A mathematical model is presented which allows one to treat the combined phenomena of heat, mass and species transfer by diffusion as they occur within smouldering fires in accumulations of dust or other solid bulk materials. The model was applied to predict self-ignition temperatures of five different dusts, where it could be shown that computed and experimental self-ignition temperatures coincide within an error margin of +/-5%. For smouldering fires, if initiated by either self-ignition or an ignition source, it could be shown that the temperature and the velocity at which the reaction front propagates both depend on the volume of the dust accumulation. In addition, the propagation velocity increases when the initial temperature of the dust accumulation is increased and decreases when the initial moisture content of the dust accumulation is increased. Comparisons of the numerical model with experiments show that the smouldering propagation is mirrored qualitatively, while the accuracy of the computations strongly depends on the accuracy of the input parameters, namely on the apparent activation energy.