Radiation, Conduction, and Convection From a Sphere in an Absorbing, Emitting, Gray Medium

1992 ◽  
Vol 114 (1) ◽  
pp. 250-254 ◽  
Author(s):  
P. D. Jones ◽  
Y. Bayazitoglu
Keyword(s):  
Radiative Transfer ◽  
Radiative Transfer Equation ◽  
Infinite Medium ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Transfer Equations ◽  
Gray Medium ◽  
Intensity Field ◽  
Radiative Transfer Equations ◽  
Combined Mode

Combined mode heat transfer is solved for an emitting, reflecting sphere in low Peclet number motion through a gray, nonscattering, absorbing, emitting, and conducting infinite medium. The coupled formulation of the energy and radiative transfer equations is solved numerically. The radiative transfer equation is expressed in a unique spatial/directional coordinate system, whose object is to exploit the axisymmetry of the problem. The radiation intensity field is solved using the discrete ordinates method. Results are presented in terms of the Planck and Peclet numbers, and serve as a combined radiation/convection analog to the well-known Nusselt number result for a radiatively nonparticipating medium.

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.

scholarly journals Effect of radiation on the flow structure and heat transfer in a 2-D gray medium

2019 ◽  
Vol 23 (6 Part A) ◽  
pp. 3603-3614
Author(s):  
Nesrine Rachedi ◽  
Madiha Bouafia ◽  
Messaoud Guellal ◽  
Saber Hamimid
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Radiative Transfer Equation ◽  
Numerical Study ◽  
Discrete Ordinates ◽  
Square Cavity ◽  
Discrete Ordinates Method ◽  
Gray Medium

A numerical study of combined natural convection and radiation in a square cavity filled with a gray non-scattering semi-transparent fluid is conducted. The horizontal walls are adiabatic and the vertical are differentially heated. Convection is treated by the finite volumes approach and the discrete ordinates method is used to solve radiative transfer equation using S6 order of angular quadrature. Representative results illustrating the effects of the Rayleigh number, the optical thickness and the Planck number on the flow and temperature distribution are reported. In addition, the results in terms of the average Nusselt number obtained for various parametric conditions show that radiation modifies significantly the thermal behavior of the fluid within the enclosure.

scholarly journals The Full-Spectrum Correlated-K Distribution and Its Relationship to the Weighted-Sum-of-Gray-Gases Method

2000 ◽  
Author(s):  
Michael F. Modest ◽  
Hongmei Zhang
Keyword(s):  
Radiative Transfer ◽  
Solution Method ◽  
Distribution Model ◽  
Weighted Sum ◽  
Full Spectrum ◽  
One Dimensional ◽  
Molecular Gases ◽  
Transfer Equations ◽  
Gray Medium ◽  
Radiative Transfer Equations

Abstract A new Full-Spectrum correlated-k distribution has been developed, which provides an efficient means for accurate radiative transfer calculations in absorbing/emitting molecular gases. The Full-Spectrum correlated-k distribution can be used together with any desired solution method to solve gray-medium radiative transfer equations for a small number of gray absorption coefficients, followed by numerical quadrature. It is shown that the Weighted-Sum-of-Gray-Gases model is effectively only a crude implementation of the Full-Spectrum correlated-k distribution approach. Within the limits of the Full-Spectrum correlated-k distribution model (i.e., an absorption coefficient obeying the so-called “scaling approximation”), the method is exact. This is demonstrated by comparison with line-by-line calculations for a one-dimensional CO2-N2 gas mixture with varying temperature and concentration fields.

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Computational Costs ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

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