Radiative heat transfer in a parallelogram shaped cavity

TL;DR

This paper presents an exact analytical method for modeling radiative heat transfer within a gray semi-transparent medium in a parallelogram cavity, providing benchmark solutions and demonstrating smooth, accurate results.

Contribution

The study introduces a novel analytical approach with double Gauss quadrature for radiative transfer in parallelogram cavities, including benchmark solutions and iterative temperature computation.

Findings

Accurate analytical expressions for radiative fields are derived.

Benchmark numerical solutions are provided for validation.

The method yields smooth and reliable results across the domain.

Abstract

An exact analytical description of the internal radiative field inside an emitting-absorbing gray semi-transparent medium enclosed in a two-dimensional parallelogram cavity is proposed. The expressions of the incident radiation and the radiative flux field are angularly and spatially discretized with a double Gauss quadrature, and the temperature field is obtained by using an iterative process. Some numerical solutions are tabulated and graphically presented as the benchmark solutions. Temperature and two components of the radiative flux are finally sketched on the whole domain. It is shown that the proposed method gives perfectly smooth results.