On the diffusion approximation for radiation transfer in glass

Abstract

The paper examines the validity of the diffusion approximation for radiative transfer in semitransparent materials. As an example, heat transfer by combined conduction and radiation is analyzed in a plane layer of material bounded by an opaque substrate and free space. The layer is heated radiatively and convectively. The radiation transfer problem is formulated rigorously as well as using a diffusion approximation for radiative transfer. As an example, numerical results are obtained for container glass and are used to establish the range of validity of the diffusion approximations. For small thickness (L = 0,1 m) of the layer the diffusion approximation underpredicts the temperature levels and temperature gradients at the cooled boundary. For large physical thicknesses (L = 1 m) the diffusion approximation yields reasonable predictions for the temperature distribution near the cooled boundary but overpredicts the temperature gradients near the heated boundary. The diffusion and modified diffusion approximations overpredict the heat transfer rate across the layer.