Numerical Comparative Study of Compressible and Incompressible Models for Predicting Combined Natural Convection and Radiation in Participating Medium

Natural convection coupled with volumetric radiation governs heat transfer in high-temperature systems, yet modeling relies heavily on the Boussinesq approximation, limited to weak density variations. This study provides the first systematic comparison of compressible and incompressible formulations for convection–radiation in participating media. The incompressible model adopts the Boussinesq approximation, wherein density is constant except in the buoyancy term, thermophysical properties are fixed, and validity requires εb≪1. Conversely, the compressible model uses a low-Mach-number (LMN) formulation, allowing nonlinear density variations through the equation of state, with viscosity and conductivity following Sutherland's law and no restriction on ΔT. A unified numerical framework is developed by coupling low-Mach-number (LMN) compressible Navier–Stokes equations with the Discrete Ordinates Method (DOM) for radiative transfer, implemented in finite volumes and validated against benchmarks (deviations <1% hydrodynamic, <4% radiative). Results uncover a regime shift with increasing Boussinesq parameter. Radiation dominates, boosting radiative Nusselt by 50% while halving convection. Radiation amplifies compressibility via temperature–density coupling, causing deviations up to 20% in radiation and 50% in convection between compressible and Boussinesq predictions. Critically, a thermal threshold ΔT ≈ 200 K emerges, below which Boussinesq holds but beyond which it fails due to strong density variations-lower than pure-convection limits. We propose a three-tier modeling hierarchy for low-, intermediate-, and high-temperature regimes. This work reveals radiation-compressibility interplay, challenging assumptions in buoyancy flows and offering a predictive framework for advanced thermal systems.