Several of these 5 inch diameter Gold coated Copper mirrors shipped out to a customer today. The holes shown here are on the rear of the mirror and are the inlet and outlet of the internal water cooling. They are threaded for a 1/4″ BSP male connector. The internal cooling would be connected into the chiller water supply with the aim of keeping the mirror to with a degree or two of the programmed water temperature. People over complicate heat transfer, fluid dynamics etc and it is complicated I agree; but if the chiller you have is too small, the supply pipes are clogged up, and the water reservoir is empty, I suggest you worry about putting those right first. It is simple enough to estimate the rough value of water flow rate needed to keep a high power laser mirror operating temperature to within a degree or two of the optimum.
For example with a 10KW CO2 laser, and a 2% absorbing mirror ( i.e it needs a clean), The answer is a water flow rate of 1.5 – 2 litres a minute is about right. Given fluid dynamics and heat transfer is a hugely complicated subject, lets call it 2.5 litres a minute !.