How Quickly Does Ice Form on a Pond at -10°C?

[ice87]

difficult problem, need URGENT help

A small pond has a layer of ice 1cm thick floating on its surface. (a) If the air
temperature is −10C, find the rate in cm per hour at which ice is added to the layer. The density of ice is 0.917g/cm3 and its thermal conductivity is 0.592 W/mK. (b) How long does it take for a 20cm layer to build up?

I think this problem requires the use of integrals. I don't know how to do that. I don't understand this problem AT ALL, so please help me out here.

 

[ice87]

no one??

 

[hotvette]

Some things to consider to get you thinking in the right direction.

1. Where is the ice being added? Bottom, because that's where the water is.

2. Why is ice added to the bottom? Because the temperature at the ice/water interface is below freezing.

3. What is the temperature of the ice/water interface? Depends in the heat transfer from the top of the ice through the ice to the bottom of the ice.

4. Consider a small thinkness of ice, dt forming at the ice/water interface, so small, in fact, that it has the same temperature as the ice/water interface.