# Heat transfer help

1. Feb 11, 2004

### Rockdog

During a cold Chicago winter, a steady thermodynamic state has been reached in a small pond with a layer of ice on the top. The air directly above the pond is at -7 oC and the ground at the bottom of the pond is held at 2 oC. The pond holds a total of 342.1 m3 of water and has a relatively uniform depth (water and ice) of 1.1 m. Assume the thermal conductivities of ice and water are 0.40 cal/m/s/oC and 0.12 cal/m/s/oC, respectively.
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What is the thickness of the ice?

Ok, this problem appears tough. How do I start this ??

2. Feb 12, 2004

### Tom Mattson

Staff Emeritus
You know that the water-ice boundary is going to be 0o, because below that the temperature will be too high and the ice will melt. Using the data on thermal conductivities, you need to set up an expression for the temperature distribution in both the water and the ice. If you let y=0 be at the bottom of the lake, then your expression for the temperature distribution in the water will be in terms of y, and that for the ice will be in terms of 1.1-y.

You can equate the temperatures at the boundary (because you know they are both zero), and solve for y.