However, some of my orchids are too big to fit into a case easily, even a full tower (it's too thin). Instead I am thinking of placing a large rad into a tray of water, that I mount as a shelf, with the pots on top of that. Therefore, if the pots leak, they drain into the water tray. The downside is that the comp is now connected to the tray, and not as portable without fitting some cut off valves.
Ok, that's an approach. (I think your solution would be cool looking, but not so cool when you have to clean the rad from dust, dirt and soil.)
I have some gardener skills, and my experience say that what you need for the orchids are heat and humidity.
For your computer you need chill and dry, witch you achieve using watercooling. (unless something starts to leak).
But when it comes to the orchid. You really don't want all that evaporated water in the same room as your computer. It will start to condensate as soon as something gets cool, probably also inside your computer. So my recomendation is to (in the case of not large enough case), build your own greenhouse, using plexi or similar. It wont be that hard, then use a pretty sealed system, air out low.
As long as you have a roof and not to large exhaust holes, then the water will condense and stay inside the box. You calculate the humidity water / m3. So it will be easier to have less m3 to humidify (new word perhaps).
And using some sort of tunnel into the box leading the hot air.
Then you both have hot air and humidity. If you have a greenhouse you won't need to arrange special evaporation devices, the stickyness of the air will take care of that. Also, you should build some kind of hatch incase the temp inside the greenhouse gets to high
Good Luck!