Q$6$ Relevance: Solidification dynamics $($metallurgical system$)$ A saturated liquid is initially at its freezing temperature Ty$.$ At some time, the face is maintained at a constant subfreezing temperature To $($To Ty$).$ As heat is removed from the liquid, it freezes. If the freezing front at any time $t$ is at $x,$ and if it can be assumed that the uniform liquid remains at $7,$ throughout the process, what the temperature profile $T(x,t)$ in the solid phase?

Extend this problem for the two$-$dimensional scenario where the freezing point is at $(x,y),$ what it the temperature profile $T(x,y,t)?$

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