Effects of graded refractive index on steady and transient heat transfer inside a scattering semitransparent slab

Coupled radiative-conductive heat transfer inside an absorbing-emitting-scattering semitransparent slab is solved. The refractive index of the media is distributed spatially in a linear relationship. The two boundary surfaces are diffuse and opaque. In this paper, the media with graded refractive index is simulated by using multilayer composite model, and in each sub-layer the refractive index is supposed to be constant and the rays of thermal radiation travel in a straight line. The multilayer model is developed by ray-tracing method combined with node analysis. A comparison of the present results with previous results shows that the multilayer simulation of media with graded refractive index is rational and correct. Considering isotropic scattering of thermal radiation, with the changes in the extinction coefficient, surface emissivities and the scattering albedo, the influences of refractive index distribution on the temperature and the radiative heat flux fields are investigated. The results show that the gradient distributing of refractive indexes can cause very different thermal behavior concerned with radiative transfer in semitransparent media compared with constant refractive indexes.