An air-fuel burner includes a heat-transfer tube, an air-fuel mixing chamber, and an air-fuel nozzle. The air-fuel nozzle is coupled to the air-fuel chamber to communicate a combustible air-fuel mixture into a combustion chamber defined between the air-fuel nozzle and the heat-transfer tube. The combustible air-fuel mixture, when ignited, establishes a flame in the combustion chamber to produce heat which is transferred through heat-transfer tube to an adjacent medium external to the heat-transfer tube.