Is this fitting:
http://superfly.co.nz/nut_pipe_flange.jpg
familiar?
The 'flange' doesn't quite tighten into my new radiator's fitting, so I'm hoping to find a transition fitting to fit between this stubby flanged pipe(8 mm diameter) and the threaded fitting, slightly deeper, and with a smaller hole in the bottom, in the new radiator.

 

That looks like an A/C line, where an o-ring fits over the end of the tube and pushed up to the shoulder.

 

Yeah, usually it's a inverted flare for the cooler. Correct?

 

Thanks, and that steel pipe's tip came out of the 8 mm hole in the upper of two identical fittings in the plastic tank of the old radiator. No O rings were found on upper or lower steel pipes removed...but this is a used car...
http://superfly.co.nz/transmission_oil_inlet.jpg

 

Thanks, and I wasn't sure if it was inverted flare, or some type of ArmyNavy fitting.
The new radiator's fittings are 2 or 3 mm too deep...so that the 'flange' compression nut becomes dangerously tight, before the nut can compress the 'flange' into the bottom of the aluminum threads...and the hole diameter in the new fittings is 5 mm, so the 8 mm pipe tip won't easily fit.
http://superfly.co.nz/oil_inlet.jpg