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he air above the surface of a freshwater lake is at a temperature T A , while the water is at its…

he air above the surface of a freshwater lake is at a temperature TA, while the water is at its freezing point Ti, where TA i. After a time t has elapsed, ice of thickness y has formed. Assuming that the heat, which is liberated when the water freezes, flows up through the ice by conduction and then into the air by natural convection, prove that

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where h is the convection coefficient per unit area and is assumed constant while ice forms, K is the thermal conductivity of ice, I is the latent heat of fusion of ice, and p is the density of ice.

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