A detailed numerical study was conducted to understand the transient flame propagation process and the flame-speed oscillation phenomenon in a carbon dust cloud. The modeling included the solution of a set of time-dependent conservation equations developed for the gas phase and the particle phase in a spherical coordinate. The gas-phase reactions used detailed chemistry, variable thermodynamic properties, and multicomponent transport properties. The particle-phase equations include the two-phase force interactions in the momentum equation by considering Stoke drag force and thermophoretic force resulting from the gas-phase temperature gradient. Mass and species transfer between the two phases were modeled as a result of both gas-phase and particle surface reactions. Energy transfer between the two phases, including convective, conductive, and radiative heat transfer, were included. Radiation absorption and emission by particles were both especially considered. The results show that because of the different inertia between particles and gas, a velocity slip occurs between the two phases in the region ahead of the flame front. The slip is more significant in the early flame propagation stage than in the later stage. The radiation heat losses of the hot gases and particles to the cold ambient and the radiation gain as a result of the absorption of unburned particles are both important in the present dust flame, because the characteristic time scale of the chemical reactions is longer than that of gaseous flames. Lastly, an analysis of the detailed numerical simulations shows that a slip between the gas and particle velocities is the cause of flame-speed oscillation. The slip leads to a periodic change in local particle number density in the reaction zone, which in turn changes the local fuel equivalence ratio periodically, causing the oscillation.