Transient radiative heat transfer in an inhomogeneous participating medium with Fresnel's surfaces

This paper studies the radiative heat transfer within an inhomogeneous and isotropically scattering medium with reflecting Fresnel's surfaces. Thermal radiation transfers in a curve inside a medium with an inhomogeneous distribution of a refractive index. The inhomogenous medium is divided into n homogenous isothermal sub-layers and in each sub-layer the radiation transfers in a straight line. By adopting a multilayer radiative transfer model and using a ray-tracing/nodal-analyzing method, a radiative transfer model is built for the inhomogenous participating medium. In the multilayer model, a criterion for refraction / total reflection at the interfaces between neighboring sub-layers is introduced, avoiding the integral singularity and reflection at physically inexistent interfaces (only the total reflection is considered). Transient thermal behavior is examined when the parameters of the radiative properties such as refractive indexes, extinction coefficients, and single-scattering albedoes vary continually along the thickness direction.