convection(?) in concentric cylinders

[CCKS]

As part of a process I am creating, I have two concentric cylinders with the outer one being heated and a gap of 0.070" between the ID of the outer cylinder (surface1) and the OD of the inner cylinder (surface2).

Since the gap is so small, its very difficult to directly measure the temperature of surfaces 1 & 2.

I've been trying to find/use heat transfer equations to calculate the temperature delta between these surfaces since that is really the number I am after, but this is not my area of expertise. Since the cylinders are not in contact, and there is just ambient atmosphere in the gap, the heat transfer mechanism from one surface to the other is predominantly convection right?

What equation or model can I use to calculate the temperature difference across the gap?

Thanks

 

[TGS4]

You're interested in a paper by Raithby & Hollands "A General Method of Obtaining Approximate Solutions to Laminar and Turbulent Free Convection Problems", in Advances in Heat Transfer, Vol. 11, pp. 265-315.

Or you could look up concentric cylinder natural convection in a heat transfer text book...

 

[prex]

With a so small gap (assuming the diameters are not of the same order of magnitude) conduction through air should control over convection, so the problem is relatively simple and can be calculated with a good degree of accuracy.
To decide whether convection is relevant, you must determine the Grashof number of the enclosed space. For horizontal cylinders, experiments show that conduction dominates when the product of the Grashof and Prandtl numbers is lower than 10³ (or just Grashof<10³, as Prandtl for air at room conditions is close to 1).
Radiation will also play a big (predominant) role, and its evaluation requires knowing the emissivities of the surfaces: if you can tightly estimate those, the calculation is straightforward and accurate.
This is a relatively simple problem but, as you can see from the above data, requires a thorough understanding of thermal problems, if you want to treat it in depth.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[IRstuff]

Air gaps generally need to be larger than about 13 mm to get convection, but that's partly dependent on temperature, so a really hot system might get more convection than a room temperature one.

As for radiation, in such an abstract problem, both surfaces can be treated as perfect blackbodies, since the radiation is always trapped between the two surfaces. This cavity problem is essentially the one Planck solved with his equation for blackbody emission.

TTFN

FAQ731-376

 

[CCKS]

Thanks for the info. Yes, without having to consider convection (at least as the main effect) this does become a lot simpler.