Helium Gas Cooling (Convection vs. Static)

I don't see how you're going to do any serious cooling with gas, static or otherwise. You need chilled water, at the least.

If I read your problem statement correctly, you're talking about a 150 K delta temperature across a 0.07-in thickness of some material, presumably steel, across an 8-in diameter. That works out to be about 140 kW of cooling load required, depending on the type of steel. If it's more like Invar, then the cooling load is a measely 27 kW. That requires a flow rate of gallons per minute.

TTFN

FAQ731-376

Thanks for the reply, IRstuff.

Helium is actually used a lot as a cooling gas for vacuum processes. The disk material can be either Silicone or AlTiC.

Any other comments are appreciated.

V

"I'm being told (by sometimes unreliable sources) that Helium is better used as a cooling gas, statically, rather than through convection by running the Helium through the system constantly. This isn't sitting right with me, however, I know that Helium is an odd gas, and it's possible"

It doesn't make sense to me either, vc66. For the same gas conditions (density, bulk temperature), a flowing gas will dissipate more heat than stagnant gas, by the addition of mdot-Cp-deltaT; the conduction thru the flowing gas would be in all cases equal to or higher than the conduction in stagnant gas. Doesn't gibe.

The idea, I'm being told, is that helium would not be used as water would (via flow), but it would be injected into a small (.003") gap under the disk under a small amount of pressure with no return line, and act almost as a "gaseous thermal paste."

Every time a helium atom hits the hot surface, it picks up a portion of the heat. Then as it hits the cold surface, it releases that heat onto it, bringing it back to its original "cold" temperature. This happens over and over, until the helium eventually seeps out of the O-Ring.

I understand how it's being done, but I still don't agree that it's more efficient than flowing the helium.

Take a look at the link, if you're interested...


V

To use a high flow rate of hellium you will have to have large flow channels and transport the gas large distances to another heat transfer surface. It is possible but probably very difficult to design such a system that would transfer more heat than using molecular diffusion across a 0.003" gap or less. There are other constraints such as you cannot use high pressures.

Not buying it, CP. Slit the O-ring. Now there is 10x more flow of helium, with the same "molecular diffusion" (call it conduction) still taking place as before. The mass transport of helium is carrying away heat, in addition to the conductive transport across the gap. You get more heat transfer with this higher flow. If the restriction is that you can't return the helium due to size constraints or other reasons, and you can't stand a high leak rate of He into the chamber spoiling your high vacuum (or because you don't have enough helium around), then the sealed approach is what you are stuck with.

Why helium, vc66? I assume it's a process requirement. If you want better heat transfer, and can use more reactive fluids, how about hydrogen gas, or steam. Much better heat transfer properties.

OK, so you're saying that there is a thermal sink adjacent to the plate? At what temperature? What is the expected temperature of the cold side of the plate?

I never disputed the notion that helium can be used as a cooling gas, the issue, as always, in a heat transfer problem, is how much heat are you trying to remove, and whether the medium chosen can support such a process.

You never answered the question as to what the actual temperature distribution should be. Without that, we're basically flapping our digital lips on pure hypotheticals. With actual numbers, you can trivially determine the cooling load, which may, or may not, show that something significantly more substantial, like water, is required to remove the heat.

TTFN

FAQ731-376

Somewhere, itsmoked probably has a lip-flapping smiley...

FWIW, the flapping of the cut edges (lips) of the slit O-ring would also probably act to enhance heat transfer due to the flow oscillations...

(insert lip flapping smiley)

Hi vc66,
I think I understand the question and set up. Wafer inside some kind of oven where perhaps radiant heating is the only heating since the wafer has a vacuum on the side being heated. Not sure how strong a vacuum, but helium on opposite side (sealed via O-ring) is only ~1000 Pa (7.5 torr or .145 psia). No doubt this is done because of stress conditions in the wafer - 200 mm diam (~8") and very thin (.02 - .07 inches). So any significant amount of pressure will overstress the disk. In addition, contamination might be an issue.

