The current study evaluates the effectiveness of the Full Spectrum k-distribution (FSK) method to model the radiative heat transfer in a mixture of gases and particles, specifically a combination of \(\rm{H}_2\rm{O}\) and \(\rm{CO}_2\) gases, along with fly ash particles, commonly found in biomass and coal combustion. The radiative transfer equation (RTE) is numerically solved for a square cavity containing the mixture of gases and particles using the Finite Angle Method (FAM). The correctness of FSK results is performed by two ways; comparing it with Line-by-Line (LBL) method and through the principle of energy conservation. The results of LBL method are also verified by the principle of energy conservation method. The k-distribution for the mixture of absorbing gases and particles is evaluated through Modest-Riazzi (MR) mixing method. Two approaches are proposed to consider the spectral scattering coefficient: generating the k-distribution of the scattering coefficient and adopting the Planck mean. Furthermore, the modelling of scattering with absorption in scenarios involving variable particle properties, non-isothermal and non-homogeneous domain are considered. The results show that for a mixture of gases and particles without scattering, the percentage relative error remains below 2% when compared with LBL. In the case of a non-isothermal and non-homogeneous medium, the percentage error remains below 10%, while achieving a significant 270-fold reduction in computational time. The current method is also investigated for anisotropic scattering phase function and a similar accuracy is achieved in calculating the radiative heat flux.
