Ray-Tracing/Nodal-Analyzing Model for Transient Thermal Behavior of a Scattering Medium with a Variable Refractive Index

ABSTRACT

Transient combined radiation-conduction inside a semitransparent scattering gray medium with a graded index is examined. By nodal analysis, the radiative source term of the energy equation is deduced through radiative transfer coefficients (RTCs), which are deduced through a multilayer model of radiative transfer, established by employing a ray-tracing method based on the zonal method. The basic idea is that a medium with a continually variable refractive index is discretized into certain number of isothermal sublayers with constant refractive index in each sublayer and the radiative transfer in a curve inside the graded index medium is regarded as that in a straight line within each sublayer. The present results accord very well with previous results. The results show that the multilayer model for radiative transfer to simulate the radiative transfer in a graded refractive index medium is reliable and correct. In addition, effects of convection boundary conditions, scattering albedo, opaque surface emission, and refractive index distribution on transient thermal behavior are also investigated for the graded index medium.

This research is supported by the key project of the National Natural Science Foundation of China (Grant 50336010), and the China National Key Basic Research Special Funds (Grant 2003CB214500). The authors are indebted to them for their financial support.