A rotating machine includes a hub portion, wherein the hub portion comprises a forward face and an aft face. The rotating machine further includes a cooling channel formed on either the forward face or the aft face and configured to direct cooling air to a location on the rotating machine, wherein the cooling channel extends from a radially inner location along the face to a radially outer location along the face, and wherein the cooling channel is configured as a recess formed into an outer surface of the face.