Modeling thermal conductivity of a vacuum space

[blueandwhiteg3]

I'm trying to work out the thermal conductivity of a vacuum. It is proving surprisingly problematic.

The theory is this: pressure has very little impact on the thermal conductivity of air. Thus, the intensive measurement of thermal conductivity does not vary with pressure. However, in terms of extensive properties, thermal conductivity in a large space of vacuum/near vacuum begins to drop with pressure due to the kinetic nature of gases. I believe this is around 10-15 pascals where this becomes notable for air.

However, I'm stuck at solving the math. I am looking to construct essentially a panel, one side will be hot, the other will be cold. I wish to use a vacuum to enhance the insulating properties of this space.

I want to model my panel's vacuum space thermal conductivity at varying thicknesses and varying pressures. From here, I can determine what is most appropriate for my application.

There will be no special gases or chemicals involved. Temperature range is 250-300 K typically. It's not rocket science, I just don't have the right math

Can anybody help?

 

[IRstuff]

The convection coefficient is a function of the Rayleigh and Nusselt numbers.

http://en.wikipedia.org/wiki/Rayleigh_number

http://en.wikipedia.org/wiki/Nusselt_number

Mathcad's Building Thermal Analysis goes through such an analysis for heat transfer through building cavities, resulting in a minimum in the htc at 13 mm for normal air.

As you can see from the articles cited above, you need a bunch of numbers that are not readily available. NIST is probably the place to go:

http://fluidproperties.nist.gov/thermal.html

TTFN

FAQ731-376

 

[blueandwhiteg3]

I'm glad we're finally starting to get to some meat here! These values are what I have been seeking.

If I got going with MathCAD, would it be capable of solving some of these problems?

I would still appreciate more guidance on solving for these numbers. I'm getting a sharper and sharper idea of the concepts, but I am still no closer to being able to actually find out the data I want.

One interesting paper:

http://www.alma.nrao.edu/memos/html-memos/alma203/memo203.html

 

[vpl]

blueandwhiteg3

I started a post on the Grasshof and Prandtl numbers, what goes into them, and how to find those values and then deleted it. I figure I need to clarify some information up front. I've read back through both this post and thread378-232020. I think that somewhere along the line you switched from being worried about the thermal conductivity to covectivity .. or did you? Also, at the very beginning of the post someone mentioned radiation and you stated that you would "handle it separately."

Conduction, Convection and Radiation (as used in this context) are all methods of Heat Transfer. They all have to be handled simultaneously. Sometimes you can determine that one method is going to be of a significantly higher magnitude than the others and thus ignore them. However, in your case, I'm not sure that you can realistically ignore any of the three.

While I can provide you standard formulas for basic heat transfer and combining the different types, and I can provide you the units for the formulas given in the wikipedia files, obtaining the values is a very different -- and difficult -- issue. Further, the Nusselt formula is going to vary dependent upon the orientation of your proposed plates. And the exact geometry is going to make a difference in how everything combines together.

So, before I proceed further, I'd like to know that what I'm doing is going to be helpful. I would appreciate it if you would think about what information you're willing to provide regarding your project and if you are willing to lay it out without worrying about what type of heat transfer is occurring -- the big thing is what are you trying to accomplish from a heat transfer point of view?

Otherwise, I feel that you are going to be frustrated because you're not getting the help you want and the people responding are going to feel frustrated because they're trying to answer the questions you ask. So far eight people (not counting me) have tried to help, some of whom (such as IRStuff) are very experienced heat transfer engineers.

In my organization we have a story about "show me a rock." The story behind it goes Person 1: "Bring me a rock." Person 2: "What kind of rock." Person 1: "Well, I don't know exactly, but I'll know when I see it." So Person 2 brings in a rock. Then Person 1 finds fault with the rock "it's too big," "this one's too small," "this is almost the right size but it's too shiny..." And after numerous iterations, Person 2 beans Person 1 with a rock and Person 1 says "Well it's not what I wanted, but I guess it will do." Moral is you need to define what you want in order to get the results you desire.

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[blueandwhiteg3]

Patricia,

Thank you for your detailed reply. I really appreciate your effort.

I started viewing this as essentially a fancy insulation panel for a special project. I began by thinking of the interior of the panel much as I would, say, a styrofoam-type insulation panel encased in another material. Once you know the thermal conductivity of the styrofoam and the external material, the problem can be solved. I was attempting to treat the vacuum like I would a solid insulating mass.

I knew that convection heat transfer was a big deal. But I assumed somebody has simply assembled an equation to solve for it at a given panel thickness and I just vary the thickness and pressure variables and I can solve it for my situation. No clean equation emerged.

As I found out that the thermal conductivity of air had only small reduction with the pressures I was talking about, I quickly realized that convection within the panel was my issue more than conduction.

This lead me to reformulate my question. I did not want to try and model a panel thickness or design, but I wanted to get a useful gauge as to the significance of the reduction of convection at the pressures I am looking at. If the reduction is negligible, this simply won't be useful. If the reduction is 95%, I could mostly write off convection as an issue. The goal was a simple sanity check and heuristic, attempting to avoid the complexity of working the whole model unless proven viable yet also necessary.

Once I either write-off convection or generate an approximation of it (which would involve more math, yes), I can then solve for the effective thermal conductivity of the vacuum space, then the whole panel, using traditional non-kinetic, non-flud thermal models. Those I can handle very easily.

I am aware of radiative heat loss. But for this particular application, I actually will be manipulating radiative heat loss through another mechanism. Conductive heat loss is my only concern for this particular vacuum.

 

[blueandwhiteg3]

I will also note that I would be very happy to simply model the thermal conductivity precisely, if you are able to give me some numbers to work on in that regard.

Panel size:
120 cm wide
240 cm tall

Panel hot / cold °K:
Typical 250 / 300
Maximum 220 / 320

Panel spacing:
20- 100 cm

Pressure range:
0.01 mbar to 0.1 mbar.

So, essentially, we're looking at a rectangular cube space that is 120 x 240 x 20 - 100 cm. The 120 x 240 cm panels will be exposed to the hot and cold temperatures. The other sides may be assumed to be highly insulated and "ambient" essentially - somewhere between the hot and cold sides.

Obviously, with a variety of temperatures, pressures and thicknesses, the number of possible solutions is quite large. The key here is not that I want somebody solve this for me, I want to know HOW to solve it myself.

Most helpful would be an example calculation using some of the above data *with clear units* so that I can adjust the units and re-do the calculations for variations within the stated range. I might even want to go a bit outside the above ranges, it just depends.

You can give a man a fish and he'll eat for a day, or teach him to fish and he'll eat for a lifetime. Teach me how to fish!

 

[vpl]

blue&white

Apologies, work has gotten busy last few days. I'll try to post something over the weekend.

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[hacksaw]

forget thermal conductivity it is essentially a radiation problem with a 50K difference between the surfaces.

there are plenty of text books that will chart you through the math

 

[blueandwhiteg3]

Yes, but I am handling radiation independently.

I have looked at a few different texts and to date, none have fully laid out the convective calculations with suitable units and calculations to allow me to alter pressure and various variables.

I know it's not exactly quantum physics, but I want to get it right.

Looking forward to hearing from Patricia.

 

[IRstuff]

Lienhard, and even Wikipedia have more than sufficient information for you to do the math.

If you get the correct value for standard atmosphere, then you've got the units right, right?

TTFN

FAQ731-376