Does anyone know the technical name or Part number for the line/pipe circled in red?
It didn't list the S4 on that etka link, but it did list the 2.7T for the RS4 quattro. The part you are looking for is a coolant pipe VAG 078 121 081 J - the ending letter might be different for the S but the same (previous model) Mine is realllly decrepit, rusty etc. I have a slow coolant leak, this or the after run pump are high on my list. Good place to check is at a you pull it yard off an allroad or a6. I have an S. It may have been easier to go the allroad or A6 now that I think of it lol. Good luck.