A Finite-Element Model for the Thermal Radiative Properties of Graded Index Fiber Coated with Thin Absorbing Film

Abstract

A finite-element model in combination with the wave optical approach is developed based on the radiative transfer equation for graded index medium in cylindrical coordinate system to predict the total hemispherical thermal radiative properties of semitransparent graded index fiber coated with thin absorbing film. The film is made of a strong absorbing medium with thickness less than or on the order of the wavelength of peak magnitude of thermal radiation. Radiative absorptance of the fiber-film system is directly obtained by solving the radiation deposited in the system. Radiative transfer in the fiber is solved by a least squares finite-element method, while radiative transfer in the thin film is treated through wave optics, and the film is formulated as a special kind of semitransparent boundary condition for the fiber medium. The results obtained by the finite-element model for uniform index fiber are in good agreement with the results in the literature obtained through the ray tracing model. The effects of fiber refractive index distribution on predicted thermal radiative properties are investigated. For the fiber with or without film, the variation of refractive index distribution has a substantial influence on the effective emittance.

The support of this work by the National Nature Science Foundation of China (50836002, 50620120442) is gratefully acknowledged.