A deep pool of water is initially at (4^{circ} mathrm{C}) and suddenly the surface is exposed to

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A deep pool of water is initially at \(4^{\circ} \mathrm{C}\) and suddenly the surface is exposed to a freezing front at \(-4{ }^{\circ} \mathrm{C}\) and remains so exposed for a long time.

Find the velocity of the freezing front as a function of time.

Determine the temperature profiles in both phases.

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