Calculating temperature drop through stainless steel

[verg70]

Hi,

I am not a thermodynamics person, so apologies for the (possibly easy) question.

I have a stainless steel cylinder and I insert a helium into it. The helium should warm by 1.95 deg (due to Joule-Thomson), but I want to know the temperature on the outside wall of the stainless steel cylinder.

I have tried to measure it with different thermocouples and get different answers. Is there a way to calculate the temperature drop through the stainless steel wall?

Any help would be greatly appreciated.

Regards

 

[IRstuff]

Why would you think that a calculation is better than a measurement?

In any case, heat flow is the same between steel and air, so thermal conduction through steel = convection in air, all related by the surface temperature. There will be a single value of surface temperature that equalizes the heat flow.

TTFN
faq731-376

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[rotw]

You don't give sufficient details. In my view you should find a solution in a heat transfer handbook. I do not assume it is air outside you have to tell us.
It is important to know if this cylinder can be assumed as infinite otherwise you do have to account for the effects of the two sides and the problem is then 3D.

apart from that, it would be good to put a unit with the temperature. 1.95 deg (?) seems relatively low delta T increase with regard to the accuracy/resolution of a classical thermocouples (plus whatever apparatus is in your measurement loop) especially when the thermocouples are on the other side of the wall where temperature increase might be even less visible.
That's maybe a reason of getting different answers?

If you calculate your temperature you still need to measure to validate your calculation I guess!
possibly you will still have a measurement problem.

When you cannot improve the resolution of the temperature measurements (because of the systematic uncertainty), see if you can take a lot of readings at same location and then take a average value in this way you reduce the random uncertainty.

 

[racookpe1978]

Define your complete environment.
Define WHY a little bitty 2 degree change is important, when you have given us no initial, intermediate, and final conditions.
Fahrenheits or Centigrades?
How big a cylinder, how thick, how long a wall, in what gas (inside and outside) at what pressure and flow (forced or natural) under what conditions?

 

[verg70]

Thanks for all the responses, apologies for not providing enough information.

The stainless steel cylinder is approx 10 cm long with a 0.4 mm wall.

The temperature increase was defined using the Joule-Thomson coefficient for He as it is expansion from a gas cylinder into this smaller cylinder.

The cylinder is inside a box filled with air t room temperature and I have several thermocouples strapped to the cylinder on the outside and they give an increase in temperature on the wall of the cylinder of 1 deg C +/- 0.3 deg C.

I was more curious than anything else if there was a way to calculate what it should be, or would there be too many assumptions to get a more accurate answer than what I am measuring.

I suppose measuring it repeatedly to reduce the uncertainty is probably the best way?

 

[racookpe1978]

Yes.

See, you are only working with a tiny 2 degree change.

The good news is: It is only a 2 degree change inside a closed room. No sunlight or outdoor air changes. With only a 2 degree change from this He addition, the difference in temperature is sol ow that the time rate of change is also very low. Compare, for example, to a 200 degree change in the same very small volume of the PV over a 15 second period. You'd see a large change in temperature that would immediately beginning losing the excess heat back to the room.

Look at your "room air" - the thermostatic isn't controlling (over any 30 minute period) the air in the room to much within a 1/2 degree C. A hotel room (very limited volume, no internal loads or air circulation) can be changed by 1 degree C within 10 minutes by a single "click" of the room thermostat. Then that hotel room goes from 19 C to 21C before the thermostat trips off!

To try to get 1/10 of one degree accuracy, you need to start restricting air flow changes around the little pressure chamber, people walking by close up that create air currents, the room air itself, how you touch the cylinder (wear gloves for example), etc.

 

[MortenA]

Verg70, I think the reason why you don't get a direction here (besides use the thermometer) is that the problem you describe is not a stationary problem. The temperature will start out at ambient (assuming the cylinder is in equlibrium before adding He, then the He will heat the wall inside and cool, as a temperature profile builds up the temperature difference between wall and gas reduces - and thus heat transfer, eventually the wall outside will be warmer and heat loss to the surroundings begins until all is back to ambient. More or less.

 

[verg70]

Hi All, thank you for the comments. I agree that as soon as the helium heats up the cylinder it will immediately begin to cool and the problem is not as simple as I thought.

I will model the heat increase with several thermocouples and hope that helps.

Thanks