Abstract: The burner (100) comprises a cylindrical porous substrate (110); and an end cap (130) at a first end of the cylindrical porous substrate (110). The cylindrical porous substrate (110) is provided for flow of a premix of combustible gas and air from the outside of the cylindrical porous substrate (110) through the pores of the cylindrical porous substrate (110) to an interior cavity (140), for the combustible gas to be combusted on the inner surface of the cylindrical porous substrate (110) thereby generating hot gas. The burner has an opening (182) at the second end of the cylindrical porous substrate (110) to exit the hot flue gas out of the interior cavity (140). The cylindrical porous substrate (110) has a higher permeability section (170), located at the opening (182) at the second end. The higher permeability section (170) has a lower resistance to gas flow than other sections of the cylindrical porous substrate (110).