Does pumping water at a faster rate have an effect on cooling?

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It makes virtually no difference unless you have a very low flow rate.

It should be a easy thing to test.

Set the pump to full power.
Run a cpu intensive benchmark until everything is up to temperature.
Then slow the pump down and see if there is any temp change.

I bet it's less than 1 degree from almost silent to full power with most modern pumps.
This, I tried. I got more from restarting the pc.
 
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The only real benefit of faster flow is to make the flow turbulent instead of laminar which helps with heat transfer to the fluid as you remove the static boundary layer at the surface of waterblocks and also the radiators.

http://www.hrs-heatexchangers.com/resource/comparison-laminar-turbulent-flow/


This.

However with what we deal with I don't think it'll matter. When a fluid goes into a block of some sort the water becomes so turbulent that the chances of their being any laminar flown within a loop (where heat transfer is occurring) is minimal.

It is just a case of turning the pump to a reasonable noise level and keeping it like that. I use Speedfan to control my PWM D5, set at 50% and never touch it.
 
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