The discrete-ordinate method using composite quadrature is further extended to the analysis of radiative transfer in a multi-layer medium with Fresnel interfaces. Since the discrete ordinates used in the present method depend on the critical angles at the interfaces and the integral over direction is split into several subintervals by the critical angles, the discrete ordinates for each of the layers may be different. Thus, in general the radiation intensity on a discrete ordinale of one of the layers can not be obtained directly from the intensity on the discrete ordinate of the others. To circumvent the difficulty, the natural cubic spline interpolation is used to approximate the angular distribution of intensity at internal interfaces. The comparisons of the present results and the existing results for some special cases show that the present scheme works well. The effects of refractive indices and scattering albedos on the hemispherical reflectivity and transmissivity of a three-layer medium with Fresnel interfaces are discussed.
|Number of pages||5|
|Journal||Heat and Mass Transfer/Waerme- und Stoffuebertragung|
|Publication status||Published - 1996 Nov|
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Fluid Flow and Transfer Processes