# What is the ideal theoretical construction for an insulative box to keep my frosty beverages frosty?

What is the ideal construction for an insulative box to keep my frosty beverages frosty? I am interested in finding the theoretical maximum as well as the practical maximum.

I was sitting on my back porch drinking a cold beverage and observing how quickly the ice in my cooler was melting. I began wondering what the ideal insulative container for my beverages might be. I know I could just go buy a Yeti but I was having fun with the thought experiment so I got on YouTube and began watching some lectures on heat transfer, fluid dynamics, etc.

I am NOT a physicist or mechanical engineer and so while the math all makes sense to me I don't have the background to fully flesh out the optimal design.

Here are some of the things I'm not sure about:

• Should the inside of the box be reflective (lower emissivity) or something else?
• Should the walls be "solid" insultation or have narrow air gaps where each side is lined with reflective material.
• If there are air gaps do both walls need to be reflective or does just the cold side need to be reflective to insulate from radiative heat transfer. What would the optimal surface be for the heat side)
• Do reflective surfaces lose their radiation reflection properties if sandwiched against other materials.
• Do the answers change as the size of the box changes (for instance is there a different answer if my box is the size of a boxcar or something)

Here are some of the constraints:

• inside volume of box is one cubic meter
• Wall thickness of no more than 6 cm
• Direct sunlight exposure
• Outside temperature 30°C
• Container no more than 50% full of ice at -18°C
• 24 pack of standard sized aluminum canned beverages pre-chilled to 4°C
• Minor error: "inside volume of box is one square meter". Volume would use units of cubic meters. Commented Jun 17, 2023 at 23:15
• Transistor...you mean we can't measure volume in two dimensions? (thanks!) Commented Jun 18, 2023 at 0:08
• how do you get ice to -18°C? Commented Jun 18, 2023 at 0:55
• Optimal design ie greatest internal volume for minimal exterior surface area (ie that gaining heat) will be a sphere. Commented Jun 18, 2023 at 8:23
• @Jstola: put it into a container at $-18^\circ \mathrm C - \epsilon$, and wait a while. Commented Jun 20, 2023 at 22:15

## 1 Answer

There are two paths to the answer, as follows:

First of all, regarding emissivity and so on, radiative heat transfer scales as the 4th power of absolute temperature so for temperatures near room temp you needn't worry about it. All you want is a cooler box material that has the lowest possible thermal conductivity and the thickest possible walls.

What does this mean in practical terms? Well, the cheap answer is to build a box out of styrofoam with 3" thick walls and preload it with crushed ice to surround your refreshing beverages. This is how things that must be kept cold like special medicines are sent through the mail or via FedEx. Thicker than 3" is considered a waste. In fact, these can be bought for a few dollars each, so why not just buy one?

The physics answer is to build a cylindrical container with double walls and a few microns of sputtered aluminum on the inside surface of the outer cylinder and on the outside surface of the inner cylinder. Provide a narrowed-down neck through which individual cans of refreshing beverage can be loaded along with ice. Draw a hard vacuum on the inter-cylinder space, and plug the neck with a cork made of real cork. In fact, this is called a dewar flask and can be bought for several hundred dollars, so why not just buy one?

• As opposed to a Dewar's flask, which is a small metal bottle full of name-brand whiskey that you can keep in a pocket. Commented Jun 20, 2023 at 1:52
• @TimWescott, yes yes, and it has its own unique uses, plus it can be bought for a few tens of dollars, so why not just buy one? -NN Commented Jun 20, 2023 at 3:43
• @TimWescott, where are you in Oregon? I am in Corvallis. Commented Jun 20, 2023 at 14:57
• Outside of Portland. Commented Jun 20, 2023 at 22:15