such arrays of ports the fins of the boxes form flame shafts because in the latter embodiment two boxes are arranged in side by side relationship if desired fins 3 could also be arranged parallel to the longitudinal axis of the tube rather than transversely thereto i e in series or in side by side relationship with relatively short length fin sections preferred to reduce the risk of heat deformation fig4 to 8 illustrate embodiments wherein selected pairs of adjacent fins 3 are arranged to form pocket shaped bodies 9 open on the sides and on top in the embodiments of fig4 to 7 gas outlet ports 1 are grouped in arrays and the pocket shaped bodies are disposed above the tube in areas 12 free of the gas outlet ports since as a rule the burner ports are disposed in equidistantly spaced arrays 6 pocket shaped bodies 9 extend transversely to the longitudinal axis of gas burner tube 2 and have bottoms 10 forming a rounded transition zone connected to fins 3 the bottoms being shaped to conform to the surface configuration of the burner tube transversely to the tube see fig3 so that the bottom of the pocket shaped body at all points is at the same distance from the surface of the tube such pocket shaped bodies may readily be shaped from suitable metallic sheets with the aid of suitable forming tools in a single operating stage since at least about ten such pocket shaped bodies 9 will have to be associated with each standard length gas burner tube 2 it will be useful to form an assembly for mounting the pocket shaped bodies on the tube comprising a common.