Portable air conditioner exhaust through door

If there is no other convenient place to exhaust the hot air the door could be used. I would look at dog doors IE cutting a hole and adding a flange and put the hole in the center area that a dog door would go. If you plan on making a panel to crack the door open and blow the hot air outside that would work but not as well as through the door. Remember the system is blowing hot air out so there will need to be a place for fresh air to enter.

To quote from Consumer Reports,

Unlike a window air conditioner, all the mechanical parts of a portable air conditioner are sitting in the room you’re trying to cool. This contributes to the noise and less-than-capable cooling, as the portable unit is using conditioned air from the room to cool the condenser and exhausts the hot air out an ungainly exhaust hose that resembles a dryer vent. That creates negative pressure causing unconditioned warm air from surrounding rooms or outdoors to be drawn into the room you’re trying keep cool

So unless the rest of your house is cool, in which case a box fan will do the job, you're not going to get much cooling in your laundry room.

In sum: yes, you can install a portable unit, and it will operate. No, it won't do much good.

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