# The air above the surface of a freshwater lake is

The air above the surface of a freshwater lake is at a temperature T4, while the water
is at its freezing point T, where T, < T,. 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
y T-TA
h 2K
PL
where h is the convection coefficient per unit area and is assumed constant while ice
forms, K is the thermal conductivity of ice, / is the latent heat of fusion of ice, and pis
the density of ice. (Hint: The temperature of the upper surface is variable. Assume
that the ice has a thickness y and imagine an infinitesimal thickness dy to form in time
dt.)
The air above the surface of a freshwater lake is at a temperature T4, while the water
is at its freezing point T, where T, < T,. 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
y T-TA
h 2K
PL
where h is the convection coefficient per unit area and is assumed constant while ice
forms, K is the thermal conductivity of ice, / is the latent heat of fusion of ice, and pis
the density of ice. (Hint: The temperature of the upper surface is variable. Assume
that the ice has a thickness y and imagine an infinitesimal thickness dy to form in time
dt.)