Air flows from places of higher pressure to those of less.
I propose to look at a very simple setup which works for short lengths of pipe:
- Choose if you want a radial fan of a direct passing fan. get one, measure the intake and the outlet side holes
- cut a fan inlet-sized hole directly into the back of the enclosure.
- mount your fan onto it, most likely with some kind of foam to keep the airstream in.
- get a flexible air vent hose (I have seen ~$10/10€ for a 100mm one) and measure the inner diameter.
- print an adapter from the fan outlet to the vent hose.
- mount the adapter, then the hose, use clamps to secure it.
- lead the air vent hose to the window and out or into a wall through.
Even if the airstream doesn't seem to be very fast, you could test it with smoke to see that it will blow out the air on the other end of the hose. The large diameter lets quite some air out with just a "gentle" airstream. This is not a very efficient system though, as we build up a pressure in the pipe the fan wors against.
To gain efficiency, we should move the fan away from the machine and closer to the outlet. That means, we need to increase the fan power. If you can get your hand on, for example, an in-pipe motor, that would be a solution, but usually an expensive one. If you are good with electrics, you could use a blower from an electric cloths-drier. You might get a clothes-drier to strip the motor from really cheap, for example from a renovation, recycling facility or Craigslist, e-bay or any other auction or classifieds-page.
Or you build your own from an electric motor (you could use your machine's power supply here), a housing made from wood and an impeller, which you can get as a "Dryer Blower Wheel" spare part for under $50. If you connect the power for its motor through a regulatable resistor, you could even control its spinning speed.
To cope with the suction, we need to use aluminium flex pipe on the arm between machine and exhaust.
If you want to go industrial like if you want to run a laser cutter, you will need to go industrial in the vent size too. You use pretty much the same diameter aluminium flex pipe and a much stronger motor than the drier one, and you don't mount the motor directly to the machine back but somewhere downstream as it's rather loud. For what to look for in that case, I found a very good article here. Note though, that this is not a small setup, but you could possibly vent a whole batch of printers through one pump, using some airstream cutoffs to control which ones get currently evacuated.