Duct tape is crap. It is actually not good for ducts (heating and cooling
causes the adhesive to quickly fail):
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POPULAR SCIENCE (December 1998)

Tape That Doesn't Live Up to its Name

DUCT TAPE is one of the most versatile materials ever invented. You can
patch a tent, seal up a box, or even repair a leaky garden house with it.
But according to the Department of Energy's Lawrence Berkeley National
Laboratory, there's one thing duct tape doesn't do well: seal a duct.

In leak tests at the lab, researchers Max Sherman and Iain Walker forced
alternating hot and cold air flows through finger-jointed metal ducts sealed
with a variety of products --including duct tape, clear plastic tape,
foil-backed tape, mastic, and injected aerosols. The researchers also baked
the sample ducts at temperatures of 140 to 187 degrees F, simulating the
conditions in many attics.

"Of all the things we tested," says Sherman, "only duct tape failed. It
failed reliably and quite often catastrophically."

Duct tape consists of a cloth backing and a rubber adhesive. "We think that
heat degrades the glue, and that's what's killing the duct tape," Walker
says.

The researchers are recommending that duct tape manufacturers reformulate
the glue to work better at higher temperatures, and that longevity standards
be developed for all duct sealants. Whether that will happen remains to be
seen; as of press time, manufacturers were studying the test results.

In the average house, 20 to 30 per cent of the energy used for heating and
cooling is lost through ducts.
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There is a different type of duct tape that works. It's black and actually
sold in better heating & cooling supply stores.

The original that I remember was available from drama supply stores called
gaffer's tape. It is of a different constitution and doesn't leave a residue
when you take it off after a week or 2.