Quality achieved of vacuum is important, or first filled the gap with inert gas and then try to achieve vacuum, as possible, would give you the best result, instead of using cheap insulating material, even at high temperature......

Henri,

There are two primary considerations for your problem, conduction and radiation.

The vacuum barrier you allude to would, if perfect, eliminate conduction as a heat loss mechanism BUT would do nothing about the problem of radiative transfer of heat between the two surfaces.

With a high vacuum between the two tanks the heat loss by conduction would not be the major problem but the radiative heat loss would be dominant and unaffected by the presence of the vacuum layer.  The radiative loss would depend on the Temperature of the inner container and the surface emmissivity of the inner tank as well as the reflectivity of the inner surface of the outer tank. Also, there would obviously be a dependence on the volume to surface area.

Hello Robert,

Yes, this is very true that the vacuum only stops the gas conduction. To stop the radiative heat transfer, there needs to be a fill, the propose fill is some cheap material like basalt wool (rockwool.) The question is, if somebody did this before, what result can be expected ?.

Radiative transfer will not be effected by "fill" with the exception of the fill being able to reflect back the radiation. Rock wool is a good insulator because of the air trapped between the fine fibrous structure - if you remove the air it does not do much and may increase thermal loss due to conduction. Any material you put between the inner and outer tanks will basically do three things with the radiation emitted by the inner tank: reflect it back, absorb it, or transmit it. In the last two, the radiated energy is lost to the out wall and hence the wool has done nothing to reduce the heat loss by radiation.  In the first case, the reflection case, there might be some hope if you could find a perfect reflector and hope that the inner tank was a perfect absorber but these types of materials only exist in the imagination.

To answer your question, my guess is that the two tank solution would lose heat very quickly with air between them. A little less quickly with a high vacuum between the two, and adding rock wool would likely increase thermal conduction while doing nothing or very little to stop radiation emitted by the inner tank.

Just an educated guess...Good luck with your project.

Hello Robert,

I am afraid I do not agree with you.

- Suppose the walls of the vacuum isolated tank are perfect black emitters, and the temperature difference is low. In that case, each wall emittance is

sigma * T**4 (sigma = 5.67e-8, T absolute temperature in Kelvin, emittance in Watt per square meter.) The heat transfer is now the first derivative

delta-T * 4 * sigma * T**3

- If you now put a screen in the middle, this formulae gives the heat transfer from the first wall to the screen, and from the screen to the second wall. The screen halves the available delta-T, and halves the heat transfer.

- The purpose of the mineral wool is to act like many screens. The first wall cannot emit, and radiate to the second wall. It will radiate to the wool, the wool will absorb and radiate again to the wool, and the heat transfer coefficient is divided by N, N being the number of times the energy is absorbed and radiated again before reaching the second wall. Hopefully, N is quite large.

Best Regards, Henri

Hello Henri,

My previous general comment seems to cover what you are saying.

"Any material you put between the inner and outer tanks will basically do three things with the radiation emitted by the inner tank: reflect it back, absorb it, or transmit it."

Art this point in this thought experiment I will agree that we disagree and it would be interesting to actually do the experiment OR create a heat flow/radiation simulation with realistic material parameters.

Practical note: putting a high surface area material such as rock wool in the vacuum will greatly increase pump power requirements and pump down times, maybe even limit the ultimate vacuum reached due to outgassing.

Cheers, Robert