A gas turbine engine includes a fan located at a forward portion of the gas turbine engine. A compressor section and a turbine section are arranged in serial flow order. The compressor section and the turbine section together define a core airflow path. A rotary member is rotatable with at least a portion of the compressor section and with at least a portion of the turbine section. An electrical machine is coupled to the rotary member and is located at least partially inward of the core airflow path in a radial direction. An enclosure at least partially encloses the electrical machine. The enclosure at least partially defines a first cooling airflow path within the enclosure that at least partially defines a first cooling airflow buffer cavity at least partially around the electrical machine. The first cooling airflow path is in communication with a second cooling airflow path located outside the enclosure that at least partially defines a second cooling airflow buffer cavity at least partially around the enclosure. A cooling duct provides pressurized air to the first cooling airflow path such that the air flows along both the first cooling airflow path and the second cooling airflow path providing the first cooling airflow buffer cavity and the second cooling airflow buffer cavity.