Temperature Trapping: Energy-Free Maintenance of Constant Temperatures as Ambient Temperature Gradients Change

Analytical realization of complex thermal meta-devices

Fourier's law dictates that heat flows from warm to cold. Nevertheless, devices can be tailored to cloak obstacles or even reverse the heat flow. Mathematical transformation yields closed-form equations for graded, highly anisotropic thermal metamaterial distributions needed for obtaining such functionalities. For simple geometries, devices can be realized by regular conductor distributions; however, for complex geometries, physical realizations have so far been challenging, and sub-optimal solutions have been obtained by expensive numerical approaches. Here we suggest a straightforward and highly efficient analytical de-homogenization approach that uses optimal multi-rank laminates to provide closed-form solutions for any imaginable thermal manipulation device. We create thermal cloaks, rotators, and concentrators in complex domains with close-to-optimal performance and esthetic elegance. The devices are fabricated using metal 3D printing, and their omnidirectional thermal functionalities are investigated numerically and validated experimentally. The analytical approach enables next-generation free-form thermal meta-devices with efficient synthesis, near-optimal performance, and concise patterns.

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

Deep Learning-Assisted Active Metamaterials with Heat-Enhanced Thermal Transport

Heat management is crucial for state-of-the-art applications such as passive radiative cooling, thermally adjustable wearables, and camouflage systems. Their adaptive versions, to cater to varied requirements, lean on the potential of adaptive metamaterials. Existing efforts, however, feature with highly anisotropic parameters, narrow working-temperature ranges, and the need for manual intervention, which remain long-term and tricky obstacles for the most advanced self-adaptive metamaterials. To surmount these barriers, heat-enhanced thermal diffusion metamaterials powered by deep learning is introduced. Such active metamaterials can automatically sense ambient temperatures and swiftly, as well as continuously, adjust their thermal functions with a high degree of tunability. They maintain robust thermal performance even when external thermal fields change direction, and both simulations and experiments demonstrate exceptional results. Furthermore, two metadevices with on-demand adaptability, performing distinctive features with isotropic materials, wide working temperatures, and spontaneous response are designed. This work offers a framework for the design of intelligent thermal diffusion metamaterials and can be expanded to other diffusion fields, adapting to increasingly complex and dynamic environments.

Adaptive multi-temperature control for transport and storage containers enabled by phase-change materials

The transportation of essential items, such as food and vaccines, often requires adaptive multi-temperature control to maintain high safety and efficiency. While existing methods utilizing phase change materials have shown promise, challenges related to heat transfer and materials' physicochemical properties remain. In this study, we present an adaptive multi-temperature control system using liquid-solid phase transitions to achieve highly effective thermal management using a pair of heat and cold sources. By leveraging the properties of stearic acid and distilled water, we fabricated a multi-temperature maintenance container and demonstrated temperature variations of only 0.14-2.05% over a two-hour period, underscoring the efficacy of our approach. Our findings offer a practical solution to address critical challenges in reliable transportation of goods, with potential implications for various fields in physical, engineering, and life sciences.

Thermal Willis Coupling in Spatiotemporal Diffusive Metamaterials

Willis coupling generically stems from bianisotropy or chirality in wave systems. Nevertheless, those schemes are naturally unavailable in diffusion systems described by a single constitutive relation governed by the Fourier law. Here, we report spatiotemporal diffusive metamaterials by modulating thermal conductivity and mass density in heat transfer. The Fourier law should be modified after homogenizing spatiotemporal parameters, featuring thermal Willis coupling between heat flux and temperature change rate. Thermal Willis coupling drives asymmetric heat diffusion, and the diffusion direction is reversible at a critical point determined by the degree of spatiotemporal modulation. Moreover, thermal Willis coupling stands robustly even when only thermal conductivity is modulated. These results may have potential applications for directional diffusion and offer insights into asymmetric manipulation of nonequilibrium mass and energy transfer.

Nonlinear thermal responses in geometrically anisotropic metamaterials

Nonlinear metamaterials have great potential in heat management, which has aroused intensive research interest in both theory and application, especially for their response to surroundings. However, most existing works focus on geometrically isotropic (circular) structures, limiting the potential versatile functionalities. On the other hand, anisotropy in architecture promisingly offers an additional degree of freedom in modulating directional heat transfer. Here, we investigate nonlinear composition effects in geometrically anisotropic (confocal elliptical) thermal medium under the framework of effective medium approximation, and deduce a series of general formulas for quantitatively predicting nonlinearity enhancement. Enhancement coefficients are analytically derived by the Taylor expansion method in different nonlinearity cases. In particular, we find that some coupling conditions can greatly promote the nonlinear modulation coefficients, introducing stronger enhancement beyond isotropic construction. Our theoretical predictions are verified by finite-element simulation, and feasible experimental suggestions are also given. For extending these results to practical scenes, two intelligent thermal metadevices are designed in proof of concept and demonstrated by numerical simulation. Our works provide a unified theory for anisotropic nonlinear thermal metamaterial design and may benefit flexible applications in self-adaptive thermal management, such as switchable cloaks, concentrators, or macroscopic thermal diodes.

