Solution of radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and diffuse gray boundaries

On the basis of medium discretization and local linear approximation of refractive index distribution, the curved ray tracing technique is used in combination with the pseudo source adding method to numerically solve the radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and two diffuse gray walls. The radiative equilibrium temperature field of a linear refractive index distribution is evaluated by this method and the results show excellent agreement with that of the previous research. For two types of sinusoidal refractive index distributions, the radiative equilibrium temperature field as well as the temperature and heat flux fields of coupled radiation-conduction are investigated in detail. The results show considerable significance of the gradient refractive index effect, and some important conclusions are to be obtained.