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

In summary, the heat transfer coefficient is not dependent on the tube diameter when laminar flow is present.
  • #1
gpsimms
30
1
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!
 

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  • #2
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
As best as I can tell, your assessment is correct. For laminar flow, Nu is virtually independent of D.
 
  • #4
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.
 
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  • #5
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
 
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1. What is laminar flow in a tube?

Laminar flow in a tube is a type of fluid flow in which the particles of the fluid move in an orderly, smooth manner. This means that the fluid particles move in parallel layers, without any significant mixing or turbulence between them.

2. How is laminar flow different from turbulent flow?

Laminar flow is characterized by smooth, orderly movement of fluid particles, while turbulent flow is characterized by chaotic, irregular movement. In laminar flow, the fluid particles move in parallel layers, while in turbulent flow, the particles mix and swirl around in a random manner.

3. What is the heat transfer coefficient in laminar flow?

The heat transfer coefficient in laminar flow is a measure of how easily heat is transferred from a heated surface to a fluid. It is typically lower in laminar flow compared to turbulent flow, as the orderly movement of fluid particles in laminar flow makes it more difficult for heat to be transferred.

4. How is the heat transfer coefficient calculated in laminar flow?

The heat transfer coefficient is calculated using the formula h = k / (D/4), where h is the heat transfer coefficient, k is the thermal conductivity of the fluid, and D is the diameter of the tube. This formula assumes fully developed laminar flow, meaning the fluid has reached a steady, uniform flow pattern within the tube.

5. Why is it important to perform a heat transfer coefficient sanity check in laminar flow?

A heat transfer coefficient sanity check is important to ensure that the calculated value is reasonable and accurate. This helps to validate the results and ensure that the assumptions made in the calculation are appropriate. It also helps to identify any errors or discrepancies in the data or calculations.

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