An elaborated diffusion mathematic model of radiative transfer in an extinction medium

Abstract

The computational method of diffusion approach, used sometimes for simulating the radiative heat transfer, differs in simplicity of its algorithm, but can not take ac-count of radiation anisotropy. The reasons of its insufficient accuracy have been re-vealed; it is shown that inadequate boundary con-ditions produce unpredictable er-rors. Ways for eliminating short-comings of the diffusion method have been developed. The accurate diffusion model has been theoretically elaborated for radiative heat transfer in dust-laden gases. To eliminate singularity of temperature curves on the surface of confining walls, the en-closed extinction medium was hypothetically considered as an unbounded one. The radiation intensity has been expanded in a se-ries and integrated over the spherical solid angle, what has allowed to obtain more precise differential equation for the resulting radiation flux both in the unbounded and enclosed extinction medium. As a result, shortcomings peculiar to the previous method of diffusion approach have been eliminated, and correct Neumann and Robin boundary conditions have been formulated. As a result, the elaborated diffu-sion model got the increased accuracy in simulating radiative heat transfer, and con-currently it offers an advantage of simplicity and universality of the diffusion ap-proach method.