Many-Body Radiative Heat Transfer Theory

In this Letter, an $N$-body theory for the radiative heat exchange in thermally nonequilibrated discrete systems of finite size objects is presented. We report strong exaltation effects of heat flux which can be explained only by taking into account the presence of many-body interactions. Our theory extends the standard Polder and van Hove stochastic formalism used to evaluate heat exchanges between two objects isolated from their environment to a collection of objects in mutual interaction. It gives a natural theoretical framework to investigate the photon heat transport properties of complex systems at the mesoscopic scale.

Figure 1

Normalized HF exchanged between two SiC spherical particles maintained at $T_1=300\mathrm{K}$ (left particle) and $T_2=0\mathrm{K}$ (right particle) with respect to the position $r_3=(x_3,y_3)$ of a third SiC particle of same radius and $T_3=0\mathrm{K}$ for (a) $2l=600\mathrm{nm}$ and (b) $2l=800\mathrm{nm}$. The HF is normalized by the HF exchanged between two isolated dipoles in the same thermal conditions. The dark zone with a negative HF corresponds to the region which cannot be occupied by the third particle. For the sake of clarity, we consider here that all particles are identical (100 nm radius) and their electric polarizability given by the simple Clausius-Mossotti form [39] $\alpha =4\pi R^3\frac{ϵ-1}{ϵ+2}$, $R$ denoting the particles radius. The dielectric permittivity of particle is described by a Drude-Lorentz model.

Figure 2

Normalized HF between two spherical particles of the same radius with respect to the position of a third one, which is equidistant to both particles ($T_1=300\mathrm{K}$, $T_2=T_3=0\mathrm{K}$).

Figure 3

TC between two spherical SiC particles separated by a distance $2l$ (top) and between the same particles when a third SiC particle is located on the mass center of this couple (bottom). All particles have the same radius. The vertical dashed lines marks the distance where the particles are touching [40].