Two-dimensional radiation in absorbing-emitting-scattering media using the P-N approximation
Radiative energy transfer in a gray absorbing, emitting, and isotropically scattering medium is considered in a two-dimensional rectangular enclosure using the P-N differential approximation. The P-1 and P-3 spherical harmonics approximations for the intensity distribution are used in this study and uniform volumetric generation of energy is included in the energy conservation formulation. The two-dimensional partial differential equations (PDE's) are formulated for the P-N approximations and 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. The P-1 approximation results are obtained from separation of variables solutions. The P-3 results are obtained numerically using successive-over-relaxation methods to solve the finite difference formulations for the four equations and associated boundary conditions. The two approximation results are compared with numerical Hottel zone results and with results from other approximation methods and show that the P-3 approximation can be used for predicting emissive power distributions and heat transfer rates in two-dimensional media with opacities of unity or greater. The P-1 approximation is found to be identical to the diffusion solution and should thus be used only if the medium is optically dense.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (USA); Texas Univ., Austin (USA). Dept. of Mechanical Engineering
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 5157152
- Report Number(s):
- SAND-82-0129C; CONF-820604-4; ON: DE82005690
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COOLING
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC RADIATION
ENERGY TRANSFER
EQUATIONS
HEAT TRANSFER
NUMERICAL SOLUTION
RADIATIONS
RADIATIVE COOLING
SURFACES
THERMAL RADIATION
THERMODYNAMICS
TWO-DIMENSIONAL CALCULATIONS