A bypass axial turbomachine includes a fan, a low pressure stator stage, a high pressure stator stage, the compressors being traversed by a flow referred to as primary flow of the turbomachine, at least one passage of discharge flow rate controlled from the primary flow in one of the stator stages toward the secondary flow, a heat exchanger of the surface air-oil (ACOC) type arranged flat on or in the wall surrounding the stator stages and defining the internal surface of the secondary flow, directly downstream of the junction of the passage of the discharge flow rate with said wall, so as to be run through by the secondary flow enriched with the discharge flow rate.