heat exchange cylindrical container

[Danijel_Bab1998]

Good morning.
I have to calculate the insulation thickness to be applied to a cylindrical reservoir of in a given volume contained water at 12 degrees. the tank is located in a place where the minimum temperature is -5 degrees. How can I do from an analytical point of view?

 

[meccanicamg]

If you're a mechanical engineering student in technical physics, you should have done these two demonstrations... and on these do the exercise.but a textbook with the things you explain do not have it?

 

[Danijel_Bab1998]

If you're a mechanical engineering student in technical physics, you should have done these two demonstrations... and on these do the exercise.View attachment 66862View attachment 66863but a textbook with the things you explain do not have it?

I have already considered this demonstration. However in my case I have a cylindrical container with hemisphere caps. the cylinder has length l=2.5 m and diameter d=4.0 m. in technical physics and other courses we have always neglected the thermal exchange through the base areas of the cylinder. However, in this case having a diameter of 4 m I assumed that the heat exchange through the caps was not negligible but I failed to find an analytical treatment of the problem. I thought it was a simple treat because it is the examination of industrial plants.

 

[meccanicamg]

Unfortunately in the university course they always say: we ignore the heat exchange on the lids of the container....and this is the result.
not doing hot mechanics daily I have no idea how to proceed. the first approximation could be considered flat walls.