Calculating Cooling Times 7

[mmelville]

I am looking for a formula to determine the cooling time of a blow-molded plastic tube with forced cold air. The pipe is 40mm o.d. with a 3-4mm wall thickness. I appreciate any help offered. Thanks in advance!

 

[zekeman]

It gets worse...

I found that the thermal conductivity of most plastics is more like 0.1 BTU/HR-FT^2_DEGF as opposed to 0.5 for the example case.
I redid the problem (assuming a similar reduction in diffusivity, kappa) and found the cooling time to be 7 minutes for the "exact" solution vs the 0.7 minutes using the lumped method or a factor of 10.

So much for using "lumped" solutions for this type of problem.

 

[zekeman]

Correction
units of thermal conductivity should be
BTU/HR-FT-DEG F

 

[ione]

Hey Zekeman,

The fact the lumped model was not applicable here (or at least the consideration it gives misleading results) was already stated in one of my previous posts (30 Mar 10 3:28). The Biot number is definitely too high (the poor thermal conductivity of plastic makes void the lumped model). I have to reassert that with a metal pipe and standing the same other conditions, the lumped model would have worked fine!

 

[zekeman]

Hey Ione,
"...........In the case of a plastic pipe the thermal conductivity is low but the wall thickness is low as well, so the lumped model should be applicable."



Your quote of Mar 29.

I only commented because someone ( like you at that writing and me for accepting it at the time) may think that a "thin" section meets the "lumped" requirement and also that the magnitude of the the error could be game changing.

So we now all agree that Biot number MUST be small for the lumped model but how small is still at issue; so why not use the more exact solution found in the plots I found. It only takes a few more minutes of work to get an accurate answer, since the "error" in using the "lumped" solution cannot be readily quantified for Biot values that are "small".

 

[ione]

I must confess this has taken me a bit, and probably nobody will be interested in this, anyhow I have found out that the “fathers” of the graphical approach for this kind of problem are Heisler and Grobler (Heisler charts and Grobler charts).

These curves could be found at the link below from page 194 to 205 (for given geometries).

http://books.google.it/books?id=g9u...resnum=1&ved=0CAsQ6AEwAA#v=onepage&q=&f=false

I have also found another link which gives a more direct access to the charts aforementioned:

http://www3.interscience.wiley.com:...cropera/0471457280/supplemental/ch05_supp.pdf

 

[zekeman]

"'fathers' of the graphical approach for this kind of problem are Heisler and Grobler (Heisler charts and Grobler charts)"


Good references, but "fathers". That's a stretch. Similar graphs in C&J date back to the early 30's, long before Heisler and Grober were even out of grade school.

 

[ione]

Ok, someone here is related to Coulson and/or Jaeger and can’t resign to terms that someone else has hijacked their work and got the glory....

Zekeman probably you are right (Heisler’s work was presented only in 1947 and Grobler improved it in 1961), but the charts I have quoted have become part of the scientific literature as Heisler charts and Grobler charts.

 

[zekeman]

Yes, I admit that I am Carslaw's second cousin twice removed.

 

[unclesyd]

You might be able to glean a little information from this paper.

http://eprints.imperial.ac.uk/bitstream/10044/1/1214/1/Leevers2004c.pdf