In my experience, a 1:1 wall/channel ratio works best when getting down to these sorts of measurements. I did try 0.75mm fins with 1mm channels and saw a (small) performance loss. Going with 3/64 fins with 1/16th channels is the same ratio (just slightly bigger). However, because it is larger, it may still work fine and my findings may have been specific to 0.75:1 mm, and not be applicable to 3/64:1/16. One way to find out....
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