The turbine inlet temperature of modern jet engines is constantly being increased in order to improve thermal efficiency. The hot gas temperature considerably exceeds the operating limits of the typically used single-crystal nickel-based alloys, requiring cooling of the thermally highly loaded components. This includes the first stage nozzle guide vane, which is internally cooled with compressor discharge air. For external cooling, the cooling air is ejected through film cooling holes. This results in irreversible pressure losses in the secondary flow path and mixing losses when the cooling air is injected into the main flow. The primary objective is to minimize these losses through the reduction of the required cooling air mass flow rate. ...