An engine cowling of an aircraft gas-turbine engine with a core engine and a bypass duct surrounding the latter, with a front cowling enclosing the bypass duct and a rear cowling movable in the axial direction, and with stator vanes arranged in the bypass duct, where recesses for removing fluid from the bypass duct are provided in the area of the stator vanes on the inside of the front cowling, where the fluid discharged through the recesses is routed by means of flow ducts through the front cowling, brought into contact with at least one heat exchanger, and subsequently discharged to the environment.