The melting of water initially at the fusion

Chapter 5, Problem 5.42

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The melting of water initially at the fusion temperature,Tf?0C, was considered in Example 1.6. Freezing ofwater often occurs at 0C. However, pure liquids that undergo a cooling process can remain in a supercooledliquid state well below their equilibrium freezing tem-perature, Tf, particularly when the liquid is not in con-tact with any solid material. Droplets of liquid water inthe atmosphere have a supercooled freezing tempera-ture, Tf,sc, that can be well correlated to the dropletdiameter by the expression Tf,sc??280.87 ln(Dp)in the diameter range 10?7?Dp?10?2m, where Tf,schas units of degrees Celsius and Dpis expressed in unitsof meters. For a droplet of diameter D?50 ?m andinitial temperature Ti?10C subject to ambient condi-tions of T???40C and h?900 W/m2?K, comparethe time needed to completely solidify the droplet forcase A, when the droplet solidifies at Tf?0C, andcase B, when the droplet starts to freeze at Tf,sc. Sketchthe temperature histories from the initial time to thetime when the droplets are completely solid. Hint:When the droplet reaches Tf,scin case B, rapid solidifi-cation occurs during which the latent energy releasedby the freezing water is absorbed by the remaining liq- uid in the drop. As soon as any ice is formed within thedroplet, the remaining liquid is in contact with a solid(the ice) and the freezing temperature immediatelyshifts from Tf,scto Tf?0C.