Temperature field of radiative equilibrium in a semitransparent slab with a linear refractive index and gray walls

The temperature field in a semitransparent slab of absorbing-emitting gray medium at radiative equilibrium is solved in this paper. The medium has a linear refractive index and the two boundaries are diffuse gray walls. A curved ray tracing technique is combined with a pseudo-source adding method to deduce the radiative intensities on the gray walls. And on the basis of the previous work done by Ben Abdallah and Le Dez, the discrete temperature field in the slab is deduced. The influences of refractive index distribution, boundary wall emissivities and optical thickness on the radiative equilibrium temperature field are examined. The results display the significant influences of the refractive index distribution and the boundary wall emissivities.