Analytical and numerical investigation of radiative heat transfer in semitransparent Media

TL;DR

This paper investigates mathematical properties and develops numerical methods for solving radiative heat transfer equations in semitransparent media, including boundary element discretization and handling complex geometries.

Contribution

It provides a rigorous analysis of the radiative integral operators, proves existence and uniqueness of solutions, and introduces a boundary element method with an element-subdivision algorithm for complex geometries.

Findings

The method accurately solves radiative transfer in complex geometries.

Convergence of the iterative scheme is established.

Numerical examples verify the method's effectiveness.

Abstract

This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and uniqueness of solution to the radiative integral system is proved by the reversibility of operator matrix. Besides, the convergence analysis of an iterative scheme is also carried out. Then, boundary element method based on the collocation scheme is used to discretize the radiative integral system. Arbitrary enclosure geometry is considered. For the non-convex geometries, an element-subdivision algorithm is developed to handle with the integrals contained the visibility factor. Finally, examples are presented to verify the effectiveness and accuracy of our method.