How to seal joints in ductwork when tape is not an option
I've used duct sealer in the past to seal up my attic air handler, it applies like a paste and dries hard. You can try that, but you options of globbing it on may be limited.

Is this duct in a basement or crawlspace? 

The handler and ducts in my unfinished basement leak a bit, but I don't bother sealing them up as it helps keep the temp in the basement that much more liveable.