Abstract: A method for assembling a combustor assembly is provided. The method includes providing at least one sleeve having a plurality of inlets, and coupling at least one airfoil to at least one of the plurality of inlets defined in the at least one sleeve. The airfoil includes a pair of opposing sidewalls coupled together at a leading edge and at a trailing edge and at least one channel is formed between the airfoil sidewalls for channeling cooling air. The cooling air is directed to flow substantially perpendicularly to a direction of air flowing around the airfoil in a portion of the combustor assembly that is to be cooled. The method also includes coupling the at least one sleeve around the portion of the combustor assembly to be cooled. Also provided are a sleeve and an airfoil for use in a combustor assembly.