TWO-DIMENSIONAL ENERGY TRANSFER IN RADIATIVELY PARTICIPATING MEDIA WITH CONDUCTION BY THE P-N APPROXIMATION

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Abstract
The combined steady state conduction and radiation heat transfer problem for a gray medium within a rectangular enclosure is considered using the differential approximation. The P-l and P-3 spherical harmonics approximations for the intensity distribution are incorporated in the equation of transfer, and modified Marshak-type boundary conditions are used in the formulation. The enclosure walls are assumed to be isothermal black surfaces. Two and five coupled second-order nonlinear partial differential equations are developed for the P-l and P-3 approximations, respectively, using the energy conservation and moment of intensity expressions. The P-l equations have been numerically solved using finite element techniques, while the P-3 relations have been solved using a finite difference successive-over-relaxation (SOR) algorithm. Two-dimensional temperature profiles and hot wall heat transfer results are presented for square enclosures and different optical width rectangular enclosures for a range of conduction-radiation parameters.

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