The paper studies the flow of a combustible mixture in a vertical channel in the presence of radiative heat transfer as a model for biomass moving bed gasifiers operating in the temperature range 750–1500 K. The simplistic binary reaction A → B is assumed, and both the optically thick (high density gas) and the optically thin (low density gas) situations are considered for the radiative heat transfer. Analytical and numerical solutions are obtained and discussed quantitatively.