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Experimental observations are presented of the effect of the flow velocity and oxygen concentration, and of a thermal radiant flux, on the transition from smoldering to flaming in forward smoldering of small samples of polyurethane foam with a gas/solid interface. Because small polyurethane foam samples were studied, the smolder propagation and the transition to flaming had to be assisted by reducing the heat losses to the surroundings and increasing the oxygen concentration. The experiments are conducted with small parallelepiped samples vertically placed in a wind tunnel. Three of the sample lateral sides are maintained at elevated temperature and the fourth side is exposed to an upward flow and to a radiant flux. It is found that decreasing the flow velocity and increasing its oxygen concentration, and/or increasing the radiant flux enhances the transition to flaming, and reduces the delay time to transition. Limiting external ambient conditions for the transition to flaming are reported for the present experimental set-up. The results indicate that transition to flaming occurs in the char left behind by the smolder reaction, as evidenced by ultrasound probing of the sample interior, and it has the characteristics of a gas-phase ignition induced by the smolder reaction. A simplified scale analysis is presented, which shows that the transition can be treated as a gas-phase ignition process.