Negative Thermal Transport in Conduction and Advection

Abstract

Negative refractive index has drawn a great deal of attention due to its unique properties and practical applications in wave systems. To promote the related physics in thermotics, here we manage to coin a complex thermal conductivity whose imaginary part corresponds to the real part of complex refractive index. Therefore, the thermal counterpart of negative refractive index is just negative imaginary thermal conductivity, which is featured by the opposite directions of energy flow and wave vector in thermal conduction and advection, thus called negative thermal transport herein. To avoid violating causality, we design an open system with energy exchange and explore three different cases to reveal negative thermal transport. We further provide experimental suggestions with a solid ring structure. All finite-element simulations agree with theoretical analyses, indicating that negative thermal transport is physically feasible. These results have potential applications such as designing the inverse Doppler effect in thermal conduction and advection.

Theory for Thermal Wave Control: Transformation Complex Thermotics

“…To solve the problem, we resort to a complex thermal conductivity κ = σ + iτ , where σ and τ are two real numbers [4]. The κ can be well understood with the complex plane shown in Fig.…”

“…where ρ, C, κ, T , and t are density, heat capacity, complex thermal conductivity, temperature, and time, respectively. The complex thermal conductivity κ can be expressed as [4]…”

“…Recently, transformation theories have been proposed to control conduction and advection simultaneously, yielding practical applications such as cloaking, concentrating, and rotating [1][2][3]. These theories apply to constant-temperature boundary conditions but are not necessarily appropriate for periodic boundary conditions supporting thermal waves.To solve the problem, we resort to a complex thermal conductivity κ = σ + iτ , where σ and τ are two real numbers [4]. The κ can be well understood with the complex plane shown in Fig.…”

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

“…It's interesting that designing nonlinear thermal elements in these systems would turn back to the nonlinear lattices models but in a continuum. Recently, wave-like temperature profile in convection (advection-conduction) systems is drawing people's attention [71,[288][289][290][291]. In addition to breaking the reciprocity [71], physics related to exceptional degeneracies like anti-parity-time (APT) symmetry breaking [288,289] have also been revealed in linear equations.…”

Thermal Metamaterial: Fundamental, Application, and Outlook

“…Thus, unique features in wave systems can be transferred to thermal conduction-convection systems by the introduced gain and loss. They successively proposed many counterparts of wave systems in thermal conduction-convection systems such as transformation complex thermotics ( Xu and Huang, 2020c ), negative thermal transport ( Xu and Huang, 2020d ), and thermal convection-diffusion crystal ( Xu and Huang, 2020e ) for modulating wave-like temperature profiles. It is expectable that more exciting phenomena can be predicted in thermotics with thermal conduction-convection systems.…”