According to the present disclosure, a flat-flame nozzle is provided for producing a flat flame in a flame chamber included in a burner assembly. The flat-flame nozzle is configured to conduct fuel from a fuel supply to an ignition zone in the flame chamber. In some illustrative embodiments, the flat-flame nozzle is also configured to conduct oxygen from an oxygen supply to the ignition zone to produce a combustible oxygen-fuel mixture in the flame chamber. In illustrative embodiments, a removable first plate-separation border frame is positioned to lie between a first lower plate and a companion first upper plate. This border frame is configured to cooperate with those plates to form in the flat-flame nozzle a fuel-discharge outlet and a fuel-transport passageway communicating with the fuel-discharge outlet.