Transient coupled radiative–conductive heat transfer in a gray planar medium with anisotropic scattering

Transient radiative and conductive heat transfer in an absorbing, emitting and anisotropically scattering gray slab is investigated. The medium is confined within parallel walls and is excited by a heat pulse stimulation on the front face. The phase function corresponds to a second-degree anisotropic scattering and includes isotropic, linearly anisotropic and Rayleigh modes of scattering. The semi-analytical approach, based on the kernel substitution consists in obtaining a differential equation for the temperature field instead of the natural integro-differential energy equation. A matrix formulation of the solution is proposed. It allows very small resulting computation times and permits to investigate the effects of anisotropic scattering on the thermal behaviour of the semi-transparent medium.