For the combustion of solid fuels, thermal radiation is of high importance. Numerical simulation of these processes requires a detailed description of thermal radiative transport. The present paper investigates the scattering of thermal radiation by particles in numerical simulations. Mie theory is assumed to provide an exact description for radiative properties. As the evaluation of the equations obtained from Mie theory is very time consuming, approximate phase functions are used to describe scattering of radiation by particles. These approximations can be evaluated very fast at the expense of shortcomings in precision. To match the accuracy achieved by elaborate models for other sub-processes of coal combustion, new models with an increased precision must be identified. In this work, a quantitative investigation of the effect of commonly used approximate phase functions (Henyey-Greenstein and Delta-Eddington) on the distribution of thermal radiation was carried out. Integration over a discrete spectral interval was performed. The influence of particle size distribution and also varying refractive indices of the particles were taken into account. The results of the approximated methods were compared to the exact solutions obtained by Mie theory. It was found that the choice of the phase function has a significant influence on the distribution of radiation. After integration, a deviation of about 10-20 % was observed for forward scattering, while for other angular directions, the results differed up to a factor larger than 3 compared to the Mie theory reference case. For the spectral discretization into a low number of bands, an influence of the distribution of radiation within each band on the total scattered intensity was found. Therefore, the use of a distribution function based on black body radiation is proposed. Furthermore, a tabulation and interpolation approach for the representation of radiative properties is presented and discussed. Finally, different approximations for the scattering phase function are applied in a heat transfer calculation and the influence is discussed.