An aerosol-generating device configured for heating an aerosol-generating article so as to generate an inhalable aerosol from an aerosol-forming substrate of the aerosol-generating article is provided, the aerosol-generating device including: a housing including a cavity configured to receive the aerosol-generating article, the housing being configured to define a cooling air flow path extending from outside of the housing, through an interior of the housing, to an air-permeable portion of a wall of the cavity, the wall being tubular, the air-permeable portion of the wall including at least one annular air-permeable band being configured to radially channel an air flow from the cooling air flow path into the cavity around a periphery of the tubular wall of the cavity. An aerosol-delivery system including the aerosol-generating device and an aerosol-generating article defining a rod is also provided. An aerosol-generating article for an aerosol-generating device is also provided.