Heat Transfer Dependence on Pressure

[DoubleEngineer]

Hello,

Here is my situation:

A hollow multi layed concentric cylinder that is placed inside a vacuum. There is a heating element in the middle of the cylinder.

Temp initial is room temp and the pressure initial is atm.

Temp is increased to 350 degs C. Pressure is reduced to about 40 milliTorr.

I have calculated the Heat Transfer for atmospheric pressure but can not seem to find enough information about thermal conductivity of different materials at vacuum pressures.

Could anyone tell me an equation for thermal conductivity of materials at vacuum pressures.

Basically, im trying to figure out an ideal pressure for my system, that is still in a vacuum, and to determine the differences between heat transfer if 1) the heating element is placed on the inside of the cylinder or 2) at the outside around the cylinder.


Thanks for any responses,
DoubleEngineer

Basic Problem--

 

[IRstuff]

Not sure if I understand your question. Solid materials' thermal conductivity have little to do with ambient pressure.

TTFN

FAQ731-376

 

[Compositepro]

The thermal conductivity of gasses changes surprisingly little with pressure until you get to very low pressures (high vacuum).It has to do with heat being transferred by molecular collisions and mean-free-path. Convective heat transfer is pressure dependent. I assume you also understand the role of radiant heat transfer.

 

[DoubleEngineer]

I know that in a vacuum, radiation and conduction are the main transports for heat and that convention plays a small role.

I was trying to determine if thermal energy transfered (mostly conduction) throughout my system is effected by pressue. Knowing that convective heat transfer is pressure dependent.

 

[vpl]

You might find these threads helpful:

thread391-210603
thread391-231539

Also, just to be sure, this isn't a school problem, right?

Patricia Lougheed

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[DoubleEngineer]

nope, the picture i posted is the first pic of an close model. not a scanned homework problem.

im trying to model the total heat transfer of all three transports for the system and how it changes with pressure.

 

[corus]

As has been said, thermal conductivity of solids doesn't change with pressure, however.. with pressure betweem solids in contact then the thermal resistance at the interface will change with pressure. In the two extremes you'd expect either perfect thermal conduction between the two bodies, or you'd have zero contact and heat transfer will be by radiation betweem the two bodies across the miniscule gap. I presume that the thermal resistance between the bodies in contact would depend on surface finish as well as pressure, so values would probably be determined experimemtally.

corus

 

[DoubleEngineer]

corus,

i do have miniscule gaps between layers that are very difficult to determine because of the multiple layers around the cylinder.

i have used grey body radition equations(and assumptions) to figure out the net transfer of a cylinder inside a rectangle.

the problem lies in the geometries that are inside the chamber. im not sure of an appropriate model or equation for the view factors of the radition

i believe i need a more accurate model for this but am having difficulties in deciding an appropriate model based on the equations and my designs/parameters.

is there a way to accurately test this? we have thermal couples placed inside the device that gives accurate readings, but im looking as of right now to understand more of the math behind it.

 

[DoubleEngineer]

the equation im using currently is

q(i) = E(bi) - J(i) / (1 - e(i) / e(i)*A(i)

and

q(i) =
sum of n surfaces with j=1 (J(i)-J(j)) / (A(i)*F(ij)^-1)

and that q= convection (till a certain pressure) + conduction(changes slighlty due to roughness and spacing with varying pressure) + radition (of mulitple surfaces)

 

[IRstuff]

Huh? You have an object floating in vacuum chamber, no?

Then, the heat flow within the object is strictly conduction. The heat flow out of the object into the chamber is convection plus radiation. AND, under ALL conditions the heat flow from the heater equals the heat flow leaving the object.

TTFN

FAQ731-376

 

[DoubleEngineer]

the cylinder is basically suspended(floating) because its placed on a stand in the middle of this vacuum chamber.

heat flow thru object is conduction, thats obvious, but radiation is still involved because the heater is bouncing off heat from the walls of the chamber.

 

[IRstuff]

You said the heater was in the middle of the cylinderin one case. The equation for that is different than for the case where the heater is on the outside of the cylinder.

TTFN

FAQ731-376

 

[IRstuff]

This might be interesting, particularly the graph:

http://eetd.lbl.gov/ECS/aerogels/sa-thermal.html

TTFN

FAQ731-376

 

[IRstuff]

see:

http://www.alma.nrao.edu/memos/html-memos/alma554/memo554.pdf

TTFN

FAQ731-376