Can anyone advise on how to fix a leaking radiator please?

one of my radiators have developed a leak, at the junction of a small piece of pipe that is coming from the back of it, sorry this is not my area so I don't know the correct term, but this small piece of pipe is actually part of the radiator, I suspect it is welded in place on the inside and has corroded, despite being only 5 years old.,to clarify the central heating pipe goes into it and is fastened with a nut.It is not leaking at the nut. I do not want to replace the radiator and would appreciate any expertise on how to seal the leak myself, and with what? Meanwhile as I am running the system at present, I have shut this particular rad off at its thermostat, will this prevent the system from draining down through this leak?