A numerical transport model was developed to study the spontaneous transition from smoldering to flaming combustion in polyurethane foam. The numerical transport model is two-dimensional with an eight-step reduced reaction mechanism. The reaction mechanism includes seven heterogeneous and a global homogeneous gas phase reaction and is capable of simulating both forward and opposed smoldering combustion. The current study examines the transition to flaming in normal gravity for flow assisted forward smoldering combustion as a function of an externally applied heat flux and the velocity and oxygen concentration of a forced gas flow. Reaction rates, species profiles, gas phase temperatures, and condensed phase temperatures are examined. Three reactions were found to play a major role in leading to the prediction of transition to flaming. Favorable agreement of temperature response, time to spontaneously transition from smolder to flaming, and location of the transition event between simulation results and experimental data is demonstrated. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.