I was reading about the accretion of ice which describes the rate at which the ice layer above a lake thickens. It said that in order for the water just below the ice to solidify,heat had to be conducted by the ice from the ice-water interface to the ice- air interface. Now this amount of heat is equal to the latent heat of fusion(as the water is changing into ice). My question is why won't the ice itself melt while it conducts heat equal to the latent heat of fusion?
Heat flux isn't temperature. As modeled by Fourier's law, for example, 10 cm of ice at -10°C and -5°C at its top and bottom will conduct approximately 30 watts per square meter—30 joules per second over that area—while staying frozen all the while.
$\begingroup$ But in this case, the heat we are supplying is equal to the heat needed to melt it. And isn't it true that if you supply the latent heat of fusion, the object will melt? $\endgroup$– S123Feb 10 at 8:32
1$\begingroup$ The latent heat to solidify a millimeter of water into ice does nothing to 20 centimeters of already formed ice below the freezing point. $\endgroup$ Feb 10 at 14:53