The second consideration is that this thermal gap is very thin - you say it's only .003" which is 5 orders of magnitude smaller than the diameter of the disk. Note, this is an important consideration in responding to your question. You ask then if the helium would work better if it is flowing in this tiny .003" gap or if the thermal conductivity is a better way of cooling this disk. It could be this gap is small because they are using electrostatic forces to hold the disk, and these forces have to operate across a very small gap to be effective.

I hope I've got your set up correct, otherwise, this responce isn't going to be meaningful.

The point is that the gap is extremely small compared to the overall length of flow. Regardless of whether helium is flowing or not, the gas will act as a thermally conductive layer between the wafer and heat sink. Consider what happens if you have no flow - all heat flows through the helium to the heat sink. Consider then what happens if you start increasing velocity by flowing helium in and out. As the flow begins (ie: just over zero flow), there will be no significant change in the temperature of the helium as it exits this thin chamber. This means there's no additional heat removed and thus the heat flux is entirely dependant on the thermal conductivity of the helium. As flow increases, there has to be a rise in temperature of the helium leaving this gap for there to be any additional heat removed above and beyond the heat removed by condution. But because the gap is small (ie: the distance the helium must flow is 100000 times longer than the path of thermal conductivity (across the gap)) there has to be considerable velocity in the helium for there to be any significant increase in the discharge temperature. Just thinking about this without putting any values to the velocity of the helium, I'd guess that the helium velocity would have to be "extremely high" to get any significant increase in heat transfer.

What does "extremely high" mean here? There are limitations on this geometry which restrict flow. The gap (.003") is just too small to allow much flow. And then you need to have inlet and outlet holes. Seems to me there's not enough real-estate to provide a significant flow path so one probably can't get enough flow to make any significant difference. This isn't to say that increasing flow WOULDN'T improve the amount of cooling, but the increased cooling is likely to be insignificant due to the geometry of your set up. The gap is just too small and distance for the helium to travel is just too long in comparison to the gap.

In addition, there's more practical considerations. Controlling the pressure (~1000 Pa) in this chamber under flow will be difficult at best. Then you have to reject the heat through a heat exchanger and re-introduce the flow. You'll need vacuum pumps, flow controllers, pressure controllers ... yikes... I think the practical considerations of trying to create forced convection through this gap will be difficult if not impossible. The chances of overpressurizing this gap and destroying the wafer are considerable with a dynamic system like this. So although it may show some improvement in cooling, one has to ask whether or not that improvement is even needed if thermal conductivity alone is sufficient. Doesn't sound economically viable to me.

I could give you the thermal conductivity of various gasses under these conditions, but suffice it to say, hydrogen is the only one that will be higher, and it will only be about 20% greater under these conditions. In addition, hydrogen is flammable and may react with the wafer. Nitrogen, argon, CO2 and other common gasses are going to have a thermal conductivity only about 1/7 that of helium, so they won't be nearly as effective. In addition, some of the alternate gasses could react with the wafer. Helium is a good selection due to high thermal conductivity and inertness.

Assuming that iainuts' suppositions are correct, there are other issues at play. Constraining the wafer in such a fashion with such a temperature loading will most likely cause a bowing of the wafer, potentially leading to film stresses that are unacceptable. Additionally, the o-ring seal will result in a radial temperature differential, leading to process nonuniformities.

TTFN

FAQ731-376

iainuts, you're almost correct. The only difference is that the wafer is not constrained electrostatically. It's held mechanically. The gap of .003" is not set in stone. If I was to flow helium, I would cut that deeper. The reason we use helium, is that it's inert, when it comes to the process we're working with. We won't use a pressure above 2 Torr, so bowing of the wafer will not be an issue. We already employ vacuum pumps, MFCs, pressure gauges, etc., so the setup is definitely used right now.

IRstuff-

Yes. Across the gap, there is a stainless heat sink. The temperature of that heat sink will be below 325K. I must be missing something when you ask about the temperature distribution... The wafer has to be held to <350K.

Thanks all for your comments, and keep them coming if there's any more info you'd like to share.

V

I wasn't refering to pressure bowing; I was refering to thermal bowing. Since the perimeter of the wafer is held mechanically, it will be at a different average temperature than the middle. Thermal expansion will cause the wafer to bow.

