Radiative-conductive heat transfer in protective coatings with scattering and graded index

A numerical study on radiative-conductive heat transfer in the protective coatings and the walls of a parallel-plate enclosure is performed. Some of the protective coatings, such as ceramics, are semitransparent and are applied in high-temperature situations where radiation effects are significant. The energy equations and the radiative transfer equations are solved by using the finite difference method and the discrete ordinates method to obtain the temperature distributions in the coatings and the opaque walls under various heating conditions. The results show that the temperature distribution is more uniform in the interior portion of each coating away from its boundary for the case with a larger average of variable refractive index and the overall effects of refractive index gradients on temperature distributions are not pronounced. Besides, the radiative heat transfer between the coatings decreases with the increase of the scattering albedo.