Radial to Planar Heat Conduction 1

[eradalia]

I've been doing some research on the subject and have had difficulty finding sources to back up my math. I'm modeling an item, simplified I drew it out as a pipe through a wall. I want to know how energy generated from the inside of the pipe affects the outside of the wall.

So imagine a cross-section of an infinite long wall with a set thickness, I assume infinite will be easier to solve, now put a pipe in the wall, so that the cross section of the pipe is a circle, aka the pipe coming out at you. I want to know the thermal resistance across the set up. Assuming you know the dimensions and materials of the set up along with T_1inf and T_2inf.

The only documentation I have found to detail the relationship is a chapter from a book explaining how radiant floor heating works. I mostly want to get another source to confirm the math listed here, and to better apply it to my need.

http://www.intechopen.com/books/developments-in-heat-transfer/radiant-floor-heating-system

Is cosh the proper function to model the relationship? is there a chart listing similar scenarios out there?

Thank you.

 

[IRstuff]

Thermal resistance from where to where? Without that, what are you calculating?

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[eradalia]

I'm calculating the equivalent thermal resistance. I can solve the convection on the inside of the pipe, the radial conduction through the pipe walls, and the convection/ radiation out from the plane wall. My issue is how to treat the pipe the wall scenario. Are there equations to find the effects of a point source in wall? Do the equations change if the heat source is not a point?

How do I find the conduction of the "wall" part, not the pipe wall, but the wall that encompasses the pipe. It may be easier to break up the resistance into two parts, if all is symmetrical, from half way out to the wall's surface.

 

[zekeman]

Would you mind telling us exactly what the problem is?
If this is a problem involving the wall reemitting the heat after conduction via the pipe, then the problem is NOY what you found in your literature search.
The problem I have is I think you are telling us about a pipe perpendicular to a wall and not explaining how you think you can heat an infinite wall whose thermal boundaries are not defined.
A drawing would be most helpful here.

 

[eradalia]

This is a quick paint job I did. I feel like the equations should be simpler if only worrying about half the problem. You can mirror the problem over the dotted line I drew in. The air, which is labeled as T_cold, would be against the face of the wall. T_hot represents the hot water flowing though the pipe. What is the corresponding heat transfer out to the face of the wall?

Thank you,
Ethan.

 

[IRstuff]

So, this is a two-dimensional thermal spreading resistance problem. You can look that up online; there are some calculators that might work.

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[eradalia]

Thank you, and I understand the simplicity of the problem, but there are very limited resources for this type of problem. I have skimmed 3 different heat transfer books, and done many different searches with various key words. There seems to not be any definitive resources which explain pipe and wall relationships.

I'm willing to search further if you can point me in a better direction, but I have spent a good deal of time looking for a solution and not found any online calculators.

What would be a good search term to find these resources? or what book could I reference to find a sample problem?

Thank you,
Ethan.

 

[IRstuff]

That's because you're looking for pipe and wall applications. I think you can adapt this:

http://www.mhtl.uwaterloo.ca/spreading/sq_edge.html

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[IRstuff]

Maybe this article:

http://www.mhtlab.uwaterloo.ca/pdf_papers/mhtl09-1.pdf

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[zekeman]

eradalia,

Having trouble opening that file.
IIf you can, plse send it another way.

 

[eradalia]

Thanks IRstuff,
The second link, the pdf, should lead me to the equations I'm looking for. I'll have to read it a few times to get fully understand it, but it looks like what I am looking for. I'll try to update with my results.