Thermal bridge

[Jacky_90]

How to calculate a heat flux through a rod with diameter 12mm (which creats a thermal bridge) cooled by the flow of nitrogen vapor (temperature on the inlet 90K, on the outlet 290K). The rod has on one side 300K and on the other 77K. Length 600mm.

 

[georgeverghese]

Though your description appears to be clear enough, can you post a sketch of this so we are all on the same page? Presume this is a hollow rod with plain internal surface -ie no internal fins ??

What is on the outside of this rod, and what is the material and wall thickness of this rod? Presume you would have selected a material with low thermal conductivity. I suspect this may be a little beyond my depth but there may be others reading this who can help - it might possibly involve solving a partial differential equation.

 

[LittleInch]

Try this

http://www.engineeringtoolbox.com/conductive-heat-transfer-d_428.html

All you need is the material of the rod and away you go. ...

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[georgeverghese]

@LittleInch,
The calc routine posted would be the one to use if the only mode of heat transfer were to be conduction through the hollow metal rod i.e. that there is no heat transfer from the od of the rod to the external environment by radiation and or natural convection. If there was, then the heat transferred across the rod would be more than if it were to be completely insulated.
Suspect there might also be a small radiation component internally from the hot end of the rod to the cold end, but an initial solution may perhaps neglect this component contribution.

 

[IRstuff]

OP is apparently on vacation, or doesn't care anymore.

TTFN (ta ta for now)
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[LittleInch]

As we don't know anything about this rod is all guesswork. This is low temp stuff so any exposure to atmosphere will rapidly create an ice wall.

All he asked for was heat flux through the rod

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[IRstuff]

"All he asked for was heat flux through the rod"

With convection to N2 gas at 90K inlet temp. That does require some lumped model partitioning.

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[Jacky_1990]

I apologize, in fact I waited a long time for any answer and then I went on leave.
Let's simplify it as much as possible...

Here is the simplify scheme -> Link[/link to picture]

How to calculate a heat flux through a rod made of stainless steel 304 a taking into account a cooling realized by vapour of the nitrogen?

 

[LittleInch]

Makes that a bit easier to understand.

So as noted above the key issue is not so much the heat flux from one end to the other, but what is the heat flux from the rod into the vapour space. Especially with such a small rod, the surface area and convection from there is key to the calculation, but you don't say anything about what the temperature in the vapour space.

How is the thermal gradient managed in the rest of the container from 77K to 290K??

Looking at this rod in isolation to everything else or considering other ways in which heat can be transmitted from the hot end to the cold end and into whatever is shown by that ~ symbol you could get a wildly different heat flux.

Unless the rod is actually insulated to a large amount then the calculation will be quite complex. There must be some insulation somewhere otherwise the heat flux from the rest of the container will be huge.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[IRstuff]

I'm guessing the nitrogen is actually waste gas from boiloff, which is often used as a secondary cooling mechanism, and the 290K is simply the ambient into which the gas eventually goes.

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[georgeverghese]

The link takes me to some strange webpage.

 

[Jacky_1990]

Indeed, it is complicated.

Of course, there are more than one heat inleak to the LN. Although I would like to define what is the conduction through the rod which, as you can see, is cooling by the vapours. The rod is on one side at 300K and on the other at 77K. The vapours on the outlet are at 290K. Tomorrow, I can give you the mass flow. But now, we can assume 0.8g/s.