> As a result the most efficient way to cool a server is to put a water filled heat exchanger in front of it and let the computer's fans draw air through that into the chassis.

What standard are you using for "efficient"? Thermo-electric coolers are neat, but the last thing they are whatsoever is efficient from a power-usage stand point.

If you're doing chilled water cooling, the only real option to consider is a mechanical heat pump (e.g. the ones in a refrigerator), but even that is silly. Hardware doesn't mind being somewhat warm, and using ambient air for cooling is far more efficient then either.

There's a reason thermoelectric refrigerators aren't really a thing. Peltiers are horrible. Mechanical heat pumps easily achieve twice the efficiency or more.