Heat transfer control using a thermal analogue of coherent perfect absorption

Recent investigations on non-Hermitian physics have unlocked new possibilities to manipulate wave scattering on lossy materials. Coherent perfect absorption is such an effect that enables all-light control by incorporating a suitable amount of loss. On the other hand, controlling heat transfer with heat may empower a distinct paradigm other than using thermal metamaterials. However, since heat neither propagates nor carries any momentum, almost all concepts in wave scattering are ill-defined for steady-state heat diffusion, making it formidable to understand or utilize any coherent effect. Here, we establish a scattering theory for heat diffusion by introducing an imitated momentum for thermal fields. The thermal analogue of coherent perfect absorption is thus predicted and demonstrated as the perfect absorption of exergy fluxes and undisturbed temperature fields. Unlike its photonic counterpart, thermal coherent perfect absorption can be realized for regular thermal materials, and be generalized for various objects.

A thermal analogue of coherent perfect absorption would allow to control heat transfer using heat, but the lack of momentum propagation in a thermal field seems to prevent any role for coherence. Here, the authors allow this by introducing an imitated momentum for steady-state heat diffusion.

Passive Ultra-Conductive Thermal Metamaterials

Ultra-conductive heat transport showcases significant potentials in popular thermal managements with convection, phase change, and heat source. However, it is captivated impossible for passive thermal manipulation, usually bounded by intrinsic thermal conductivities of natural materials, to outperform these active recipes in need of extra energy payload. Here, a robust recipe to create passive ultra-conductive thermal metamaterials consisting of nothing but bulk natural materials is reported. Thanks to the local thermal resistance regulation by vertical thermal transport channel, the proof-of-concept thermal metamaterials experimentally demonstrate extreme effective conductivity (1915 W m^-1  K^-1 ) solely with naturally occurring materials. The purely conductive modulation without any external energy is comparable to active counterparts, and further reveals its robustness and unexpected convenience. The findings construct a high-efficient paradigm of passive thermal management with ultra-conductive heat transport, and further hint potentials in other Laplace fields, e.g., DC and magnetostatics.

Reciprocity of thermal diffusion in time-modulated systems

The reciprocity principle governs the symmetry in transmission of electromagnetic and acoustic waves, as well as the diffusion of heat between two points in space, with important consequences for thermal management and energy harvesting. There has been significant recent interest in materials with time-modulated properties, which have been shown to efficiently break reciprocity for light, sound, and even charge diffusion. However, time modulation may not be a plausible approach to break thermal reciprocity, in contrast to the usual perception. We establish a theoretical framework to accurately describe the behavior of diffusive processes under time modulation, and prove that thermal reciprocity in dynamic materials is generally preserved by the continuity equation, unless some external bias or special material is considered. We then experimentally demonstrate reciprocal heat transfer in a time-modulated device. Our findings correct previous misconceptions regarding reciprocity breaking for thermal diffusion, revealing the generality of symmetry constraints in heat transfer, and clarifying its differences from other transport processes in what concerns the principles of reciprocity and microscopic reversibility.

Path-Dependent Thermal Metadevice beyond Janus Functionalities

Janus metamaterials, metasurfaces, and monolayers have received intensive attention in nanophotonics and 2D materials. Their core concept is to introduce asymmetry along the wave propagation direction, by stacking different materials or layers of meta-atoms, or breaking out-of-plane mirror asymmetry with external biases. Nevertheless, it has been hitherto elusive to realize a diffusive Janus metadevice, since scalar diffusion systems such as heat conduction normally operate in the absence of polarization control, spin manipulation, or electric-field stimuli, which all are widely used in achieving optical Janus devices. It is even more challenging, if not impossible, for a single diffusive metadevice to exhibit more than two thermal functions. Here a path-dependent thermal metadevice beyond Janus characteristics is proposed, which can exhibit three distinct thermal behaviors (cloaking, concentrating, and transparency) under different directions of heat flow. The rotation transformation mechanism of thermal conductivity provides a robust platform to assign a specific thermal behavior in any direction. The proof-of-concept experiment of anisotropic in-plane conduction successfully validates such a path-dependent trifunction thermal metamaterial device. It is anticipated that this path-dependent strategy can provide a new dimension for multifunctional metamaterial devices in the thermal field, as well as for a more general diffusion process.

