Convectional free flame combustion causes the temperature rise in the vicinity of the flame to be very steep, resulting in high temperatures, consequently NOx formation enhances. The fact is that the thermal conductivity of gases are very low, i.e., poor thermal conductors. Combustion in porous media elevates this problem by enhancing heat conduction and thermal radiation from the flame zone, which reduces the flame temperature and NOx formation. Also, heat transfer from the free flame to a load is mainly by convection, while heat transfer is by convection and radiation from combustion zone in porous medium to a load. Moreover, it is easy to stabilize the flame in a porous medium, where the thermophysical properties of the porous medium can engineered for specific application. Most of the work is done on flat type porous burner, where the axial flow of gaseous fuel air mixture forces through a layer of porous medium. In this report a concept of cylindrical porous burner is introduced, where the fuel air mixture is forced to flow radially. Mathematical models and simulation results are introduced for both burners, axial and radial flow burners. Preliminary results of the comparison between the thermal performances between the mentioned burners are discussed. The results revealed that the cylindrical burner has superiority over the convectional flat burner. The cylindrical burner has a wide range stability limits and may produce less NOx than the flat type burners.