convection(?) in concentric cylinders
convection(?) in concentric cylinders
(OP)
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
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





RE: convection(?) in concentric cylinders
Or you could look up concentric cylinder natural convection in a heat transfer text book...
RE: convection(?) in concentric cylinders
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.
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RE: convection(?) in concentric cylinders
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.
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RE: convection(?) in concentric cylinders