Abstract: A numerical study on the heat transfer in the thermal
barrier coatings and the substrates of a parallel-plate enclosure is
carried out. Some of the thermal barrier coatings, such as ceramics, are
semitransparent and are of interest for high-temperature applications
where radiation effects are significant. The radiative transfer equations
and the energy equations are solved by using the discrete ordinates
method and the finite difference method. Illustrative results are
presented for 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
varying refractive index and a positive gradient of refractive index
enhances radiative transfer to the substrates.