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If I want to purify phosphours by zone melting.
i.e., purification of pure phosphours fomr keff<1 materials.
Then we need to apply a heater to heat the rod of phosphours.

How can I find the optimal radius (least energy, most area ) melt?
Assuming the room tempreture is 25 deg C and the melting point of phosphours is 44.1 deg C.

I have been studying the heat equation.
I am thinking if this link can help.
http://www.tufts.edu/as/tampl/en43/lecture_notes/ch4.html


Thanks