Just one opinion, but have used Kroil years ago. Hands down THE best available, as Cheryl said. If Kroil doesn't loosen it, it ain't stuck, it's welded. I think they used to claim a "creepage" of 1 millionth of an inch. :o
In a case of a broken off rod (down inside the piece), if nothing else will work, I have used LEFT handed twist drills. Have to be sure that you're in the center, and use the smallest size possible to start with, gradually increasing if necessary. (careful not to hit the female threads). The combination of the "loosening" direction, and the heat works great! Soak in Kroil first though.