Melting Ice in Seawater: Cooling Steel on Seabed with 30kg Ice Block at -20degC

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To cool a 1kg steel piece on the seabed using a 30kg ice block at -20°C, the melting ice will absorb heat from the steel, which is initially at 12°C. The final temperature of the steel before the ice completely melts depends on the rates of heat transfer between the ice, steel, and surrounding seawater. A temperature gradient will form around the ice during the melting process, creating a non-equilibrium situation. If the steel is assumed to be a good conductor and not influenced by the seabed or seawater, the final temperature will be determined by the specific heat transfer rates involved. Ultimately, without reaching thermal equilibrium, the steel's temperature will not stabilize at 12°C until the ice has fully melted.
patfee
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Using a 30kg cubic block Ice at -20degC, I want to cool down a piece of steel which is resting on the seabed. The mass of steel is 1kg and the ice block is place on top of the steel.
The current sea temperature as well as the steel temp is estimated at 12degC

Assuming that the piece of steel is not "heated" by the seabed, nor the sea water, the ice melts while cooling the steel.

Question is till what temperature can the steel be cooled before the ice is completely melted and dissolved.

I'm kinda lost here on the thermodynamics, since the "energy out" does not equal the "energy in" as the unlimited amount of seawater volume will melt the ice without increasing in temperature.

can someone push me in the right direction please.

thanks
Patrick
 
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I am afraid you cannot find the answer from pure energy balance.
The answer will depend on the rates of heat transfer from the water to the ice and steel to the ice.
There will be a temperature gradient building up around the ice block.
During melting you have a non-equilibrium situation. Water, ice and steel have different temperatures. I understand that you want to know what will be the temperature of the steel (assuming it is uniform, which may be a good approximation for a good conductor) at the very moment when the ice is completely melted.
So the answer will depend on the specific rates of heat transfer.

Unless you want to wait until equilibrium is reached again and then everything will be pretty much 12 degrees.
 
I am looking for the 'nub' of this question. Is the fact that the ice and steel are on the sea bed relevant to the question? (You say the steel is not heated by the sea bed or the sea water).
 

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