# Projected temperature rise of insulated ice block

## Main Question or Discussion Point

OK, I am attempting to calculate the reuirements for creating a 3-ton, 90-day air conditioner using nothing but ice and an exchange loop between that ice and a heat exchanger in my house. I can calculate everything except knowing how much I can practically insulate a storage vessel, and, given that practical maximum insulation, what its given cooling loss, or more accurately, BTU absorption, would be each day during the lag time between when the coldest part of winter ends and air conditioning season begins, as well as the daily loss during the air conditioning season.

Assume an approximately 40,000 gallon container of water that is 40ft. x 40ft. x 14ft. tall. Alternatively, I could use underground storage tanks like those at gas stations. That tank would be 12 feet in diameter and about 50 ft. long.

Next, assume that I can freeze that water and that I can lower the temperature of the ice to 0 degrees F via the use of an ethylene glycol loop and simple outdoor heat exchanger run during the coldest parts of our winter (We can see -10 degrees F at times). Assume that I can freeze the water in the vessel without damaging it.

Next, assume that I can insulate the tank equally well on all sides, whether it is rectangular or circular, and that the tank is buried 12-14 feet underground, well below the frost line, and I am assuming deeply enough that I can tap into the 52 degree F ground temperature year round.

My question is this: Using conventional insulation technologies such as sprayed-on foam, fiberglass batting, reflective thermal blankets, etc., what would be the least amount of heat energy in BTU's that the ice block would absorb each day? In other words, I want to keep the ice block as cold as possible for a couple of months between the time winter ends and the air conditioning season begins. Let's also assume that the vessel, whether the equivalent of an underground swimming pool, or a fiberglass storage tank, has essentially no insulating value on its own.

I realize this is a subjective question, since one could say something along the lines of "spray the foam on 3 feet thick" or "use 10 feet of fiberglass batting around the holding tank", but I am trying to get an achievable minimum heat absorption (and hence loss of cooling capacity) by the ice block each day.

Thanks for any help.

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Work out the surface area and the temperature difference (easy) then from the R values of normal building insulation materials you can see what heat loss you will get for different thicknesses.

It's a bit more complicated to get the total heat loss because the rate drops as the tank heats up and the temperature difference is reduced - but it's easy to get the worst case initial loss rate.

see http://en.wikipedia.org/wiki/R-value_(insulation [Broken])

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Exactly the reference I was looking for. Thanks for the link.

A day-ton of refrigeration (sometimes incorrectly called a ton of refrigeration) is the amount of refrigeration produced by melting 1 ton of ice at a temperature of 32°F in 24 hours. For example, a 1-ton air-conditioner can remove as much heat in 24 hours as 1 ton of 32°F ice that melts and becomes water at 32°F. So, a "1-ton" air-conditioner would have a cooling rating of 12,000 Btu per hour. Carnot cycle "efficiencies" (ratio of heat removal (BTU/hr) to power input (BTU/hr)) can be greater than 1 for refrigeration systems. (http://web.me.unr.edu/me372/Spring2001/Refrigeration Cycles.pdf).

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A day-ton of refrigeration (sometimes incorrectly called a ton of refrigeration) is the amount of refrigeration produced by melting 1 ton of ice at a temperature of 32°F in 24 hours. For example, a 1-ton air-conditioner can remove as much heat in 24 hours as 1 ton of 32°F ice that melts and becomes water at 32°F. So, a "1-ton" air-conditioner would have a cooling rating of 12,000 Btu per hour. Carnot cycle "efficiencies" (ratio of heat removal (BTU/hr) to power input (BTU/hr)) can be greater than 1 for refrigeration systems. (http://web.me.unr.edu/me372/Spring2001/Refrigeration Cycles.pdf).
Yes, my concern was calculating the apparent duty cycle of my 2 3-ton AC units via electrical consumption, efficiency, etc. to try and get a rough idea of how many BTU's per day I am removing from my house, e.g., if my AC units total 6 tons and have a 40% duty cycle than I am looking for a formula that would consider the energy efficiency of the AC units and such, to see how much energy of that "apparent" 2.4 day-ton-needed energy use is going to the AC units and how much is really being pulled out of my house since no AC unit is 100% efficient, like everything else.

I can't just use my electric bill because it does not differentiate between watts used for AC units and regular use, and I also work out of my home with several servers that not only consume power and generate heat load for the AC, but they also skew my electric bills up because they are in use during winter months when I could normally say "ok, my energy bills for November, December, January and February average \$200 per month less than my bills for mid-May through mid-September". I can't even roughly remove my electrical usage that way and then say that my AC units are using 2000 Kwh per month at 10 cents per Kwh.

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