Determine temperature profile in cylinder wall

[monster_me]

I am conducting an experiment where I have a cylinder heated from the outside and a fluid flowing through the inside. I know the heat flux into the cylinder and I know the temperature at two points within the cylinder wall. However, I am not confident on the radial position of the temperature measurements. Is there a way for me to determine the radial position of the two temperature measurements?

 

[gsal]

what kind of heat flux are we talking about? how long is the cylinder? how thick is the wall of the cylinder? how much flow inside the cylinder?

The thing is this...you may be able to input your heat uniformly onto the outside wall of the cylinder, not just around, but lengthwise. BUT, you may not end up absorbing the heat uniformly in the inside, because the fluid is heating up as it flows...and so, the heat going into the cylinder does not just travel straight radially to the inside wall, instead, it travels a bit along the length of the cylinder...this is a bit of a 3D problem...

If conditions did not change along the length of the cylinder, then, it would be a simple 2D problem, and you could easily find the answer you are looking for.

Then again, if the wall of the cylinder is relatively thin, maybe you could assume that the axial distance the heat travels is negligible and treat it as a 2D problem.

Simply simulate a thermal resistance circuit put the heat flux thru and figure your temperature difference to match what you need. Remember that the thermal resistance through the wall of the cylinder varies, you will need to integrate to calculate your dR's from the outside to the inside wall of the cylinder.

enough...I am afraid I might be making things more confusing than anything else.

 

[boneh3ad]

Even with all of that it is a relatively simple 3-D problem, all things considered. You may even be able to get an analytical solution to it, though I certainly can't do it in my head.