I'm trying to figure out how to get started in calculating how much ice I would need in pounds, to cool 25 cubic feet of water. The water's initial temperature is 80 degrees F, and the ice is assumed to be 30 F. How or what formulas could help me figure out how much time it would take a certain amount of ice to cool the water to 55 degrees F. Any advice would be greatly appreciated. This is not my main problem, but it is the primary step in solving and developing my project. I'm pretty confident on how to conduct the rest of my reseach, but I'm just stuck with this thermodynamic problem. Thanks again.
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How much ice would I need 3
- Thread starter Mook
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3
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To solve the steady state problem from temperature initial to temp final, you should be able to get a reasonable answer by just doing an energy balance. Check any college physics book for some good examples. Equations will something of the form:<br>
<br>
heat from water=heat to ice + heat/losses to surroundings<br>
where heat = specific heat*mass*(change in temp)<br>
<br>
Assume all the heat in the water goes into the latent heat of melting the ice. Some things to consider 1) will all your ice be converted to water or do you want some solid ice left once equilibrium achieved? the calculation will differ depending on the final state desired of the ice(i.e different specific heats depending on phase of liquid). 2) This will also assume all heat makes it into melting the ice (i.e. perfectly insulated on all other surfaces) and will predict a non-conservative amount of ice required. You may want to account for some heat loss to the surroundings.<br>
<br>
The transient problem is much harder(i.e. time to reach equilibrium). You might be able to scour some heat transfer books or tech journals for some applicable correlations. If you can find one, it will give you a nice closed form solution in the form of an equation. You don't give specifics on your setup, but look into the applicability of using the 'lumped capacitance' model for heat transfer transients model. This model basically assumes your entire system is at a unform temp during the cooldown. Check some heat transfer textbooks for more info. There should be some clearly stated limitations to the calculations. If you fall within them, the calc will give good approximations. If no closed form solution exist, you are stuck with some form of computer analysis. If you access to a commercial heat transfer software package, go have some fun and ignore everything I have said
If not, you can try doing your own. A finite difference approach is good for two-dim problems with reasonable accuracy. It can even be programmed without alot of difficulty in a spreadsheet (each node is a cell in a spreadsheet). Or if your quick with MATLAB it could be done there as well. Again, check a heat transfer textbook. The last hurdle in heat transfer problem is the convection coefficient (h). This can be the hardest part. Even if you have a cray computer at you disposal, h can be difficult to determine. Without experimental determination, you will be required to first assume the mode of convection (forced or natural or both) and then try to find a correlation that predicts the h value for your given geometry.<br>
<br>
Good luck and post back if you have followup questions.
<br>
heat from water=heat to ice + heat/losses to surroundings<br>
where heat = specific heat*mass*(change in temp)<br>
<br>
Assume all the heat in the water goes into the latent heat of melting the ice. Some things to consider 1) will all your ice be converted to water or do you want some solid ice left once equilibrium achieved? the calculation will differ depending on the final state desired of the ice(i.e different specific heats depending on phase of liquid). 2) This will also assume all heat makes it into melting the ice (i.e. perfectly insulated on all other surfaces) and will predict a non-conservative amount of ice required. You may want to account for some heat loss to the surroundings.<br>
<br>
The transient problem is much harder(i.e. time to reach equilibrium). You might be able to scour some heat transfer books or tech journals for some applicable correlations. If you can find one, it will give you a nice closed form solution in the form of an equation. You don't give specifics on your setup, but look into the applicability of using the 'lumped capacitance' model for heat transfer transients model. This model basically assumes your entire system is at a unform temp during the cooldown. Check some heat transfer textbooks for more info. There should be some clearly stated limitations to the calculations. If you fall within them, the calc will give good approximations. If no closed form solution exist, you are stuck with some form of computer analysis. If you access to a commercial heat transfer software package, go have some fun and ignore everything I have said
If not, you can try doing your own. A finite difference approach is good for two-dim problems with reasonable accuracy. It can even be programmed without alot of difficulty in a spreadsheet (each node is a cell in a spreadsheet). Or if your quick with MATLAB it could be done there as well. Again, check a heat transfer textbook. The last hurdle in heat transfer problem is the convection coefficient (h). This can be the hardest part. Even if you have a cray computer at you disposal, h can be difficult to determine. Without experimental determination, you will be required to first assume the mode of convection (forced or natural or both) and then try to find a correlation that predicts the h value for your given geometry.<br><br>
Good luck and post back if you have followup questions.
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