RADIATIVE TRANSFER IN AN ABSORBING AND ANISOTROPICALLY SCATTERING SLAB WITH REFLECTING BOUNDARIES: THE NON -AZIMUTHALLY SYMMETRIC CASE

1982 ◽  
Author(s):  
P. Vestrucci ◽  
G. Spiga ◽  
F. Santarelli ◽  
C. Stramigioli
Keyword(s):  
Radiative Transfer ◽  
Symmetric Case ◽  
Reflecting Boundaries

An Iterative Solution for Anisotropic Radiative Transfer in a Slab

1979 ◽  
Vol 101 (4) ◽  
pp. 695-698 ◽  
Author(s):  
W. H. Sutton ◽  
M. N. O¨zis¸ik
Keyword(s):  
Radiative Transfer ◽  
Iterative Method ◽  
Integral Form ◽  
Iterative Solution ◽  
Single Scattering ◽  
Anisotropic Scattering ◽  
Initial Guess ◽  
Isotropic Scattering ◽  
Wide Range ◽  
Reflecting Boundaries

An iterative method is applied to solve the integral form of the equation of radiative transfer for the cases of isotropic scattering, highly forward, and backward anisotropic scattering in plane-parallel slab with reflecting boundaries. Calculations are performed for the values of single scattering albedo from ω = 0.7 to 1.0 where the convergence was previously reported to be poor. It is found that the convergence is significantly improved for most cases if the P-1 approximation of the spherical harmonics method is used for the initial guess. Results are presented for the hemispherical reflectivity and transmissivity of the slab over a wide range of parameters.

An Evaluation of the Differential Approximation for Spherically Symmetric Radiative Transfer

1969 ◽  
Vol 91 (1) ◽  
pp. 73-76 ◽  
Author(s):  
E. A. Dennar ◽  
M. Sibulkin
Keyword(s):  
Radiative Transfer ◽  
Heat Generation ◽  
Symmetric Case ◽  
Spherically Symmetric ◽  
Differential Approximation ◽  
Concentric Spheres ◽  
All Optical ◽  
Exact Calculations ◽  
Comparison Of The Results ◽  
Equal Temperature

The problem of radiative transfer between concentric spheres enclosing a gray gas has been solved for the case of unequal temperature walls with uniform heat generation in the gas by using a differential approximation based upon half-range moments. Comparison of the results with exact calculations illustrates the deficiencies of the differential approximation for the spherically symmetric case. Large errors exist in the optically thin limit for walls of different temperature. Smaller but appreciable errors are also found at all optical depths for equal temperature walls with heat generation in the gas.

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