Refractive index effects on radiative behavior of a heated absorbing-emitting layer

Temperature distributions and other heat transfer characteristics are analyzed for a heated plane layer of semitransparent material with refractive index >1. The analysis includes heat conduction, emission, and absorption within the layer. The layer has diffuse interfaces; examples are a frosted quartz window used to diffuse incident radiation in high temperature surroundings, or a ceramic layer with small scattering used in hightemperature applications. Each side of the layer is heated by radiation and convection, and interface reflections are included. When the index of refraction is larger than unity, there are total internal reflections of some of the energy within the layer. This has a substantial effect on distributing energy across the layer, and considerably alters the temperature distribution from when the refractive index is unity. Results are given for a gray layer and for a two-band spectral variation of the absorption coefficient. Radiant energy leaving the surface was examined to determine when it could be used to measure surface temperature accurately.