ductshvac
In remodeling my bathroom I had to convert a 6"x6" square duct underneath the floor joists in the basement to flex so I can get around my new toiler drain. I cannot for the life of me find a 6"x6" square to 6" round transition anywhere.
Do I need to fabricate one myself? I don't know what to do.
I am aware that a 6" round duct is smaller than 6"x6" square by ~20%. It feeds the foyer which I have kept the damper nearly closed anyways because it gets very hot/cold in that location.
Duct Tape is good for a lot of things, except duct work! It will eventually dry up and pull away from the heat in the vent.
I would bend/dent one of the ends slightly so that it will fit easily inside of the other. Then I'd secure it with proper HVAC foil tape, followed by a clamp around it.
Foil Tape
(source: homedepot.ca)
Metal Gear Clamp
(source: homedepot.ca)
It is difficult to properly cool two spaces with vastly different heat loads and only one thermostat.
Assuming typical computers and monitors and two users, you probably have about a kilowatt of heating or 3400 BTUs per hour.
Rather than run ducts, have you considered a dedicated cooling unit for your office? You can go with a small window unit. Even the smallest one is 5000 BTU and only uses about 500 watts when running. That's just a few pennies per hour and even that is offset by the reduction in load on the main unit. With the thermostat in the same room, its load response will be much better and the temperature extremes you have been suffering with will be eliminated. Plus you can turn it off when no one is there and save energy that way.
Lately my thinking is that ducts are basically parasites and efficiency goes up when the heater/cooler is in the same room as the load. In the past, the equipment cost was lower with a shared unit but operating costs (energy) have gone up a lot (and will continue to go up) and that could change the equation on selecting shared or dedicated equipment. Comfort will always be superior with dedicated equipment.
Best Answer
They do exist. Best bet is probably to contact a local sheet metal shop, if they don't have one they can build one. Expect this to cost in the tens of dollars range.
You could potentially cap the end, and then use a round duct takeoff. The downside is it will restrict flow to the vent because of the abrupt end and sharp angles internally.
There's another type of side takeoff that is rectangular, and if you can find one you could potentially modify it yourself using a couple strategic cuts and copious amounts of foil tape.