Thermal Gradient in Platform Support

[Elise]

I have a De-ethaniser Column operating at Minus 20 Deg C. The top platform is supported from an inverted skirt welded onto the top tan line.
The inverted skirt is 667mm long and has a flat ring onto which the platform is supported.
If the Column operates at Minus 20 Deg C, how can I calculated SIMPLY the temperature at the top of the inverted skirt.
The vessel is insulated with 50mm thick cold insulation, and the skirt is uninsulated.
I want to ignore the effects of the sun, wind etc and just calculated the natural cooling in the steel ?

 

[prex]

The calculation may be easily done with the formulae for a fin of constant section.
However the detailed calculation is probably not useful, as you should find that the temperature will rise to the ambient much before the end of the inverted skirt.
Just to get an order of magnitude:
suppose your skirt is 10 mm thick, and is in carbon steel (k=16 W/m°C). Using h=20 W/m²°C (meaning of symbols should be easily understood), the parameter that appears in the formula for a fin is
n=sqrt(hP/kA)=16 m^-1 where A/P=t/2=5 mm, (if there is no exchange inside the skirt, A/P=t).
This means that in a length of x=0.2 m the temperature difference dies out by a factor of e^-nx=0.04 prex

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