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Realization of a Thermal Cloak–Concentrator Using a Metamaterial

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Realization of a Thermal Cloak–Concentrator Using a Metamaterial www.nature.com/scientificreports OPEN Realization of a thermal cloak– concentrator using a metamaterial transformer Received: 2 November 2017 Ding-Peng Liu, Po-Jung Chen & Hsin-Haou Huang Accepted: 23 January 2018 By combining rotating squares with auxetic properties, we developed a metamaterial transformer Published: xx xx xxxx capable of realizing metamaterials with tunable functionalities. We investigated the use of a metamaterial transformer-based thermal cloak–concentrator that can change from a cloak to a concentrator when the device confguration is transformed. We established that the proposed dual- functional metamaterial can either thermally protect a region (cloak) or focus heat fux in a small region (concentrator). The dual functionality was verifed by fnite element simulations and validated by experiments with a specimen composed of copper, epoxy, and rotating squares. This work provides an efective and efcient method for controlling the gradient of heat, in addition to providing a reference for other thermal metamaterials to possess such controllable functionalities by adapting the concept of a metamaterial transformer. Te concept of controlling energy can be traced back to the pioneering proposals by Pendry1 and Leonhardt2, whose approaches to cloaking provided means of manipulating electromagnetic waves. Following their research, eforts have been devoted to modeling and designing coordinate transformation-based metamaterials, also known as thermal metamaterials3–5, in the feld of thermodynamics. Owing to the unconventional nature of thermal metamaterials, various applications such as the thermal cloak6–14, thermal concentrator15–17, thermal inverter18–20 and thermal illusion21–24 have been proposed. Recently, thermoelectric components25 have ofered a method for actively controlling heat fux. Other alterna- tives such as the shape memory alloy26 have also been demonstrated, theoretically and experimentally, for use as a thermal diode26, a thermal cloak–concentrator (TCC)27, and a temperature-trapping device28. Analogous to the thermal cloak and concentrator, a practical idea for adapting the concept of manipulating the heat fow in elec- tronic components has been applied29,30. In this method, the temperature within a shield area can be reduced and the concentrator can be employed to collect the low-grade waste heat of electronic components. Consequently, thermal metamaterials have been considered an important subject for future technology and applications. However, fabrication of such materials is extremely challenging owing to the continuous change in their thermal properties. Te notion of discretizing thermal metamaterials into unit-cell thermal shifers, representing heat fux lines in local spots, was therefore recently proposed31. Te method not only simplifes the manufacture of thermal metamaterials but also maintains their functionalities, including the cloak, concentrator, difuser, and rotator. Recent research on thermal metamaterials has thus focused on the controllability of functionalities. In this study, we propose a new class of thermal metamaterials, namely a metamaterial transformer (MMT), by combin- ing unit-thermal shifers and rotating squares32,33, a form of auxetic metamaterials34. Rotating squares become thicker as the rotation angle increases to 45°. Tey gradually close and shrink until the rotation angle is 90°. Te rotating squares remain in the same confguration, whereas the unit cells of the rotating squares rotate 90° rela- tive to each other. Te proposed thermal metamaterials can possess tunable functionalities by transforming the confguration of the device. Te designed MMT acts as a type of TCC that initially works as a cloak and then as a concentrator afer the rotation of all squares. In contrast to previous approaches that are based on shape memory alloys, our MMT-based TCC can realize dual functions that can be freely controlled without out-of-plane defor- mation. We then developed a theoretical model of the MMT-based TCC for predicting the property of the TCC afer the rotating squares have rotated 90°. In the following section, we demonstrate the cloaking and concentrat- ing efect of the proposed device in both simulations and experiments. Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, 106, Taiwan. Correspondence and requests for materials should be addressed to H.