Comment by georgefrowny

Even diffusion into air is too slow for some use cases. The whole complaint of datacentres "consuming" water is due to heating it and dumping it back or evaporating it for cooling. This is done because mass air cooling is much less efficient and requires lots of energy to run the fans to force the air through the heat exchangers, which is also extremely loud. And that is, in turn, much more effective than passive radiation, even if you have a ~3K background.

The ISS ammonia-based active heat rejection system is Two units, each 13x3 metres in size and each unit can radiate 35kW.

So to radiate a "mere" 1MW, you need a quarter-acre of radiator. A square km per GW.

The engineering is obviously more than tricky because you have lots of plumbing, gigantic flat structures, and you can't have the radiators facing each other or the sun. Moreover, unlike the ISS, if you want to run the system at full whack the whole time on solar power, it's never in shadow. Which you presumably do want, as that's the putative point of the whole thing. You also can't be sending up service missions without the cost exploding even further, so hopefully you can design everything to last the 5 years despite each handful of fully loaded GPU racks requiring a structure somewhere around the size of the ISS, humankind's crowning glory of high technology, to support.