Abstract: Self-sustaining smolder propagation is a balance between the heat generated by and the heat lost from the smolder reaction. In this work we investigate the effect of bulk heat losses on one-dimensional, unsteady, microgravity, forced low-flow, opposed and forward smolder in flexible, open-cell, polyurethane foam. We also examine how the addition of homogeneous reactions affect one-dimensional forward smolder. These investigations are achieved through the development of three respective numerical models, and the coding of a solver. Opposed smolder is modeled using a two-step exothermic kinetic scheme: oxidative pyrolysis followed by exothermic oxidation. In accordance with experimental evidence, forward smolder is modeled using a two-step kinetic scheme: endothermic pyrolysis, followed by an exothermic oxidative reaction that provides the heat to drive the pyrolysis front. In the absence of bulk heat losses, opposed and forward smolder velocities are found to increase with increasing inlet oxidizer mass flux. In both opposed and forward smolder, increasing bulk heat losses result in a decrease of the smolder velocity. If the bulk heat losses are sufficiently large, extinction occurs. When energetic homogeneous reactions at the char/degraded foam interface in forward smolder are incorporated via a global, single-step homogeneous reaction, large bulk heat losses can be an effective way to prevent the onset of thermal runaway. Our results demonstrate the efficacy of applying bulk heat losses to promote microgravity smolder inhibition and extinction. The use of bulk heat losses to suppress microgravity smolder is a viable alternative to traditional means of extinguishment.