-H.H. (email: [email protected]) SCIENTIFIC REPORTS | (2018) 8:2493 | DOI:10.1038/s41598-018-20753-y 1 www.nature.com/scientificreports/ Results Numerical and experimental setup. Te commercial fnite element sofware COMSOL Multiphysics 5.3 was used for numerical simulations in this study. We performed simulations with a two-dimensional heat con- duction module under a steady-state condition. Te MMT-based TCC was analyzed in the following three cases. First, a theoretical model was constructed to simulate the functionality of an ideal TCC and was then rotated 90°. Second, an efective model composed of unit cell thermal shifers with a contact interface was constructed for verifcation. Finally, a revised efective model of the MMT-based TCC was constructed to take radiation heat loss into consideration. For the theoretical model, we set the top and bottom surfaces as the insulators, whereas the lef and right boundaries were prescribed temperatures in accordance with the experimental measurements. Te model com- prised a background material with thermal conductivity k = 1W/(mK) in both the interior and exterior of the circle, and the circular material was given theoretical anisotropic thermal conductivity (see Methods) with R = 70 2mm, R = 35 2mm and L = L = 210 mm, as shown in Fig. 1(a). 2 1 2 x y Te efective TCC model was constructed based on Supplementary Tables S1 and S2. Te thermal conduc- tivity of copper, epoxy and background materials were defned as k1, k2, and k3, respectively. Te boundary con- ditions were set identical to those in the theoretical model, and the confguration of the proposed TCC is shown in Fig. 1(b), with k1 = 400W/(mK), k2 = 0.3W/(mK), k3 = 90W/(mK), Lx = Ly = 210 mm and lx = ly = 140 mm. Moreover, we further considered mimicking the experimental setup by adding a thin layer of thermal compound in between adjacent unit cells, and set the thin-layer (0.1 mm) thermal compound with a low thermal conductiv- ity k4. Te choice of k4 is described in Supplementary Section 1 and discussed later. The experimental setup consisted of a thermal infrared (IR) camera (Fluke Ti-450), heat baths (Aron WB-500D), a fxing device, and a specimen, as shown in Fig. 1(c). Te heat bath on the lef side served as the source applied to the specimen, whereas the heat bath on the right side, flled with an ice–water mixture, was used as the heat sink. Te specimen was assembled into 4 × 4 unit-cell thermal shifers composed of copper and epoxy, with 4 × 4 rotating squares serving as the base connected with joints, as shown in Fig. 1(d1),(d2), and (d3). Te design of joints connecting the rotating squares in the present study is illustrated in Supplementary Figure S2. In addition, the assembled specimen was connected to the thin copper plate with 0.3 mm thickness at each end. We polished the interfaces of the unit-cell thermal shifers and added the thermal compound (Cooler Master RG-ICF-CWR2-GP) (Termal conductivity k = 1W/(mK), from the product sheet provided by the man- ufacturer) in between adjacent unit cells to reduce the thermal resistance. As illustrated in Fig. 1(c), the temper- ature profle on the topside of the specimen was obtained through a calibrated IR camera, with a thin coating of high-emissivity (ε = 0.94) black acrylic paint, ART-ANDREA-S-72075801, applied on the topside for accurate thermal imaging. Numerical simulations of MMT-based TCC. Te results of the theoretical model are summarized in Fig. 2(a). Figure 2(a1,a2) illustrate the simulated temperature profle and isothermal lines of the theoretical model, respectively, with the red arrows indicating the directions of the heat fux. Te simulation revealed the properties of the proposed TCC, where no external distortion existed and no internal gradient was observed (no heat fux through the inner region). Afer the specimen was rotated 90°, no external distortion existed, but a much greater internal gradient was observed (with greater heat fux through the inner region), as shown in Fig. 2(a1,a2). Figure 2(b1,b2) present the temperature profle and isothermal line of the TCC, respectively. An annular ring of the theoretical model was plotted to clarify the diference between the theoretical and efective models. As illus- trated in Fig. 2(b1), the temperature inside the annular ring was almost constant, with the isothermal lines outside the annular ring exhibiting minimal disturbance, similar to the properties displayed by a thermal cloak. As shown in Fig. 2(b2), the model rotated 90°, demonstrating the ability to guide the heat fux into the inner region of the annular ring, thus causing more temperature variations inside the annular ring and a slight disturbance outside the ring. Te preceding results show that the proposed MMT-based TCC can control the gradient within a particular region. However, it is reasonable to question whether such an ability can still exist when the radiation heat loss as well as the thermal resistance in the contact interfaces are considered. To explore this question numerically, in the final case we applied a surface-to-ambient radiation boundary condition in COMSOL; that is 44 Q(=−εσuaTTmb ), where Q is the thermal energy leaving the surface, εu = 0.94 is the emissivity of the surface, σ is the Stefan–Boltzmann constant, and Tamb = 28.9 °C is the ambient temperature. To compare the experimental results, the revised efective model and the experimental specimen were constructed as similar as possible. For the revised model, we simultaneously simulated the thermal radiation with the thermal resistance due to the contact interface (see Supplementary Section 1) and concluded that the temperature profle along y = 0 when setting k = 0.5 W/(mK) is closest to that of the experimental data.
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