Thermal metamaterials: functions and prospects

The phenomenon of heat transfer has been of great practical importance, going all the way back to the days when heat was believed to be a fluid that flowed between media of different temperatures. By properly guiding this flow of caloric, engines could generate work, objects could be warmed or cooled, and thermal equilibrium could be achieved. While today these simple theories of heat transfer have been replaced by a more modern understanding of heat as disordered energy, the control of its flux is of no less importance. Rather, heat transfer and thermodynamics are now also of central importance to modern technologies including power generation and conversion, night vision, microelectronics, aerospace, etc. The significance of controlling heat flow is, however, matched by its difficulty. While, for simple tasks, like increasing the insulation of an object, the material requirements are well understood, guiding heat flux in other scenarios is more difficult. Not only are there multiple forms of heat transfer—conduction, convection and radiation—but these processes are inherently less ordered than ballistic/wave transport, making confinement and steering more challenging. In this article, we shall consider one technique, the use of thermal metamaterials, which has recently been developed to control thermal conduction (principally in solids, where conduction is the dominant heat-transfer mechanism). There are two principal aspects to thermal metamaterials: the structuring of conventional media to create thermal properties not found in nature and the arrangement of these structured media to create new thermal devices. The second aspect, transformation media theory, was originally developed in optics [1,2], with the devices created by this theory (including all of those discussed in this article) disseminating to other fields, such as acoustics and fluid dynamics, as the theory was modified to account for the varying physics. We shall begin this perspective with a summary of transformation media theory’s application to thermal transport (variously called thermal transformation media, transformation thermodynamics, transformation thermotics, transformation calorics, transforming heat transfer, etc. (this last one being perhaps the most accurate description of the technique)), illustrating its basic operation with a study of the most common devices. An extended discussion of this topic can be found in existing reviews, notably Ref. [3]. We will then discuss the physical implementation of these devices and their limitations. Finally, we shall consider the outlook for thermal metamaterials and potential directions for the field. By selecting different coordinate transformations for J, then, we can find the inhomogeneous, anisotropic forms of |κ ̂| and ρcp that replicate it. Note that the equation for transforming |κ ̂| is always required, whereas for a steady state we can neglect the transformation of ρcp [6]. Experimental demonstration of different thermal metamaterial devices. (a) Cloak. (b) Concentrator. (c) Rotator/inverter. (d) Camouflage: single conducting cylinder appears like two insulating segments. (e) Equivalent temperature profile of camouflage illusion, with two insulating segments actually present and no conducting cylinder. Images from Refs. [7,8]. Another device, which has the opposite function to a cloak, is the concentrator. To create a concentrator, a finite volume r ∈ (0, R) gets shrunk down to r΄ ∈ (0, a), where a < R, concentrating the thermal flux within this smaller region. To maintain continuous contact with the exterior r > R, the region r ∈ (R, b) is stretched to r΄ ∈ (a, b) (see Fig. 1b) [5 ,7]. The most common thermal metamaterial devices, their effects and their underlying coordinate transformations. The most common thermal metamaterial devices, their effects and their underlying coordinate transformations. In addition to these purely radial transformations, azimuthal transformations are also possible. The characteristic example of this is the thermal rotator/inverter, which can effectively change the direction of a heat flux within a domain (see Fig. 1c) [7]. The last principle transformation is camouflage, where the thermal properties are shifted to mimic some other object, possibly with very different properties or a very different shape (see Fig. 1d, e) [8]. Notably, this only shifts the thermal conduction; thermal radiation will follow a different pattern and potentially allow the camouflage to be ignored (similarly, a cloak may be seen through by radiation/convection). These four transformation devices are summarized in Table 1. As mentioned in the initial discussion of the thermal cloak, transformation techniques are unable to change the steady-state temperature distribution. This is actually a more general constraint upon thermal metamaterials than has been previously appreciated: while the magnitude and direction of the heat current can be controlled by these techniques, this only constrains the gradient of the temperature, not its absolute magnitude. The absolute temperature is held fixed by virtue of the thermodynamic definition of temperature: if two objects differ in temperature, then a heat current will exist until they reach the same temperature. To maintain a temperature difference, then, a current between sites x1, x2 must be balanced by another current between x2, x3 (i.e. |Q⃗₁₂+Q⃗₂₃=0|⁠). This implies that the temperature at any point in a domain must be the average of its surroundings at steady state (more formally, this follows from the properties of the Laplacian operator). This implies that any promise of thermal metamaterials for controlling the relative magnitude of a local temperature (rather than its temperature gradient) will be limited to transient effects, not steady state. But since temperature is often more relevant than heat flux for thermal engineering applications, this has presented perhaps the most important limitation to thermal metamaterials: the field still lacks a compelling application. The devices that have been developed (particularly cloaks and camouflage) are adaptations of devices from optics and acoustics, where detection of scattered waves and gradients is more important than controlling the absolute value. Even when heat distributions are relevant for detection, what is detected is typically the thermal radiation, not the thermal conduction. Since controlling thermal conduction does not allow for a change of temperature, this greatly limits the applications here. Thermal inverters and concentrators have more promise, but here too it is unclear what the proper applications are. As these can control the direction and magnitude of heat flux, these devices could potentially have some utility when incorporated into other thermodynamic devices (in particular, engines or refrigerators), but applications here have not been explored. Rather surprisingly, too, these techniques in engineering thermal conduction have not been combined with advances in controlling thermal radiation. As this sort of multiphysics thermal metamaterial would be able to control all of the thermal-coupling pathways, it would give a much firmer control of heat transfer (although here, too, the absolute temperature would be fixed at steady state). Such devices could then be useful in controlling the speed of thermal equilibration (i.e. improved thermal insulation) or in improving the efficiency of heat engines by suitably channeling the heat currents. While there are promising new developments in the field of thermal metamaterials (such as extensions to temperature-dependent materials in thermal transformation media [10] and the incorporation of convection [11] (similar work appears in Ref. [12])), the need for applications is vital to the continued survival of this field. Without a compelling justification to motivate the fabrication of carefully structured metamaterials and arrange them to mimic coordinate transformations, the field risks obscurity or irrelevance.