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>The mass analysis also doesn't appear to include the massive number of heat pipes you would need to transfer the heat from the chips to the radiators. For an orbiting datacenter, that would probably be the single biggest mass allocation.

And once you remove all the moving parts, you just fill the whole thing with oil rather than air and let heat transfer more smoothly to the radiators.

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Oil, like air, doesn't convent well in 0G, you'll need pretty hefty pumps and well designed layouts to ensure no hot spots form. Heat pipes are at least passive and don't depend on gravity.
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Mineral oil density is around 900kg / cubic meter.

Not sure this is such a great idea.

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Does using oil solve the mass problem? Liquids aren't light.
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I would wager that its lighter than:

Repair robots

Enough air between servers to allow robots to access and replace componentry.

Spare componentry.

An eject/return system.

Heatpipes from every server to the radiators.

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I would wager it isn't.
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First, oil is much heavier than air.

Second: you still need radiators to dissipate heat that is in oil somehow.

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