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How to find the temperature of meniscus during capillary filling

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Hello,            I am trying to simulate 3d rectangular capillary filling using Leve set and two-phase flow, but simultaneously heat or (put at T+Tref) the one wall of the capillary, everything including (meniscus position(ls.Vf1), velocity, etc.) I found easily. The problem is, I am not able to calculate/plot the temperature profile along with the meniscus at some instant (look at attached figure). Thanks in advance!


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