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I came up with this too (exact setup, only four long in the campaign) so we can all say that great minds think alike and this has to be one of the best designs for this!
You can see it in the gif, two of them aren't even running.
As you can't supply enough sand to keep this running with just three titanium conveyors.
Also this is all expecting that the input is uninterrupted.
And a junction overflow gate chain is not faster than a titanium conveyor, at most same speed. (I did just test this.) If you wanted speed you would use an inverted sorter+overflow chain which is nearly instant (few ticks of deviation).
[h1] Compactness [/h1]
5x22 (110, not including input and output) isn't compact for 11 silicon smelters, 10 tiles for a single smelter.
A design based on the one I posted that I just made is 5x6 (30, including input but not output) and has four smelters, is 7.5 tiles per smelter. That is 35% smaller footprint per smelter.
[h1]Numbers[/h1]
Craft time of the silicon smelter is 40 (around 0.66666... seconds) and you got 11 of them.
Every 0.666666... seconds it uses 11 coal and 22 sand, a single titanium conveyor can movee around 12 items per second (this is excluding the deviation caused by delta time).
While using 0.50 power per tick per smelter (that is 5.5, admittedly you can run this with six combustion generators).