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Based on a three-step kinetic mechanism, a one-dimensional, time dependent, numerical model is presented forthe smoldering propagation in a horizontally packed bed of cellulosic material. The kinetic processes include pyrolysis andoxidation degradation of fuel and oxidation of char. Heat transfer between solid and gas is taken into account, and the diffusioncoefficient varies with the temperature. Radiative heat transfer is included by using the diffusion approximation. The effectsof airflow velocity and oxygen concentration are simulated on the smoldering velocity and the averaged maximum temperatureof smoldering fuel. The results indicate that the spread rate varies linearly with increasing airflow velocity, and the inlet airvelocity has little effect on the maximum temperature. The evolutions of gas species and solid compositions are predicted.The effects of frequency factors (A1, A2 and A3) are analyzed. Simulations show that the smoldering spread rate increaseswith increasing A2 (fuel oxidation), but decreases with A1 (fuel pyrolysis) and A3 (char oxidation).