We analyze the flame front speed in the downward combustion of multiple parallel samples of thermally thin fuels at normal gravity and far from extinction conditions. In contrast with the single sample case, where conduction through the gas-phase is the dominant heat transfer mechanism, in the multiple parallel samples case, radiative heat fluxes may become very relevant, which compromises the application of the well-known formula of de Ris for determining the burning rate. Here we study the downward combustion of multiple parallel sheets by (1) obtaining new experimental data at different oxygen atmospheric levels; (2) generalizing a previous comprehensive energy balance model now expected to be valid for a wide range of scenarios; and (3) deriving an analytical approximation for the burning rate that generalizes the classical de Ris formula for those cases where radiative effects cannot be neglected. The comparison with own as well as with external data reveals the strengths and weaknesses of these types of models.