Dwindling energy resources and strong demand for better power sources as compared to conventional batteries have sparked research interest in micro power generation. The invention of state-of-the-art electronic devices requires more energy capacity, shorter charging period and light in weight, characteristics of which batteries lack. Therefore, in recent years micro power generation systems have been seen as a potential alternative to batteries owing to the obvious advantages that it has. It is essential to fully understand the underlying factors that affect the combustion stability in meso and micro-scale combustors. One of the popular methods to examine these factors is by performing numerical simulations. This paper demonstrates an axisymmetric two-dimensional steady state numerical simulation of propane-air combustion in meso-scale cylindrical tube combustors with concentric rings. The inner diameter of the tube is set to 3.5 mm and the wall thickness is specified to 0.7 mm. The concentric rings are placed between the unburned and burned gas region. The main function of these rings is to act as a flame holder where a stable flame can be easily established. The wall thermal conductivity in the unburned and burned gas region is varied from 1 W/m/K to 1000 W/m/K and the results in terms of gas, inner wall, outer wall surface temperature distribution, the blowout limits and combustion efficiency are analyzed and presented. In addition, the effect of the inlet velocity and the equivalence ratio is also investigated. The results show that the inlet velocity and equivalence ratio have significant impacts on the flame temperature, which in turn change the wall temperature distribution. Although the wall thermal conductivity has minimal effect on the flame temperature, both inner and outer wall surface temperature are greatly affected. Consequently, this variation of wall temperature contributes to the significant changes on the blowout limits. It is also shown that the combustion efficiency is influenced by the wall thermal conductivity of the combustors.