We numerically solve the problem of a premixed flame in the region between two concentric cylinders, in which the combustible mixture is fed in through The inner cylinder, and combustion products are removed through the outer cylinder and through the sides. We employ a model which accounts for the full coupling between fluid and transport effects and chemical reactions. The model accounts for heat loss through both the outer and inner cylindrical walls. We find that as heat loss is increased or as the inflow velocity is decreased, a transition from stationary to pulsating combustion occurs prior to extinction. For certain parameter ranges a transition to apparently chaotic dynamics occurs via a period doubling cascade.