Radiative Transfer: Asymptotic Solutions of the Kinetic Equation of Radiation Propagation, $n$th Order Asymptotic Approximation and Improved Boundary Conditions

TL;DR

This paper develops a new, higher-order asymptotic approximation for radiation transfer in optically thick media, providing simpler, more accurate solutions and improved boundary conditions for practical calculations.

Contribution

It introduces a novel nth-order asymptotic approximation for radiation transfer, surpassing the diffusion approximation in accuracy and simplicity, along with improved boundary conditions.

Findings

New nth-order asymptotic approximation derived

Diffusion and heat conduction equations obtained from the approximation

Enhanced boundary conditions for radiation calculations

Abstract

In the article, new asymptotic approximation of the $n$th order is obtained and proposed to be used in calculations of radiation propagation without scattering in optically thick media; the asymptotic approximation is much simpler and more precise than the known diffusion approximation. The rigorous derivation of the diffusion approximation equation and the equation of the radiation heat conduction approximation is obtained from the constructed asymptotic solution of the kinetic equation of radiation propagation in optically thick media. It is shown, that for optically thick media the asymptotic solution of the kinetic equation of radiation propagation without scattering is asymptotic expansion of the exact integral solution of that kinetic equation. Improved boundary conditions, which are essential for practical application in calculations of radiation propagation, are derived (for inner boundaries and outer boundaries with vacuum).