Heat transfer and diffusion of particles
A lake freezes
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The temperature of the air is and the temperature of the liquid water is .
We give the massic latent heat of fusion of ice , its density and its thermal conductivity .
The thermal capacity of ice is supposed to be negligible.
Let be the height of ice at time . At , .
Establish the differential equations which have and as solutions.
Solve them and determine .
The heat equation in the ice :
So if we suppose that is almost :
We make the approximation of the quasi-stationary mode.
The heat flow in the ice is due to its solidification, that is to say, between and :
That is to say :
After integration :