Yeah if you can get around the metal bad for fish thing, and find a heat conducting material that's fish friendly that'd be a cool idea. Isn't there a heat conducting silicone?
Algae won't be a problem in the dark pipes to your computer, but bio film will be. You don't want small tubing that could bung up on you.
As the guys said, copper bad.
General Rule is no metal touching fish water other than stainless steel. First because metals are generally bad for fish in a recirculating system if they manage to leach and second, because fish water can be corrosive and eventually give you leaks in metal containers/piping which I'm sure you don't want to happen near your computer system.
Also agree about the bio-slime being more issue than algae. Provided you avoid the metal issue, You would want to make sure the water sent through the heat exchanger is filtered and I would not use anything smaller than 1/2" tubing or clogging could become an issue.
Other than those challenges, it is a possibly useful idea.
The issue with copper is more to do with the recirculating nature of aquaponics. One trip through some copper or galvanized piping to get into your system isn't going to be a problem since the incoming water will not be acidic on it's trip in and it is only making the journey once.
Having any copper continually in contact with water in an aquaponics system is where the problem shows up. See, aquaponic water tends to be more acidic than tap water and the continual re-circulating of the water past or through anything metal that can corrode becomes a problem and would not be a good idea.
Now if you were to keep the computer cooling system on a closed loop and do the pex heat exchanger or something in the fish tank, that might work (might not be worth the trouble) but it may work. I would recommend longer loops in the water as heat exchanger, PEX is not the best heat exchange pipe after all.
about copper: if i use tap water from my house to fill the tank via copper plumbing, does letting the water sit a few days eliminate any problems the copper introduces?
I've kicked this same concept around in my head for a few years, but haven't built it as I don't have a water cooled computer.
Like they said above, you don't want to run aquarium water through your computer.
I would probably put the coil of plastic tubing in the sump - assuming you will have one on a 275 gallon tank (tanks that size tend to have sump filters). I would oversize the tubing in the sump so the water velocity slows down. It will stay in contact longer with the aquarium water, giving you more heat transfer.
This would probably work quite well, actually. I am going to assume a few things, your computer and aquarium are indoors & you keep the house at a fairly constant temperature. If you keep the house at 70, the tank will want to be that temperature too. So dumping some heat from the PC into the tank will give you the bump in temperature that you need. It probably won't heat the tank all the way up, but a traditional heater would take up the slack and it's thermostat will compensate for the differences in PC heat generated between sitting idle and playing video games.
It wouldn't be too terribly expensive to try, and it will allow you to discontinue the fans in the radiator. I would probably keep the radiator in the system, between the aquarium and the inlet to the water block so you can bleed just a few degrees more after the tank soaked up most of the heat. It also gives you a bit of a safety net in case the water level is low in the sump or something and it doesn't soak up all the heat available to it. Just turn the fans off, as they shouldn't be needed anymore.
Copper is a metal, and isn't present in the atmosphere, so it won't out-gas into the atmosphere like chlorine will by letting the water sit.
Here is the fact:
It takes 1 btu to increase 1lb of water 1 degree. ( if your fish tank would be fully insulated )
It takes about 940 btu to turn 1 lb of 32 F ice into 32 F water.
1 gallon of water = about 8.5 lb
1 watt = 3.41 btu
Lets say your CPU in your CP uses 125 watts per hour and you have a 100 gallon insulated fish tank.
125 w X 3.41 = 426.25 btu
100gal X 8.5lb = 850 lb
426.25 btu / 850 lb = 0.5 degrees increase per hour, if your fish tank would be fully insulated and if your fish tank would have no heat loss at all.
If you know the power consumption of your cpu and gpu, you could figure how many btu's you could add to your fish tank, but use food grade stainless steel tubing ( usually 304 or better use 304L (lower carbon content) ).
Stainless steel is made with different materials for different applications.
The above calculation do not reflect any heat losses, which you would have in a fish tank and / or growing beds.