Thermal Metamaterial: Fundamental, Application, and Outlook

Thermal metamaterials have amazing properties in heat transfer beyond naturally occurring materials owing to their well-designed artificial structures. The idea of thermal metamaterial has completely subverted the design of thermal functional devices and makes it possible to manipulate heat flow at will. In this perspective, we review the up-to-date progress of thermal metamaterials starting from 2008. We focus on both the key theoretical fundamentals and techniques for applications and give a perspective of scale-based classification on thermal metamaterials' theories and applications. We also discuss the junction between macroscale and microscale design methods and propose some prospects for the future trend of this field.

Thermal-rectification coefficients in solid-state thermal rectifiers

The thermal rectifier is an analog of the electrical rectifier, in which heat flux in a forward direction is larger than that in the reverse direction. Owing to the controllability of the heat flux, the solid-state thermal rectifier is promising from both theoretical and applicational points of view. In this paper, we examine analytical expressions of thermal-rectification coefficients R for thermal rectifiers with typical linear and nonlinear model functions as nonuniform thermal conductivities against temperature T. For the thermal rectifier with linear (quadratic) temperature-dependent thermal conductivity, a maximum value of R is calculated to be 3 (≃14). With use of a structural-phase-transition material, a maximum value of R is found to ideally reach to κ_{2}/κ_{1}, where κ_{1} (κ_{2}) is the minimum (maximum) value of its κ(T). Values of R for the thermal rectifiers with an inverse T-dependent function and an exponential function of κ are also analytically examined.

A Continuously Tunable Solid-Like Convective Thermal Metadevice on the Reciprocal Line

The emerging thermal metamaterials and metadevices demonstrate significant potential to transform thermal conduction. However, the thermal conductivities of existing devices are all restricted at fixed values if the configuration or constituent materials are static. Thermal convection provides an additional tool to boost and flexibly modify the heat transfer in moving matter, but it is essentially distinct from thermal conduction since the Onsager reciprocity is generally broken in the former but preserved in the latter. Therefore, it is difficult to use convective components for sophisticated control of conductive heat. Here, it is shown that a convective system can be made undistinguishable from a conductive one in principle, by discovering and operating on the reciprocal line of mechanically rotating systems. The realized thermal metadevice can thus mimic a solid-like material whose thermal conductivity dynamically covers a wide range. It offers great possibilities of real-time smooth control over heat transfer for broad applications.

Designing bistability or multistability in macroscopic diffusive systems

We theoretically design a kind of diffusion bistability (and even multistability) in the macroscopic scale, which has a similar phenomenon but different underlying mechanism from its microscopic counterpart [Phys. Rev. Lett. 101, 267203 (2008)10.1103/PhysRevLett.101.267203]; the latter has been extensively investigated in literature, e.g., for building nanometer-scale memory components. By introducing second- and third-order nonlinear terms (that opposite in sign) into diffusion coefficient matrices, a bistable energy or mass diffusion occurs with two different steady states identified as "0" and "1." In particular, we study heat conduction in a two-terminal three-body system and show that this bistable system exhibits a macroscale thermal memory effect with tailored nonlinear thermal conductivities. The theoretical analysis is confirmed by finite-element simulations. Also, we suggest experiments with metamaterials based on shape memory alloys. This theoretical framework blazes a trail on constructing intrinsic bistability or multistability in diffusive systems for macroscopic energy or mass management.

Multi-Physics Bi-Functional Intelligent Meta-Device Based on the Shape Memory Alloys

Transformation theory, succeeding in multiple transportation systems, has enlightened researchers to manipulate the field distribution by tailoring the medium’s dominant parameters in certain situations. Therefore, the science community has witnessed a boom in designing metamaterials, whose abnormal properties are induced by artificial structures rather than the components’ characteristics. However, a majority of such meta-devices are restricted to the particular physical regimes and cannot sense the changes taking place in the surrounding environment and adjust its functions accordingly. In this article we propose a multi-physics bi-functional “intelligent” meta-device which can switch its functions between an invisible cloak and a concentrator in both thermal and DC electric conduction as the ambient temperature or voltage varies. The shape memory alloys are utilized in the design to form a moveable part, which plays the crucial role in the switching effect. This work paves the way for a practicable method for obtaining a controllable gradient of heat or electric potential, and also provides guidance for efficiently designing similar intelligent meta-devices by referring to the intriguing property of shape memory alloys.

