Two-dimensional radiation in absorbing-emitting media using the P-N approximation
Radiative energy transfer in a gray absorbing and emitting medium is considered in a two-dimensional rectangular enclosure using the P-N differential approximation approximation. The two-dimensional moment of intensity partial differential equations (PDE's) are combined to yield a single second-order PDE for the P-1 approximation and four coupled second-order PDE's for the P-3 approximation. P-1 approximation results are obtained from separation of variables solutions, and P-3 results are obtained numerically using successive-over-relaxation methods. The P-N approximation results are compared with numerical Hottel zone results and with results from an approximation method developed by Modest. The studies show that the P-3 approximation can be used to predict emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater. The P-1 approximation is identical to the diffusion solution and is thus applicable only if the medium is optically dense.
- Research Organization:
- Sandia National Laboratories, Albuquerque, New Mexido 87185
- OSTI ID:
- 5853528
- Journal Information:
- J. Heat Transfer; (United States), Journal Name: J. Heat Transfer; (United States) Vol. 105:2; ISSN JHTRA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
420400* -- Engineering-- Heat Transfer & Fluid Flow
ABSORPTION
CONFIGURATION
CORRELATIONS
DATA
DIFFERENTIAL EQUATIONS
EMISSIVITY
ENERGY ABSORPTION
ENERGY TRANSFER
EQUATIONS
HEAT TRANSFER
INFORMATION
MATERIALS
NUMERICAL DATA
NUMERICAL SOLUTION
OPACITY
OPTICAL PROPERTIES
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
RADIATIONS
RECTANGULAR CONFIGURATION
SURFACE PROPERTIES
THEORETICAL DATA
TWO-DIMENSIONAL CALCULATIONS