Lattice Boltzmann approach for near-field thermal radiation

The lattice Boltzmann (LB) approach is presented for the near-field thermal radiation (including the contributions of the propagating and evanescent waves). The radiative transfer equations in the medium and on the interface are derived for the propagating and evanescent waves from the Maxwell equations, respectively. The Chapman-Enskog analysis is adopted to derive the LB model to recover the radiative transfer equation. The scattering parameter coefficient η is proposed to demonstrate the wave behavior of photons on the interface between medium and vacuum. The numerical tests are implemented to solve the near-field radiative heat transfer between two slabs by using the proposed LB approach. The accuracy of the LB model can be improved by increasing the resolution of the wave-number space. By comparing with the benchmark of analytical solutions, the proposed numerical approach enables computing the near-field thermal radiation with good accuracy and exhibits promising applications in dealing with complicated near-field thermal radiation processes.

Figure 1

Schematic profile of the interface between medium and vacuum.

Figure 2

Schematic profile of the D1Q2 lattice model in the proposed LB approach.

Figure 3

Schematic sketch of the structure in the numerical simulation.

Figure 4

(a) TM mode propagating wave of the near-field thermal radiation. (b) TM mode evanescent wave of the near-field thermal radiation. (c) TE mode propagating wave of the near-field thermal radiation. (d) TE mode evanescent wave of the near-field thermal radiation.

Figure 5

The results of the TM mode evanescent waves by using the refined resolutions for the wave-number space in the simulations.