The point here is that water tends to build impurities over time. The simple fact is that these impurities are from impurities in the water (both to start with and as it oxidizes parts in the system. The easiest way to remove the impurities is to turn them from solids that drop out of solution back into salts. In order to do this, we alter the pH of the solution in the system.
So, we're looking just to remove the stuff that has fallen out of solution. This means that the lower the pH the faster you'll clean. At the same time, the faster you clean the more your acid has the chance to begin etching the metal components in the system. I'm assuming the science here is less than interesting, so you'll want to know what chemicals to use. Acids that are easily available, from strongest to weakest, are as follows:
Muriatric - Gardening store - dillute Hydrochloric acid
Battery Acid - Car battery - Sulphuric acid
Vinegar - grocery store - Acetic acid
Vitamin C - grocery store - Citric acid
As hydrochloric tends to take a ton of precautions in order to mix, I'd shoot for either white Vinegar or Vitamin C pills. Both may require multiple flushes throughout the system in order to full dissolve crap (assuming it is very dirty). If you're looking for something very quick dillute muriatric acid into tap water at about 20:1 (this is based on concrete whitening solutions, you may want to increase the water to acid ratio higher if you're not comfortable), add about a table spoon of table salt (NaCl) per 2 liters of water, and run that through the system. The table salt will act as a buffer, while the acid easily eats away mineral build-up. Anywhere between 30-40 minutes later, and you'll be able to drain the system. Flush and refill the loop with clean water at least twice. Once all of that is done the metal components in the system should be spotless.
Cleaning the film that develops on the tubing is foolish. It will be much easier to scrap it, and start new.
I cannot speak to this process for your hardware, but it's worked crazy well on plenty of cars. The heated wash that oil change places offer doesn't hold a candle to better living through chemistry...