A two-dimensional elliptic, computational fluid dynamics (CFD) model of a microbumer is solved to study the effects of microburner dimensions, conductivity and thickness of wall materials, external heat losses, and operating conditions on combustion characteristics and flame stability. We have found that the wall conductivity and thickness are very important as they determine the upstream heat transfer, which is necessary for flame ignition and stability, and the material's integrity by controlling the existence of hot spots. Two modes of flame extinction occur: a spatially global type for large wall thermal conductivities and/or low flow velocities and blowout. It is shown that there exists a narrow range of flow velocities that permit sustained combustion within a microburner. Large transverse and axial gradients are observed even at these small scales under certain conditions. Periodic oscillations are observed near extinction in cases of high heat loss. Engineering maps that delineate flame stability, extinction, and blowout are constructed. Design recommendations are finally made. (C) 2003 Elsevier Ltd. All rights reserved.