Thermal metamaterials: From static to dynamic heat manipulation

Static and dynamic metamaterials have been extensively studied for their ability to manipulate different physical fields and directed to broad applications. Because the governing equations of heat transfer consist of nonlinear terms with conservation of mass, momentum and energy, the equations can exhibit elliptical, parabolic, hyperbolic and hybrid configurations under different transfer modes. Such multi-mode transfer characteristics intrinsically make thermal metamaterials distinguish themselves from other metamaterials with unique static and dynamic manipulation mechanisms. Therefore, numerous studies have emerged that use the transformation theory and other methods to control static thermal metamaterials. It leads to the development of thermal cloaks, thermal concentrators, thermal diodes, and so on. Originating from the static style, the manipulation of heat transfer has expanded to dynamic systems in recent years. The introduction of hydrodynamics in metamaterial design leads to numerous novel physics effects, such as dynamic cloaking, zero-drag characteristics, topological heat transfer, nonreciprocal diffusion, and non-Hermitian physics. Moreover, the dynamic thermal metamaterials allow accurate control at both time and space dimensions, leading to exciting applications such as adjustable, reconfigurable, and intelligent thermal meta-devices. However, few studies have systematically analyzed thermal metamaterials from the perspective of static and dynamic manipulation. In this review, we aim at clarifying the connection and distinction of static and dynamic manipulation from the scopes of principle, application, and physical effects. We start with the development of static thermal metamaterials and its application. Subsequently, the development of dynamic thermal metamaterials is presented both in fundamental theory and application. Finally, we summarize the research directions and prospect future research challenges for static and dynamic thermal metamaterials.