How do you analyze radiation heat transfer in participating media such as combustion gases?

Participating media (gases like CO₂, H₂O, and particles) absorb, emit, and scatter radiation. Analysis requires solving the Radiative Transfer Equation (RTE): dI_λ/ds = κ_λI_bλ - κ_λI_λ + σ_s/(4π)∫I_λ(s')Φ(s',s)dΩ. Methods include: P1 approximation (fast but inaccurate for optically thin/thick extremes), Discrete Ordinates Method (DOM/S_N) solving along discrete directions, Monte Carlo (accurate but computationally expensive), and Weighted Sum of Gray Gases (WSGG) for combustion gases reducing spectral complexity. Key parameters: absorption coefficient (κ) from HITRAN database or WSGG coefficients, optical thickness (τ=κL). For furnaces, gas emissivity charts (Hottel charts) provide engineering estimates. Combined with CFD, participating radiation adds 30-50% to computational cost but is essential for furnaces, combustion chambers, and high-temperature processes above 1000K.