Laminar flow in a tube, heat transfer coefficient-sanity check

  • #1
30
1

Main Question or Discussion Point

Hi there,

Hopefully this is a very easy question and you all can just confirm this for me.

When calculating heat transfer into a fluid from a heated tube, is it correct to say that the heat transfer coefficient is *not* dependent on the tube diameter?

upload_2018-8-7_18-42-39.png


So, if we solve for T_{out}, we get:

upload_2018-8-7_18-45-32.png

Substituting h for K*N/D, which is fluid thermal conductivity K, Nusselt number (depends on flow conditions and location in flow), and D is diameter, we get:

upload_2018-8-7_18-47-58.png

Finally, for our circular duct, A = pi*D*dx, so we get:

upload_2018-8-7_18-49-52.png


So, is there no dependence on tube diameter? I know that Nusselt number is *weakly* dependent on diameter when the flow is still developing, but that seems like it. In other words, given a large enough furnace, I could put a tube of any size in that furnace, and the flow would heat just as quickly regardless of tube diameter. That feels wrong to me, is there something I am missing?

Thanks!
 

Attachments

Answers and Replies

  • #2
19,935
4,099
For laminar flow in a tube (with constant wall temperature), what is the equation for the local Nussult number as a function of the Reynolds number, Prantdl number, and x/D in the thermal entrance region?

For laminar flow in a tube (with constant wall temperature), what is the equation for asymptotic Nussult number at large distances along the tube?
 
  • #3
19,935
4,099
As best as I can tell, your assessment is correct. For laminar flow, Nu is virtually independent of D.
 
  • #4
19,935
4,099
Dimensional analysis of the partial differential heat balance equation shows that the dimensionless temperature ##\frac{T-T_0}{T_w-T_0}## is a function only of the dimensionless axial position ##\frac{kz}{WC_p}## and the dimensionless radius r/R. The dimensionless axial position is independent of diameter.
 
  • #5
30
1
Yup. After sleeping on it, I felt pretty correct about what I had written. But it is nice to have had someone else look it over. Thank you for your time!

Go Blue!

'06 School of Education
 

Related Threads on Laminar flow in a tube, heat transfer coefficient-sanity check

Replies
2
Views
5K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
1
Views
993
Replies
4
Views
15K
  • Last Post
Replies
8
Views
714
Replies
0
Views
2K
Replies
2
Views
887
Replies
3
Views
2K
Replies
4
Views
2K
  • Last Post
Replies
1
Views
837
Top