擬與實驗的量測結果，發現兩者的溫度分布相似，都可以達到熱遮罩的效果。本文提出等效面積的方法搭配上雙層理論可以去估算所需要的材料參數並以自然界中存在的材料製作出熱遮罩裝置。

Thermal cloaks often have a circular or symmetrical design, thus this study focuses on whether an arbitrary shaped thermal cloak also possesses a heat shielding effect, that is, the temperature gradient of the protected area is quite small and the temperature distribution in the background region is not affected by the device. This study was carried out by simulation and experimental methods. For the simulation, COMSOL was used to observe the effects of different combinations between thermal conductivity and geometrical size of the cloak. Then an effective area approach was introduced to compare simulation results with known analytical solutions available in literature. In the case of arbitrary shaped cloak, the difference between simulation results and effective area calculations for the ratio of outer layer conductivity and background conductivity is less than 5%, but in the case of an elliptical cloak, the difference can be as high as 57.6%. After examining the simulation results, the optimal material and geometrical combination was selected and a thermal cloak device was fabricated. For the experiment, temperature distribution was measured by an infrared camera. Two water tanks serve the purpose of heat and cold source. The interaction between the device and air was minimized as much as possible to create an insulated boundary, consistent with the boundary conditions used in the simulation. The last step is to compare simulation and experimental results. It was observed that the temperature distribution of simulation and experimental is similar, thus demonstrating the desired thermal cloak effect.

[1] Kante, B., D. Germain, and A. de Lustrac, Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies. Physical Review B, 80(20): p. 4, (2009).
[2] Leonhardt, U., Optical conformal mapping. Science, 312(5781): p. 1777-1780, (2006).
[3] Liu, R., C. Ji, J.J. Mock, J.Y. Chin, T.J. Cui, and D.R. Smith, Broadband Ground-Plane Cloak. Science, 323(5912): p. 366-369, (2009).
[4] Yang, T.Z., K.P. Vemuri, and P.R. Bandaru, Experimental evidence for the bending of heat flux in a thermal metamaterial. Applied Physics Letters, 105(8): p. 3, (2014).
[5] Vemuri, K.P. and P.R. Bandaru, Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials. Applied Physics Letters, 103(13): p. 4, (2013).
[6] Vemuri, K.P., F.M. Canbazoglu, and P.R. Bandaru, Guiding conductive heat flux through thermal metamaterials. Applied Physics Letters, 105(19): p. 4, (2014).
[7] Bandaru, P.R., K.P. Vemuri, F.M. Canbazoglu, and R.S. Kapadia, Layered thermal metamaterials for the directing and harvesting of conductive heat. Aip Advances, 5(5): p. 26, (2015).
[8] Pendry, J.B., D. Schurig, and D.R. Smith, Controlling electromagnetic fields. Science, 312(5781): p. 1780-1782, (2006).
[9] Cummer, S.A. and D. Schurig, One path to acoustic cloaking. New Journal of Physics, 9: p. 8, (2007).
[10] Norris, A.N., Acoustic cloaking theory. Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences, 464(2097): p. 2411-2434, (2008).
[11] Sanchis, L., V.M. Garcia-Chocano, R. Llopis-Pontiveros, A. Climente, J. Martinez-Pastor, F. Cervera, and J. Sanchez-Dehesa, Three-Dimensional Axisymmetric Cloak Based on the Cancellation of Acoustic Scattering from a Sphere. Physical Review Letters, 110(12): p. 5, (2013).
[12] Urzhumov, Y., F. Ghezzo, J. Hunt, and D.R. Smith, Acoustic cloaking transformations from attainable material properties. New Journal of Physics, 12: p. 21, (2010).
[13] Zhang, S., D.A. Genov, C. Sun, and X. Zhang, Cloaking of matter waves. Physical Review Letters, 100(12): p. 4, (2008).
[14] Brun, M., S. Guenneau, and A.B. Movchan, Achieving control of in-plane elastic waves. Applied Physics Letters, 94(6): p. 3, (2009).
[15] Milton, G.W., M. Briane, and J.R. Willis, On cloaking for elasticity and physical equations with a transformation invariant form. New Journal of Physics, 8: p. 20, (2006).
[16] Stenger, N., M. Wilhelm, and M. Wegener, Experiments on Elastic Cloaking in Thin Plates. Physical Review Letters, 108(1): p. 5, (2012).
[17] Raza, M., Y.C. Liu, E.H. Lee, and Y.G. Ma, Transformation thermodynamics and heat cloaking: a review. Journal of Optics, 18(4), (2016).
[18] Han, T.C., X. Bai, D.L. Gao, J.T.L. Thong, B.W. Li, and C.W. Qiu, Experimental Demonstration of a Bilayer Thermal Cloak. Physical Review Letters, 112(5), (2014).
[19] Bernardes, M.A.D., Experimental evidence of the working principle of thermal diodes based on thermal stress and thermal contact conductance - Thermal semiconductors. International Journal of Heat and Mass Transfer, 73: p. 354-357, (2014).
[20] Dames, C., Solid-State Thermal Rectification With Existing Bulk Materials. Journal of Heat Transfer-Transactions of the Asme, 131(6), (2009).
[21] Fan, C.Z., Y. Gao, and J.P. Huang, Shaped graded materials with an apparent negative thermal conductivity. Applied Physics Letters, 92(25), (2008).
[22] Chen, T.Y., C.N. Weng, and J.S. Chen, Cloak for curvilinearly anisotropic media in conduction. Applied Physics Letters, 93(11), (2008).
[23] Yang, T.Z., L.J. Huang, F. Chen, and W.K. Xu, Heat flux and temperature field cloaks for arbitrarily shaped objects. Journal of Physics D-Applied Physics, 46(30), (2013).
[24] Narayana, S. and Y. Sato, Heat Flux Manipulation with Engineered Thermal Materials. Physical Review Letters, 108(21), (2012).
[25] Han, T.C., T. Yuan, B.W. Li, and C.W. Qiu, Homogeneous Thermal Cloak with Constant Conductivity and Tunable Heat Localization. Scientific Reports, 3, (2013).
[26] Kang, S., J. Cha, K. Seo, S. Kim, Y. Cha, H. Lee, J. Park, and W. Choi, Temperature-responsive thermal metamaterials enabled by modular design of thermally tunable unit cells. International Journal of Heat and Mass Transfer, 130: p. 469-482, (2019).
[27] Park, G., S. Kang, H. Lee, and W. Choi, Tunable Multifunctional Thermal Metamaterials: Manipulation of Local Heat Flux via Assembly of Unit-Cell Thermal Shifters. Scientific Reports, 7, (2017).
[28] Alu, A. and N. Engheta, Achieving transparency with plasmonic and metamaterial coatings. Physical Review E, 72(1), (2005).
[29] Caretto, L., Coordinate transformations, (2010).
[30] Maxwell, J.C., A treatise on electricity and magnetism. Vol. 1. 1881: Clarendon press.