Dynamical behaviour of a far-field radiative thermal transistor

Heat flux management have never been efficiently realized by the use of components that can guide, amplify or modulate radiative thermal transfer. In order to pave the way to thermal logical circuits and heat management, we study the dynamical behaviour of such theoretically conceptualized components. Using recent proposals of thermal diodes and transistors, we aim to numerically simulate their thermal behaviour in order to describe their dynamical thermal properties. We determine a cutoff frequency delimiting the domain where functions like amplification and modulation can be obtained. Considering phase-changing VO₂, we applied a Bruggeman modelling to get its dielectric permittivity according to its temperature. Integrating the heat equation over angle of emission and wavelength, we obtain the heat flux between VO₂ and blackbody semi-infinite planes according to their temperatures. Then we set these calculations aside a modelling of the specific heat of a VO₂ layer into a numerical simulation over time. By varying the input frequency and amplitude we measured the output amplitude. The cutoff frequency of the thermal transistor is below 0.1 mHz for a layer thickness of 1 mm. That frequency would vary inversely proportional to the thickness of the layer. Amplification ratio would be around 12 for input amplitudes of 1 W.m^-2 and below, and would decrease as the amplitude increases.