Concentric Cylinders with Radiation Reflector

[lharsch]

Good Day!

I am hoping that someone can help me figure out my supposedly straightforward problem.

I have a system that is comprised of two concentric cylinders with a reflective heat shield in between the two. The process has the inner cylinder at a constant temperature and I am trying to find the temperature of the outer cylinder.

The inner cylinder is a resistance heated aluminum cylinder which is maintained at T1=280C, D1=0.0953m, L=0.24m

A thin, aluminum heat shield/reflector D2=0.146m is polished on the inside and not on the outside.

The outer cylinder is D3=0.197m and has a thickness of 0.0031m thick.

The temperature outside the outer cylinder is ambient and air.

The space between the inner cylinder and outer cylinder is evacuated.

I believe that this is a combined heat transfer problem with the cylinders acting as a two body enclosure for the radiation part, and the outer cylinder using free convection to the ambient air.

I suppose my question is...is the heat flux due to radiation inside the cylinders equal to the heat flux due to free convection and radiation from the outer cylinder to the room, at steady state conditions? – Fa is the arrangement factor, Fe is the emmissivity factor of the three concentric cylinders, Csb is the Stefan-Boltzmann constant

Fa*Fe Csb A1(T1^4 – T3^4)= hA (T3-Tamb) + Csb A3(T3^4 – Tamb^4)

And I have to guess T3 to find Ra and Nu number and iterate until I get a solution, right?

Thanks
LMH

 

[prex]

Well, the answer is rather obvious, I wonder what you are trying to state.
If other paths for heat transfer are irrelevant and you can neglect them, your statement, as already stated, is obvious.
However your cylinders will have to be supported, and this will hardly have a negligible impact on heat transfer, especially under vacuum.
Also in your equation some details should be better stated, especially concerning the surfaces to which the heat exchange coefficients are attributed. I also see that you neglect the heat resistances through cylinder walls, and this should be correct in most situations.

prex

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