Ion Write Microthermotics: Programing Thermal Metamaterials at the Microscale

Considerable advances in manipulating heat flow in solids have been made through the innovation of artificial thermal structures such as thermal diodes, camouflages, and cloaks. Such thermal devices can be readily constructed only at the macroscale by mechanically assembling different materials with distinct values of thermal conductivity. Here, we extend these concepts to the microscale by demonstrating a monolithic material structure on which nearly arbitrary microscale thermal metamaterial patterns can be written and programmed. It is based on a single, suspended silicon membrane whose thermal conductivity is locally, continuously, and reversibly engineered over a wide range (between 2 and 65 W/m·K) and with fine spatial resolution (10-100 nm) by focused ion irradiation. Our thermal cloak demonstration shows how ion-write microthermotics can be used as a lithography-free platform to create thermal metamaterials that control heat flow at the microscale.

Encrypted Thermal Printing with Regionalization Transformation

Artificially structured thermal metamaterials provide an unprecedented possibility of molding heat flow that is drastically distinct from the conventional heat diffusion in naturally conductive materials. The Laplacian nature of heat conduction makes the transformation thermotics, as a design principle for thermal metadevices, compatible with transformation optics. Various functional thermal devices, such as thermal cloaks, concentrators, and rotators, have been successfully demonstrated. How far can it possible go beyond just realizing a heat-distribution function in a thermal metadevice? Herein, the concept of encrypted thermal printing is proposed and experimentally validated, which could conceal encrypted information under natural light and present static or dynamic messages in an infrared image. Regionalization transformation is developed for structuring thermal metamaterial-strokes as infrared signatures, enabling letters of the alphabet to be written, paintings to be drawn, movies to be made, and information to be displayed. This strategy successfully demonstrates an extreme level of manipulation of heat flow for encryption, illusions, and messaging.

Metathermotics: Nonlinear thermal responses of core-shell metamaterials

Thermal metamaterials based on core-shell structures have aroused wide research interest, e.g., in thermal cloaks. However, almost all the relevant studies only discuss linear materials whose thermal conductivities are temperature-independent constants. Nonlinear materials (whose thermal conductivities depend on temperatures) have seldom been touched; however, they are important in practical applications. This situation largely results from the lack of a general theoretical framework for handling such nonlinear problems. Here we study the nonlinear responses of thermal metamaterials with a core-shell structure in two or three dimensions. By calculating the effective thermal conductivity, we derive the nonlinear modulation of a nonlinear core. Furthermore, we reveal two thermal coupling conditions, under which this nonlinear modulation can be efficiently manipulated. In particular, we reveal the phenomenon of nonlinearity enhancement. Then this theory helps us to design a kind of intelligent thermal transparency devices, which can respond to the direction of thermal fields. The theoretical results and finite-element simulations agree well with each other. This work not only offers a different mechanism to achieve nonlinearity modulation and enhancement in thermotics, but also suggests potential applications in thermal management, including illusion.

Realization of a thermal cloak-concentrator using a metamaterial transformer

By combining rotating squares with auxetic properties, we developed a metamaterial transformer 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 configuration is transformed. We established that the proposed dual-functional metamaterial can either thermally protect a region (cloak) or focus heat flux in a small region (concentrator). The dual functionality was verified by finite element simulations and validated by experiments with a specimen composed of copper, epoxy, and rotating squares. This work provides an effective and efficient 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.

Theory of transformation thermal convection for creeping flow in porous media: Cloaking, concentrating, and camouflage

Heat can transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has seldom been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop a theory of transformation thermal convection by considering the convection-diffusion equation, the equation of continuity, and the Darcy law. By introducing porous media, we get a set of equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite-element simulations confirm the theoretical findings. This work offers a transformation theory for thermal convection, thus revealing novel behaviors associated with potential applications; it not only provides different hints on how to control heat transfer by combining thermal conduction, thermal convection, and thermal radiation, but also benefits mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time.

Structured thermal surface for radiative camouflage

Thermal camouflage has been successful in the conductive regime, where thermal metamaterials embedded in a conductive system can manipulate heat conduction inside the bulk. Most reported approaches are background-dependent and not applicable to radiative heat emitted from the surface of the system. A coating with engineered emissivity is one option for radiative camouflage, but only when the background has uniform temperature. Here, we propose a strategy for radiative camouflage of external objects on a given background using a structured thermal surface. The device is non-invasive and restores arbitrary background temperature distributions on its top. For many practical candidates of the background material with similar emissivity as the device, the object can thereby be radiatively concealed without a priori knowledge of the host conductivity and temperature. We expect this strategy to meet the demands of anti-detection and thermal radiation manipulation in complex unknown environments and to inspire developments in phononic and photonic thermotronics.

Thermal camouflaging techniques typically use bulky structures and require a well-defined and unchanging background. Here, the authors propose a strategy for thermal camouflage using a structured thermal surface, independent of the background material for many practical situations.