Analysis of radiative transfer in a one-dimensional nonlinear anisotropic scattering medium with space-dependent scattering coefficient using spectral collocation method

2013 ◽  
Vol 67 ◽  
pp. 569-574 ◽  
Author(s):  
Jing Ma ◽  
Ya-Song Sun ◽  
Ben-Wen Li
Keyword(s):  
Radiative Transfer ◽  
Collocation Method ◽  
Anisotropic Scattering ◽  
Spectral Collocation Method ◽  
Scattering Coefficient ◽  
Scattering Medium ◽  
Spectral Collocation ◽  
One Dimensional

Parametric Study of Simultaneous Radiative Transfer in Plane-Parallel Scattering Medium With Variable Refractive Index by Spectral Collocation Method

2013 ◽  
Author(s):  
Jing Ma ◽  
Yasong Sun ◽  
Benwen Li
Keyword(s):  
Refractive Index ◽  
Radiative Transfer ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Scattering Medium ◽  
Spectral Collocation ◽  
Plane Parallel ◽  
Derivative Term ◽  
Scattering Phase Function ◽  
Angular Domains

In this work, a spectral collocation method is developed to simulate radiative transfer in a refractive planar medium. The space and angular domains of radiative intensity are discretized by Chebyshev polynomials, and the angular derivative term and the integral term of radiative transfer equation are approximated by spectral collocation method. The spectral collocation method can provide exponential convergence and obtain high accuracy even using few nodes. There is a very satisfying correspondence between the spectral collocation results and available data in literatures. Influence of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the emissivity of boundary are investigated for the plane-parallel scattering medium with variable refractive index.

Spectral Collocation Method for Transient Combined Radiation and Conduction in an Anisotropic Scattering Slab With Graded Index

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Ya-Song Sun ◽  
Ben-Wen Li
Keyword(s):  
Heat Transfer ◽  
Collocation Method ◽  
Transfer Problem ◽  
Anisotropic Scattering ◽  
Spectral Collocation Method ◽  
Discrete Ordinates ◽  
Spectral Collocation ◽  
Discrete Ordinates Method ◽  
Conduction Heat Transfer ◽  
Graded Index

The spectral collocation method for transient combined radiation and conduction heat transfer in a planar participating medium with spatially variable refractive index is introduced and formulated. The angular dependence of the problem is discretized by discrete ordinates method and the space dependence is expressed by Chebyshev polynomial and discretized by spectral collocation method. Due to the exponential convergence of spectral methods, very high accuracy can be obtained even using a small resolution for present problem. Numerical results in one-dimensional planar slab by Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of various parameters such as the variable thermal conductivity, the scattering albedo, the emissivity of boundary, the conduction-radiation parameter, the optical thickness, and the graded index are studied for absorbing, emitting, and anisotropic scattering medium. The SP-DOM has been found to successfully and efficiently deal with transient combined radiation and conduction heat transfer problem in graded index medium.

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