Abstract: Honeycomb structure assemblies comprising walled structures which admit fluid such as air for purposes of cooling or heating the walls thereof or for other purposes. The assemblies comprise spaced inner and outer walls united by means of an internal honeycomb structure comprising aligned cells having opposed interior and exterior gaps open to adjacent cells, which causes the admitted fluid to undulate through said gaps into contact with both of the walls, such as for uniform cooling or heating. The honeycomb structure contains flanges which are secured to one or both walls for uniform strength and resistance to separation under the stress of use.