Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics

Abstract

Nonlinear heat transfer can be exploited to reveal novel transport phenomena and thus enhance people's ability to manipulate heat flux at will. However, there hasn't been a mature discipline called nonlinear thermotics like its counterpart in optics or acoustics to make a systematic summary of relevant researches. In the current review, we focus on recent progress in an important part of nonlinear heat transfer, i.e., tailoring nonlinear thermal devices and metamaterials under the Fourier's law, especially with temperature-dependent thermal conductivities. We will present the basic designing techniques including solving the equation directly and the transformation theory. Tuning nonlinearity coming from multi-physical effects, and how to calculate effective properties of nonlinear conductive composites using the effective medium theory are also included. Based on these theories, researchers have successfully designed various functional materials and devices such as the thermal diodes, thermal transistors, thermal memory elements, energy-free thermostats, and intelligent thermal materials, and some of them have also been realized in experiments. Further, these phenomenological works can provide a feasible route for the development of nonlinear thermotics.

Theory for Thermoelectric Effect Control: Transformation Nonlinear Thermoelectricity

“…Recent advances in metamaterials and metadevices for controlling diffusion systems have witnessed a development tendency of adaptability, adjustability, and integration [1][2][3][4][5]. The nonlinear transformation thermotics [6][7][8], evolving from the linear transformation theory [9-13], provides a definite method to exactly map the diffusive single-field distribution to a required one in temperature-dependent backgrounds.…”

Thermal hysteresis and the heat shuttling effect

“…This thermal dependence generates an asymmetric system response that has been used to manipulate heat flows carried by phonons (phononics) and photons (photonics) in the same manner as the flow of electrons is controlled in electronic circuits. This gave rise to applications both at nanoscale 1 and at macroscopic scale 2 , among them thermal diodes [3][4][5][6] , thermal transistors 1,[7][8][9] , thermal logic gates 10 , thermal memories 11 , and thermal memristors 12,13 . When submitted to temporal modulation, devices supporting nonlinear heat flow may give rise to novel and intriguing phenomena, among them heat shuttling, a net heat current that shows up even in the absence of a mean temperature gradient.…”

Configuration-Induced Directional Nonlinearity Enhancement in Composite Thermal Media

“…By means of nonlinear mechanisms applied in artificial complex systems, various devices or concepts such as transistors, lasers, and artificial intelligence were created, leading to the dramatic revolution in modern science and technology [3][4][5][6]. On the other hand, nonlinearity in macro-scale heat transport systems is lacking study in both theory and applications [7,8], although its counterpart at micro or nano scale has been a significant topic of phononics in the last two decades [9][10][11]. Comparable to the coupling-induced inharmonic interaction in phonon transfer [12], nonlinearity in macro-scale heat diffusion is mainly reflected in the intrinsic response to external fields, for example, thermal conductivity or capacity is varying with temperature [13,14].…”

“…More recently, various design methods have been generalized from linear to nonlinear systems, in which thermal parameters are temperature dependent [24][25][26][27], and lead to a broad category of smart or self-adapting thermal metadevices [28,29]. In particular, composites of artificial architectures can result in a larger value on the coefficient of an effective nonlinear term than building-unit materials, which is usually called nonlinearity enhancement [8]. This effect in random [30], periodic [31], and core-shell [32] structures have been proposed.…”