week ending PRL 108, 214303 (2012) PHYSICAL REVIEW LETTERS 25 MAY 2012

Heat Manipulation with Engineered Thermal Materials

Supradeep Narayana and Yuki Sato The Rowland Institute at Harvard, Harvard University, Cambridge, Massachusetts 02142, USA (Received 6 March 2012; published 21 May 2012) Utilizing a multilayered composite approach, we have designed and constructed a new class of artificial materials for . We show that an engineered material can be utilized to control the diffusive flow in ways inconceivable with naturally occurring materials. By shielding, concentrating, and inverting heat current, we experimentally demonstrate the unique potential and the utility of guiding heat flux.

DOI: 10.1103/PhysRevLett.108.214303 PACS numbers: 44.10.+i, 05.70.a, 81.05.Zx

Thermodynamics is a well-established discipline in sci- To gain control over the path of energy transport via ence, and the concept of heat has been known for a long thermal conduction, one needs to engineer an artificial time. That often makes us forget how difficult it really is to material with prescribed anisotropy in its thermal conduc- manipulate heat flow in real life. Compared to the field of tivity. One of the most practical ways to introduce such electric conduction armed with nonlinear -sate de- anisotropy is to build a stacked composite from macro- vices, heat conduction management is still in its infancy. scopic layers of isotropic materials. Consider, for example, The ability to precisely control heat current has significant a composite made of alternating sheets of materials A and implications beyond scientific curiosity, and can poten- B. In a perpendicular direction, the two alternating con- tially lead to the development of thermal analogues of ductances add in series, while they add in parallel in a electronic transistors, rectifiers, and diodes. Here we transverse direction. Thus, the overall show that an artificial material can be utilized to guide of the effective medium becomes anisotropic, and the heat the heat flow in ways inconceivable with naturally occur- flux density vector changes direction as it propagates ring materials. We demonstrate this concept by engineer- through the material. Building on this effect, one can ing a new class of artificial material for thermal conduction design and assemble an artificial composite material that and experimentally shielding, concentrating, and inverting forces the heat flux to follow a particular path of interest. the applied heat flux. The results constitute a vivid dem- A concentric layered structure consisting of alternating onstration of extreme heat flux control with artificial ma- layers of materials A and B of different homogeneous terials and provide a conceptual insight that heat current, isotropic thermal conductivities A and B is depicted in like electric and photonic current, should be viewed as a Fig. 2(a). For the host background material, we use a 5% medium that can be manipulated, controlled, and agar-water block with thermal conductivity h 0 56 W ðmKÞ processed. : = [4]. For the device to blend into the back- The ability to manipulate the path of energy propagation ground thermally and not perturb the external field is a trait that distinguishes artificial materials from ordinary profile, the of the host material should materials. In a solid material supporting heat current, the be close to the reduced average of those of the two properties induced from artificially arranged thermal con- ductivities can be counterintuitive. Although some theo- retical work including the prediction of a thermal cloak has been carried out [1–3], such thermal ‘‘meta’’-materials have, so far, not been investigated experimentally. We first discuss the shielding operation and then proceed to con- centrating and inverting heat flux. See Fig. 1(a). When a block of material is placed between a heat source and a sink, a uniform gradient is established across the material. Heat current flows from left to right as indicated by the arrows. Figure 1(b) depicts the same block with a hollow cylindrical shield inserted at the center. Here we require the exterior region to exhibit FIG. 1 (color online). (a) A block of material is placed be- the same temperature profile as Fig. 1(a) without the shield, tween two heat baths. (b) Concept of thermal shielding by flux while the interior region now needs to have no temperature manipulation. (c) Concept of concentrating thermal flux. gradient. (d) Concept of inverting thermal flux.

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results for the temperature profile and the heat flux lines are shown in Figs. 3(a) and 3(b). These should be com- pared with the experimentally measured temperature map shown in Fig. 3(c). The cross-sectional temperature profile is captured with a Flir E50 camera. It is apparent that the presence of the shield completely alters the tem- perature gradient profile. The extremely high thermal con- ductivity of the attracts the heat flux lines and shunts them within the material. This keeps the inner region (as well as the region inside the annulus) free of thermal gradient. We measure the temperature gradient in the region r

214303-2 week ending PRL 108, 214303 (2012) PHYSICAL REVIEW LETTERS 25 MAY 2012 shown in Figs. 3(d) and 3(e), and they should be compared with the measured thermal profile of Fig. 3(f). Although polyurethane is often used for in various applications, its thermal conductivity is not quite low enough to completely shield the thermal gradient. We measure rT 3:5K=cm ( 70% of the applied gradient) in the region r

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FIG. 5 (color online). (a) Simulated temperature profile for the reported device. (b) Simulated heat flux lines. The device’s inner FIG. 6 (color online). (a) Experimentally measured thermal structures are not shown for the flux density plot for clarity. image showing the rotation of thermal gradient. Dotted lines Arrows are guides to the eye to indicate flux direction. outline the inner and outer diameters of the reported material. (b) Isothermal line for 20:3–20:7 C.

