Hyperbolic Conduction–Radiation in Participating and Inhomogeneous Slab With Double Spherical Harmonics and Lattice Boltzmann Methods

Abstract

This work deals with the combined mode of non-Fourier conduction and radiation transfer in isotropically/anisotropically scattering, homogeneous, and inhomogeneous planar media with reflective boundaries subjected to the constant internal temperature of the medium and the externally isotropic diffuse incidence at one boundary. An analytical double spherical harmonics method (DPN) is proposed to solve the radiative problem. The non-Fourier conduction is described with the Cattaneo–Vernotte model, and the governing hyperbolic energy equation is solved using the lattice Boltzmann method (LBM). For radiative problems through the layer/layered media, the radiative heat fluxes, hemispherical radiative intensities, transmissivity, and reflectivity are found, while for coupled conduction and radiation, the temperature distributions are found for various optical thicknesses, space-dependent scattering albedo, conduction–radiation parameters, and boundary reflectivities. Results of the present work are in excellent agreement with those available in the literature. Moreover, these results demonstrate that the proposed analytical double spherical method is an efficient, robust, and accurate method for radiative transfer through inhomogeneous layer/layered planar media analysis. Furthermore, it is observed that space-dependent scattering albedo and boundary reflectivities have a very significant effect in the hyperbolic sharp wave front of non-Fourier conduction.