Re: Ice versus water in cooler?

Robert Bonomi wrote:
In article <48e83fba$0$10448$c3e8da3@xxxxxxxxxxxxxxxxx>,
bill horne <redydog@xxxxxxx> wrote:
Robert Bonomi wrote:
In article <04435c96$0$29452$c3e8da3@xxxxxxxxxxxxxxxxx>,
bill horne <redydog@xxxxxxx> wrote:
Robert Bonomi wrote:
In article <0442874a$0$29442$c3e8da3@xxxxxxxxxxxxxxxxx>,
bill horne <redydog@xxxxxxx> wrote:
But I have a variation on the question for the experts:
Start with 12 beers in a cooler filled with new ice.
The cooler is sitting under a juniper at a flatspot in the UT desert.
Bottles will be removed periodically at irregular intervals. For this situation, figure that 3 bottles are removed every 24 hours.

The object is to keep the beer at 32-33 degrees for as long as possible (think days). The primary purpose of this is to extend the time between trips to civilization to get ice.

Which will do that? Draining the water every now and then, or never draining the water?
"As asked" this one is _simple_ to answer --

If you are _not_ adding any fresh ice to the situation, do =NOT= remove
any of the water. The larger the 'thermal mass' at the desired temperature
is, the longer it takes for a fixed rate of heat absorption (that which gets
in from the outside world) to raise the overall temperature by a
given amount.
If the water has warmed up "some" -- all the ice has melted -- and you're
having to re-stock with ice, the situation is _way_ different. (And *MUCH*
more complicated to answer :)
The heat gain will be through the walls of the cooler. What does theory say about the rate of heat gain with the cooler walls being completely in contact with cold water, as opposed to the cooler walls being partly in contact with ice and partly in contact with cold air?
You have the same amount of heat 'percolating' through the walls of the cooler in either situation. Thus, for the same 'thermal mass' inside the cooler, the overall heat absorption will be the same.
Why? I thought the rate of heat gain (btu's/hr) depended on the temp difference between the inner and outer walls. If, as you say below, with just ice, there'll be a slightly higher internal wall temp. That means heat gain will be slower.

Seems contradictory, doesn't it? <grin>

The -average- temperature of the inner surface will be slightly higher, yes.
But heat flow is not linear with temperature difference. The 'colder' spots
on the wall pull more heat out of the wall than the warmer spots retain.

In 'fancy math' terms, a linear average of point on a non-linear function does not accurately reflect the behavior of the function. :)

If you have a mix of ice and water, you'll have a uniform temperature across
the inner surface of the cooler -- effectively the same as the water temp.,
and a constant temperature internally until all the ice has melted.

If you have 'just ice', you'll have ("slightly") non-uniform temperatures at different points on the inner surface of the cooler, with a -slightly-
higher internal wall temperature. *But*, as soon as the situation stabilizes, the rate of heat gain into the interior of the cooler is the
same as the ice-and-water case.

Lastly, "exactly" what happens at the inner surface of the cooler is irrelevant to the cooling of the beer itself -- because the beer is only
in contact with the ice, or ice-and-water, not the walls of the cooler.
The beer will cool faster, in contact with ice-and-water, than it will in
contact with '32F' ice, due to the better thermal coupling because of the
larger contact area.
How fast the beer cools is not relevant in this situation. The goal is not to cool the beer faster, but to keep the beer at 32-33 - or less - as long as possible.

In any case (half a case in this situation), you seem to be saying that as a result of slightly higher internal wall temps with "just ice", the internal (or beer) temp will stay at 32-33 - or less - slightly longer with just ice (water drained periodically). Is that what you're saying?

Nope. A slightly different path during the initial cool-down, but once
things stabilize, at roughly 32F throughout the interior, you have a
"difference that makes no difference".

Pulling water out is significant _only_ if all the existing ice has
melted, internal temperature is above 32F, _and_ you are adding new
ice. If all those conditions are met, you want to minimize the amount of 'excess' water that needs to be cooled back to 32F by the newly added
ice.

However, draining the water necessarily sucks in some hot ambient air, the effects of which haven't been addressed.

Letting in 1 cubic foot of 96F air is the rough equivalent of a 2F change
in the temperature of _one_ 16 oz beer. Of course, to let 1 cu.ft of
air in, you have to take out 7.5 gallons of water (62-1/2 lbs worth).

Spread that over a 12-pack, and it's a 1/2 degree change per beer.

Assume you've got 5 times as much ice / water as beer, and it works out to a 1/12 degree change. To counteract that increase, you have to melt ice that weighs 1/10 of 1% of the weight of the all the stuff (beer,
ice, melted ice) inside the cooler

Maybe it effectively neutralizes the slight gain obtained from slightly higher temp internal walls? Or maybe it doesn't.

Hey GB. Do you see why that, in my pondering of this in the past, I said the hell with it, and shifted to sloshing and soggifying as the determining variables for draining or not draining?

I suspect that I'm going to learn nothing this time around that will cause me to replace practical considerations with thermodynamic theory considerations.

You want to start out with 'just ice' (and optionally beer) in the cooler. Putting the beer in at the 1st instant, or letting the cooler
stabilize for several hours first makes no difference.

1) If you add stuff to the cooler, you may have to remove some water to make room for it, obviously. :)

2) If you have a stabilized (32F) mix of ice and water, do _not_ remove
water 'just' to be removing it. The excuse for violating this is to
comply with #1, above.

3) If all the ice has melted, and you are adding ice, *then* you want to
want to remove 'excess' water, but -only- the excess.

If I've absorbed all that correctly, it looks like I can just continue to base draining on sloshing and soggifying and space considerations, and draining or not draining won't make much difference to long-haul cold or ice life.

But I do one other thing when I'm out actually flatspotting - I replace last night's removed beer the next morning, after the cold night has pre-cooled it some.

--
bill
Theory don't mean squat if it don't work.
.

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