The ability to cool heat this way would allow scientists to pack more processing power into a smaller space or even fatten up otherwise flat computer chips into block-like structure. Right now that can't be done, because chips rely on circulating air to stay cool and piling processors on top of each other traps too much heat.
The "electronic blood" cooling system could save on energy costs, too. Google, for example, spends millions of dollars on air conditioning bills to keep its data centers cool, which expend enough energy per year to power 200,000 homes.
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Ruch and Michel's system for cooling has a way to go. There's the matter of choosing a workable electrolyte and fabricating chips with tiny channels in them.
But more than that, the project is part of an effort to get computers to work the way a brain does. Brains are pretty efficient - most of the energy a human brain uses goes to processing information. Only a small fraction of the energy in the brain gets turned into heat. That isn't true of computers.