scholarly journals New half-range differential approximation for spherically-symmetric radiative transfer.

AIAA Journal ◽  
1971 ◽  
Vol 9 (12) ◽  
pp. 2385-2391 ◽  
Author(s):  
JAMES B. MORENO ◽  
ISAAC GREBER
Keyword(s):  
Radiative Transfer ◽  
Spherically Symmetric ◽  
Differential Approximation

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.

Differential Approximation to Radiative Transfer in Semitransparent Media

1985 ◽  
Vol 107 (2) ◽  
pp. 478-481 ◽  
Author(s):  
F. H. Azad
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Exact Formulation ◽  
Differential Approximation ◽  
Reflection And Refraction ◽  
Integrated Intensity ◽  
Dielectric Interfaces ◽  
Semitransparent Medium

Radiative transfer in a semitransparent medium is treated using the differential approximation. Boundary conditions are formulated to accommodate direction-dependent reflection and refraction at a dielectric interfaces. The approximate results are compared to numerical solution of the exact integral equation. Also, a modification based on the exact formulation of the integrated intensity at the interface is presented that significantly improves the accuracy of the differential approximation in the optically thin regimes.

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