Temperature field inside an absorbing-emitting semi-transparent slab at radiative equilibrium with variable spatial refractive index

The temperature field inside an absorbing-emitting slab of semi-transparent grey medium at radiative equilibrium has been determined with the help of a curved ray-tracing technique when the spatial variation of the refractive index in the medium is assumed to be linear. The integration of the radiative transfer equation has been carried out on the trajectories on which radiation propagates inside the medium, leading to the absorbed radiative energy at an internal point. For a linear refractive index, existence of totally reflected internal trajectories producing mirage effects have to be taken into account in the resolution of the radiative problem. Results obtained for different optical depths with low and strong gradients of refractive index display significant differences from the case of a constant refractive index. (C) 2000 Elsevier Science Ltd. All rights reserved.