An aerosol-generating system is provided, including: an aerosol-generating device including a power source; and a cartridge removably coupled to the device, the cartridge including a liquid storage portion including a housing having an open end and containing a liquid aerosol-forming substrate, a substantially flat heater assembly fixed to the open end of the housing and including an electrical heating element arranged in a curved manner and configured to heat the substrate to form an aerosol, and a capillary material disposed in contact with the heating element and being configured to convey the substrate to the heating element, the liquid storage portion being disposed at a first side of the assembly and an airflow channel at a second side of the assembly, the airflow channel defining an airflow path over the assembly and configured to convey the aerosol, and the power source being configured to supply power to the assembly.