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

[gpsimms]

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?

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

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:

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

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!

 

[Chestermiller]

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?

 

[Chestermiller]

As best as I can tell, your assessment is correct. For laminar flow, Nu is virtually independent of D.

 

[Chestermiller]

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.

 

[gpsimms]

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