Two Methods for Solving Radiative Transfer in a Two-Dimensional Graded-Index Medium

Two methods are presented for the study of radiative heat transfer in a two-dimensional graded-index semitransparent medium. One is a combination of the cell model and the ray-tracing technique, and the other is a combination of the linear refractive-index cell model and the discrete curved-ray-tracing technique. The medium is discretized into many cells. The constant-refractive-index assumption is used in the first model and the linear approximation of refractive index is used in the second model. We have compared the results and the calculation efficiency of these two methods, as well as the heat transfer at radiative equilibrium. The results of the two methods show little difference. We also studied the radiative heat transfer properties of the medium, and the results show that the refractive-index distribution has great influence on the temperature field. That is, the medium with various types of graded index has a higher or lower temperature than the medium with a constant refractive index. The medium also has a flat temperature field or a sharper temperature field than the constant-refractive-index medium. This is due to internal total reflection in the graded-index medium.