External flow heat transfer, concentric pipes

[KevinH673]

Hi guys, I have what I assume is a pretty basic problem but haven't found the correct formulas in my heat transfer book (I'm a bit rusty, admittedly). There are two concentric pipes (I believe it's referred to as annulus). The larger diameter has water running through it, to pull heat away from the internal pipe (a YAG rod).

I have all the properties of water, of course, and the "k" value for the YAG rod. I also know the power output of the rod (Q), and the desired flow rate (q) of the water. The area of the YAG rod is set, but the area of the outside pipe the water runs through has some room to work with (though we have a set flow rate in mind, so I can't really alter it much) I have a theoretical delta T in the water, though I'm not entirely sure it's correct. I'm also interested in the delta T of the internal pipe (YAG rod) How would I go about calculating this?

I know from examining flow rate that the Reynold's number says it is turbulent flow.

I have included an image of the pipes incase my explanation was confusing. Thank you in advance for any help!

 

[corus]

Look at this site

http://www.cheresources.com/convection.pdf

for flow in cocentric pipes, otherwise use the difference in the pipe diameters and use standard formulae for flow inside a pipe of that diameter.

corus

 

[KevinH673]

Thanks, but what about for the difference in temperature of the solid rod, inside?

 

[IRstuff]

That's a bit trickier, since the heat is generated throughout the YAG. One option is to treat the rod as a series of concentric annuli, and determine the temperature distribution as a radial function. AFAIK, such distributions usually wind up with a parabolic radial temperature function.

TTFN

FAQ731-376

 

[KevinH673]

What about if this was simplified as a flat plate with external flow over it. Taking it as a convection problem, I haven't found helpful equations that would deal with a temperature gradient in the fluid and the plate. My heat transfer books only deal with heat exchangers that have two moving fluids.

To model the fluid, could I use an equation such as:

Q=m*Cp*(To-Ti)

Where "Q" is the power of the Yag rod? I'm not sure if I'm using Q correctly.

 

[IRstuff]

The gradient in the fluid is moot, is it not, since the fluid is constantly flowing?

As for the YAG, the same approach previously mentioned would have to be used, i.e., a series of layers that are individually treated as isothermal layers separated by layers of YAG.

TTFN

FAQ731-376