[kerryandersonx]

I have a problem and was wondering if anyone could shed some light.

I am concerned with a carbon steel exhaust stack at 300 degrees celsius.

A protective cage is to be placed around this. The temperature of this cage must not exceed 70 degrees celsius.

How can I determine the distance away from the stack that the cage must be in order to ensure it is no more than 70 degrees celsius by radiation/convection heat transfer?

[Enthalpy]

Radiative transfer is still moderate at 600K (<7kW/m2) and less than convective transfer.

To fight radiative heating, you may as well coat the inner face with a clean metal (nickel) and the outer face with an emitter (rust! Char, tar, paint, ceramic...). A factor of 15 between absorptivity and emissivity is difficult but possible if the inner face stays clean, and does the trick at any radius.

Against convective transfer, the answer is really complicated. Experiment instead. You may corrugate the outer face, maybe blow it, to reduce the necessary radius.

[pankajshah]

you need to define ambient temperature as there should be an equilibrium between the heat absorbed by the shell & heat released by it to atmosphere so that the temperature is maintained at 70*C.