B 0:22 W=ðmKÞ. There are 96 alternating layers total, 2 and the structure is housed in 5 layers of the same poly- background with AB h. However, in the inverter urethane sheet. The overall dimensions are 6.4 cm (OD), case, the difference between the thermal conductivities of 2 cm (ID), and 5 cm (H), and this object is cast in a host the copper sheets and the background is much larger than it material of agar-water block. is for the polyurethane sheets and the host. The overall Figure 5(a) shows the simulated temperature map for the object, therefore, tends to appear more conductive to the artificial material described above. The isothermal regions background, resulting in finite distortion of the exterior rotate in a spiral manner within the composite material in temperature profile. We note that if the flux-guiding de- such a way that the thermal gradient changes its sign in the vices are engineered with materials with temperature- inner region. The simulated heat flux pattern is shown in dependent thermal conductivities [15], one can turn the Fig. 5(b), which reveals the rotation of the heat flux vector. designed functionalities on and off with a temperature The rotation angle based on the employed spatial geometry change in the environment. Such thermal devices may and the materials’ physical dimensions and their thermal provide the nonlinearity necessary as building blocks for properties is 204. This particular angle is chosen here thermal circuits [16]. so that the experimentally observed rotation angle, which In summary, utilizing the multilayered composite ap- is always less than the ideal simulation result, ends up as proach, we have designed and constructed a new class of full inversion (i.e., 180). The loss of jrTj in the inner artificial material for a diffusive energy transport of ther- region compared to the case without the hollow cylindrical mal conduction. By employing only isotropic elements but device is 48%. prescribing particular spatial patterns, we have introduced We show the experimentally observed thermal image in the anisotropy required for thermal guiding. By shielding, Fig. 6(a). Rotation of the isotherms is clearly visible from concentrating, and inverting heat current, we have experi- their swirling patterns resembling the simulated result of mentally demonstrated some of the potential and the utility Fig. 5(a). We highlight the isothermal line representing the of guiding heat flux. Artificially engineered thermal mate- temperature range 20:3–20:7 C in Fig. 6(b), which dem- rials can yield characteristics that go far beyond those onstrates the nontrivial inversion of the thermal gradient in obtainable with conventional media, and such materials the inner region with respect to the exterior. The observed should lead to unprecedented heat flux control and novel rotation angle is 179. For the externally applied tem- applications. perature gradient rT 4:3K=cm (from left to right), The authors thank D. Rogers for machining, S. Bevis for we observe rT þ1:7K=cm in the inner region, con- infrastructure support, and M. Burns, C. Fan, N. Fang, J. firming the heat flow reversal. For the same external rT Huang, C. Stokes, and F. Vollmer for discussion. This applied in the experiment, the temperature gradient in the research was supported by the Rowland Institute at inner region expected from simulation is rT Harvard University. þ2:2K=cm. If a conventional isotropic material is used for the situation depicted in Fig. 1(d), the reversal of temperature gradient becomes unrealizable. For the heat current flowing from left to right, the heat flux vector will [1] C. Z. Fan, Y. Gao, and J. P. Huang, Appl. Phys. Lett. 92, 251907 (2008). never pick up a component pointing from right to left [2] T. Chen, C. N. Weng, and J. S. Chen, Appl. Phys. Lett. 93, within the material, let alone invert in the inner region. It 114103 (2008). is the engineered thermal properties of the artificial mate- [3] J. Y. Li, Y. Gao, and J. P. Huang, J. Appl. Phys. 108, rial here that make such a phenomenon observable. 074504 (2010). For the shield and the concentrator, constituent elements [4] M. Zhang, Z. Che, J. Chen, H. Zhao, L. Yang, Z. Zhong, give the reduced thermal conductivity that is close to the and J. Lu, J. Chem. Eng. Data 56, 859 (2011).

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