I want to know the relation between temperature heat conductivity and time for a pcm to melt completely?
You need to solve the Stefan problem. There are lots of literature references in Thermal Energy Storage by Dincer and Rosen.
http://au.wiley.com/WileyCDA/WileyTitle/productCd-0470747064.html
The Stefan problem is a simplified solution of the one dimensional heat equation. In reality it depends on your setup, because convection may enhance your heat transfer.
Experimental, then small ax + b law
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