Radiation equilibrium temperature field in a gradient index medium with specular surfaces

The radiation equilibrium temperature field in a gradient index semitransparent absorbing-emitting gray medium is analyzed. The medium is bounded by two semitransparent specular surfaces and possesses a refractive index varying spatially or dependent on temperature. By discretizing the medium into many sublayers and adopting a linear refractive index approximation for each sublayer, the curved ray tracing technique is developed to solve the radiation transfer in medium. The temperature field at radiation equilibrium is obtained based on the energy conservation. The influences of refractive index distribution and optical thickness on the temperature field as well as the coupled effect of temperature and refractive index are examined. The results display the significant influences of gradient index on radiation transfer and the temperature distribution.