The Improved Differential Approximation for Radiative Transfer in Multidimensional Media

1990 ◽  
Vol 112 (3) ◽  
pp. 819-821 ◽  
Author(s):  
M. F. Modest
Keyword(s):  
Radiative Transfer ◽  
Differential Approximation

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.

Hybrid SN-PN Solution of the Radiative Transfer Equation in Multi-Dimensional Media

2011 ◽  
Author(s):  
Maathangi Sankar ◽  
Sandip Mazumder
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Complex Geometry ◽  
Radiative Transfer Equation ◽  
Discrete Ordinates ◽  
Differential Approximation ◽  
Discrete Ordinates Method ◽  
Surface Exchange ◽  
New Formulation ◽  
Ray Effects

The Modified Differential Approximation (MDA) was originally proposed for solution of the radiative transfer equation (RTE) in order to remove the shortcomings of the P1 approximation in scenarios where the radiation intensity is strongly directionally dependent. In the original MDA approach, the wall-emitted component of the intensity is determined using a surface-to-surface exchange formulation that makes use of geometric viewfactors. Such an approach is computationally very expensive for complex geometry and/or inhomogeneous media. This article presents a new formulation in which the wall-emitted component is solved using the Discrete Ordinates Method (SN approximation), while the medium-emitted component is solved using the P1 approximation, resulting in a hybrid SN-PN RTE solver. Results show that the hybrid Discrete Ordinates-P1 method (DOM-P1) is computationally very efficient, but its accuracy is poor in optically thin situations where ray effects, inherent in the Discrete Ordinates Method, are pronounced. To circumvent this problem, the control-angle Discrete Ordinates Method (CADOM) is finally employed, and the accuracy of the hybrid CADOM-P1 method is found to be far superior to the hybrid DOM-P1 method.

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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