[esterna]

Capillaries cannot defeat the divergence theorem: If you have a volume where heat is produced but the temperature does not increase, the heat has to leave via the surface. It is true that the surface area available to diffusion can scale at any rate (eg. Menger sponge), but the heat still has to leave the volume via its boundary. In the case of capillaries, this is by convection which means that the product of coolant temperature differential and flow speed has to scale.

[don_esteban]

Thanks, this is what I wanted to say, but perhaps I was a bit too terse.

Perhaps a good coolant with a good flow speed can gain you a decent constant factor versus a classical heat sink, but once the third dimension of your chip gets bigger, you will hit a barrier. Just do the math.