Question regarding heat transfer through a solid bar
Question regarding heat transfer through a solid bar
(OP)
Hi all,
It's been a while since Thermodynamics so my memory is a bit faded. I've got Mark's Hanbook cracked, I'm sure all of the info is in there, but I'm a bit slow in getting started. I'm hoping someone can give me a gentle shove in the right direction. I have a titanium shaft partially inside a furnace. An external pneumatic cylinder is connected via threads to the titanium shaft. I need to make sure the cylinder will not be damaged by the heat conducted through the shaft.
An alloy steel block 2.5"x6"x10" is inside an oven at 1400 F. The block is attached to (4) 3/4" dia. titanium solid bars 9.375" long. Each bar is connected independently to a cylinder. When the cylinder is extended 5.5" of the bar is exposed inside the oven, then it passes through a 2" thick heater element and enters into 3" of insulation. Inside the insulation the rod of the pneumatic cylinder is threaded onto the end of the titanium shaft. The cylinder rod continues through the insulation, followed by a 2.75" (I think) airgap and finally into the cylinder body.
Can someone provide some insight on how to handle this calculation? I appreciate any input you guys have.
Thanks in advance,
Aaron
It's been a while since Thermodynamics so my memory is a bit faded. I've got Mark's Hanbook cracked, I'm sure all of the info is in there, but I'm a bit slow in getting started. I'm hoping someone can give me a gentle shove in the right direction. I have a titanium shaft partially inside a furnace. An external pneumatic cylinder is connected via threads to the titanium shaft. I need to make sure the cylinder will not be damaged by the heat conducted through the shaft.
An alloy steel block 2.5"x6"x10" is inside an oven at 1400 F. The block is attached to (4) 3/4" dia. titanium solid bars 9.375" long. Each bar is connected independently to a cylinder. When the cylinder is extended 5.5" of the bar is exposed inside the oven, then it passes through a 2" thick heater element and enters into 3" of insulation. Inside the insulation the rod of the pneumatic cylinder is threaded onto the end of the titanium shaft. The cylinder rod continues through the insulation, followed by a 2.75" (I think) airgap and finally into the cylinder body.
Can someone provide some insight on how to handle this calculation? I appreciate any input you guys have.
Thanks in advance,
Aaron





RE: Question regarding heat transfer through a solid bar
Assuming the latter is, as an example, 100°C, this would be:
Q=kAΔT/L and should give a figure not far from 50 W, if I'm not grossly mistaken.
That amount of heat would have to be evacuated into the surrounding air, using the outer surface of the cylinder. To evacuate 50 W under a temperature differential of 50°C in air a surface of 1000 cm² is sufficient. It is a fairly high surface for a small cylinder, however much of the heat would also go into the cylinder support.
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RE: Question regarding heat transfer through a solid bar
Let us know how it ends!
Good on ya,
Goober Dave
RE: Question regarding heat transfer through a solid bar
1)let ends of titanium bar (TB) be at 1400 dF
2)Estimate radiation heat transfer at the exposed end of TB's with equation Q=e*s*SA*T^4 where e,s are the emissivity and plank's constant,SA=surface areas exposed to radiation,T=oven temperature in absolute units. Also discount convective HT.
3) Use PREX conduction equation to determine temperature at threaded end to cylinder rod; you already know Q and T on one side of TB. Also discount HT thru insulation.
4) Knowing T at threaded connection, determine temperature gradient throughout length of cylinder rod using the steady state relaxation method. It's a little bit complicated to explain here, so get a book on heat transfer for reference. In essence you establish nodes along the length of the threaded road and develop two dimensional heat transfer equations at each node.
You'll have conduction and convection at each node.
Conductive HT in - conductive HT out - conductive HT out thru the air gap= Residual HT value.
To do this method you will need to estimate initial temperatures at each node and establish a deleta length for node.
If you establish 10 nodes of equal lengths, you will have 10 algebraic equations which can be solved by the relaxation method. If you can program a spread sheet or a use FORTRAN or BASICs, you can solve these equations a lot faster.
As I said get a book on HT to relearn this relaxation method.
Good Luck!
RE: Question regarding heat transfer through a solid bar
That being said, I found my old themo book and have started reading about Fourier's. Q=(k * dT)/dX Am I correct that Q is not a constant based soley on material performace, rather it is also based on geometry? As such, if geometry changes so does Q?
I have to correct a bit on my first message. The rid design is actually two piece. The first piece is 3/4" dia. and is 316 stainless. Then the previous designer used a 1" dia. X 2" piece of titanium to act as an insluator between the stainless rod and the pneumatic cylinder rod. So, I need to figure out how to calculate the temperature at the joint between the stainless rod and the titanium insulator as well as the between the insulator and the pneumatic cylinder rod.
As I said, I am considering all of your input. If you have any other thoughts to throw at me, by all means fire away.
Thanks again,
Aaron
RE: Question regarding heat transfer through a solid bar
TTFN
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RE: Question regarding heat transfer through a solid bar
AaronH, there is not much more to say with your data, besides that fundamental equation and the other one for convection to ambient air Q=hS(T-Ta).
If the SS section is also within the insulation, you solve it just by putting it in series with the titanium section (the same Q flowing through both of them). However you'll need a better understanding of heat transfer to manipulate the formulae and get to a meaningful result.
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RE: Question regarding heat transfer through a solid bar
RE: Question regarding heat transfer through a solid bar
RE: Question regarding heat transfer through a solid bar
You normally wouldn't calculate dT (or ΔT), as this is known to a close extent. It is in fact close to the difference between the inside temperature and the outside one. What you don't know and need to calculate is Q.
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RE: Question regarding heat transfer through a solid bar
RE: Question regarding heat transfer through a solid bar
Sometimes you just have to iterate until you arrive at a reasonable answer.
Patricia Lougheed
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RE: Question regarding heat transfer through a solid bar
> Figure out the entire serial path for the heat. If there are parallel paths, you'll need to add the thermal conductivities
> Take each individual segment of different material or cross-section, and determine the °C/W, the thermal resistance of each segment
> Sum all the thermal resistances to get net_thermal_resistance
> Determine the deltaT across the entire stack
> DeltaT/net_thermal_resistance = Q
> Use that Q with the individual segments to determine each segment's deltaT
TTFN
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RE: Question regarding heat transfer through a solid bar
I believe the tests clearly show that the TI insulator will not provide enough thermal resistance @ 1400 F to protect the seals in the pneumatic cylinder. However, I don't know for certain if the ceramic insulator will. Moreover, the ceramic may not mechanically hold up to the abuse of this application. We're running out of time and may end up trying the ceramic insulators while at the same time search for a material with equal (or better) thermal properties, but improved strength properties.
RE: Question regarding heat transfer through a solid bar
RE: Question regarding heat transfer through a solid bar
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RE: Question regarding heat transfer through a solid bar