If by stringing them together you mean in series, think parallel instead. The temperature difference between the water and air will be greater over a larger surface area in parallel than in series.
Interesting thought with the chimney... I have had a similar notion but less passive. Some thought experiments and validation by tinkering have led me to believe that most fan shrouds are way too close to the radiators. For purposes of footprint, I figured going vertical would be best. I have been contemplating a vertical duct of about 3 foot height with the radiator mounted about 1/3 of the way up the length with a pair of side-by-side fans exhausting upwards about 1 foot above the radiator.
Another notion I am kicking around has parallel runs of 1/4 ID copper tubing run back and forth several times in a long narrow rectangular box, open at the bottom, vented at the top with some quiet fans to aid convection. I suppose that's a chimney of sorts, too. The idea was inspired by a Xice passive cooler that used plastic tubing wound around a frame in a convection box to do a barely adequate job for a single CPU. I am thinking it could be built into my desk as a combination backsplash/modesty panel.
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