Stator device for an electric machine, and electric machine

A stator device for an electric machine, comprising:

• a stator body;
• a plurality of cooling channels:
• configured to cool the stator body,
• extend parallel to an axis of the stator body, and
• wherein a cross-sectional area of each one of the cooling channels is asymmetric to the axis of the stator body;
• and
• a cooling fluid connection device:
• that axially outwardly and radially delimits a circumferentially extending connection channel,
• wherein a cross-sectional area of the connection channel is continuous and symmetric to the axis of the stator body,
• into which a respective axial end of the cooling channels opens, and
• wherein the connection channel extends radially further inward than the cooling channels.