A plane one-dimensional problem of the propagation of slow-speed combu
stion in methane-air-coal dust suspensions is solved. Methane containe
d originally in the gas is assumed to burn-up completely in the flame
front. The front velocity relative to the gas is calculated from relat
ions derived in analysis of the stationary problem using the theory of
thermal explosion. The gas suspension is regarded as a two-temperatur
e and two-velocity medium. Heterogeneous reactions of carbon (coke) co
mbustion and carbon monoxide reduction, and the yield of volatile comp
onents and their gas-phase combustion together with carbon monoxide ar
e taken into account. Based on numerical calculations, the coal dust i
s shown to affect unambiguously the flame velocity, with moderate cont
ent of the dust. In lean mixtures: with a moderate content of the dust
the intensity of the combustion wave increases and decreases under co
nditions close to stoichiometric ones.