okay logic, but flawed. In your fire example, the fire is many hundreds of degrees or more. Standing 10ft from the fire, you most likely get most heat from the radiated heat, not by air flow.
The copper pipe now has a huge temerature delta, it only needs to get to 60 or 70 degrees before it gets too hot to hold. The end in the fire though will probably be melting.
The issue is this. Your case is maybe 20-25 degrees (due to ambient temperature. You want your cpu under 60 degrees ideally (not overclocked) or way lower to overclock.
For heatsinks to work, the surface area must be as physically (thermally) close to the heat source as possible.
Look at your example - even if you dip the copper pipe in liquid nitrogen, is it going to cool the fire?
Heatsinks work to expand surface area as rapidly as possible as close to the cpu (heat source) as they can. They need a good base to act as the heat spreader, and then usually many fins from the base to dissipate the heat into an airflow. Your idea is okay, but it needs work.
Either:
Build/modify a PC such that the cpu can be strongly attached to a huge, highly thermally conductive sink (not by 8 inches of copper) such that that sink also has very good cooling, or increase the surface area and thermal conductivity of the materials that are close to the cpu.
You could, theoretically, build a sink larger and more effective than, say, a swiftec 462, however it would be custom for your board and be a devil to prevent cpu crushing. Potentially you could go to very low levels of active cooling even on an overclocked Athlon.
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