In any case, you appear to still be in a situation where you're trying to move lots of kW to the heat sink, with a relatively small delta temperature. I think that when you crank the numbers you'll find it unsupportable with a gas medium. Even air, running at a fairly high flow rate will only sustain about 20 W of heat flow with a 25-K delta T, across your wafer diameter.

(25 W/m^2-K)*(200mm/2)^2*pi*(25 K) = 19.6 W

TTFN

FAQ731-376

"As the flow begins (ie: just over zero flow), there will be no significant change in the temperature of the helium as it exits this thin chamber." and "As flow increases, there has to be a rise in temperature of the helium leaving this gap for there to be any additional heat removed above and beyond the heat removed by condution."

Hunh? Presumably somewhere the He supply is at room temp. It reaches some higher temperature somewhere along the path to the hot end of the device. The temperature of the helium changes along this path, which requires heat to flow into the helium. The helium then exits the hot end, carrying away heat at a rate of mdot*Cp*dT...unless we've undergone a change in the laws of physics.

btrueblood,
You've misunderstood the set up.

Nope. Just quoting physics.

Hi vc66,

The gap of .003" is not set in stone. If I was to flow helium, I would cut that deeper.

Click to expand...

I agree that if you wanted to flow helium through this gap, you'd need to increase the size of this gap. At .003" flow is going to be negligable and the thermal conductivity to your heat sink is going to dominate.

Note that as this gap increases, the thermal conductivity across the gap increases proportionally. That is to say, that increasing the gap to .030" increases this conductive resistance by a factor of 10 and an increase to .300" increases this conductive resistance by a factor of 100. Without doing the math, if you want to allow for convective heat transfer from this wafer, I'd guess you'd need to open the gap to about ~.1" - at which point the thermal conductance across this gap becomes huge compared to the thermal conductance of the Tadin system you reference and the total heat that can be rejected across this gap becomes negligable.

We won't use a pressure above 2 Torr...

Click to expand...

This doesn't change the thermal conductivity of helium at all, believe it or not. So the conductive heat flux your system will be capable of is a measure only of the gap length.

Now if you decide to increase this gap AND start flowing, then the transfer of heat away from the backside of your wafer quickly becomes a function strictly of the convective heat transfer. If the Tadin system needs a .003" gap, and if your heat transfer rates are comparable to that system, then I suspect if you increase this gap to ~.1" then you will need to provide helium flow through this gap and heat transfer then becomes primarily convective.

So to answer your original question:

I'm being told (by sometimes unreliable sources) that Helium is better used as a cooling gas, statically, rather than through convection by running the Helium through the system constantly.

Click to expand...

This statement is a function of the gap dimension. With the Tadin system, the .003" gap dimension allows for conductive heat transfer away from the wafer, but if this gap is increased significantly, and assuming other parameters are maintained including total heat transfer, then conductive heat transfer drops off rapidly and you will need to provide helium flow so you have sufficient convective heat transfer from the back side of the wafer.

At the end of the day, if you're designing this system then you'll need to 'do the math' and determine how you're getting your heat rejection from the wafer.

Hope that helps.

btrueblood, the point I'm trying to make is that this isn't your conventional 1 dimensional heat exchanger. If you look at temperature as a function of length, and as you start to flow (assuming the .003" gap and very low flow) the temperature INSIDE this 'heat exchanger' remains constant along the length. The temperature of the helium would almost instantly jump up to some given temperature and remain there as it travels along the length of the wafer to the outlet. This tells you either:
A) the heat exchanger is too long (nope)
or
B) the heat is being sucked away in the dimension perpendicular to flow. (yup)

So for very low flow, and given a small gap, you have essentially all of your heat flux in the direction normal to velocity. The problem is you can't increase velocity with the .003" gap enough to make the mdot*Cp*dT heat flux significant. You have to open up this gap, in which case, there is a detrimental affect to the conductive heat transfer, perpendicular to the flow velocity. Hope that's more clear.

Ok, I agree with your last post. But, your wording changed from 1st to last post, from "no added heat transfer" to "no significant increase in heat transfer". Certainly you can engineer a heat exchanger that doesn't exchange much heat.