Time-dependent radiative transfer through thin films: Chapman-Enskog-maximum entropy method

Approximate solutions to the time-dependent radiative transfer equation, also called the phonon radiative transfer equation, for a plane-parallel system have been obtained by combining the flux-limited Chapman-Enskog approximation with the maximum entropy method. For problems involving heat transfer at small scales (short times and/or thin films), the results found by this combined approach are closer to the outcome of the more labour-intensive Laguerre-Galerkin technique (a moment method described recently by the authors) than the results obtained by using the diffusion equation (Fourier's law) or the telegraph equation (Cattaneo's law). The results for heat flux and temperature are presented in graphical form for xL = 0.01, 0.1, 1 and 10, and at τ = 0.01, 0.1, 1.0 and 10, where xL is the film thickness in mean free paths, and τ is the value of time in mean free times