Heat transfer - laminar curved duct flow

[vic chan]

Hi,

I'm trying to find some data on the entrance region of a curved duct with a rectangular cross section. Its a heat transfer problem where the fluid flows through a rotated duct. The distance of the duct is smaller than the entrance region for a straight rectangular duct of same aspect ratio. What I would like to find is the Nusselt number and friction factor for this type of flow. The convective boundary condition along the bottoom and side walls is a constant heat flux with an adiabatic condition on the top wall. I've done a thorough search of current literature but have come up empty. Thanks for the help/advice. I've also gone through a couple of Heat Transfer Handbooks, but they mention that few studies have been done, only with a aspect ratio of infinity(parallel plates).

Thanks,

vic chan

 

[jaap de vries]

You did not give us a whole lot of information to work with. Since you say the flow is laminar, I do not suspect a very strong effect from the curvature. A good starting point would be to assume a straight piece of rectangular tube. You can find the friction factor if you know the surface roughness and use a moody diagram.

I quickly found that for both thermally and hydro-dynamically fully developed laminar flow in a rectangular duct of width a and height b:

Local Nusselt number (hD/k), constant q, (constant T)
a = b: 3.63 (2.98)
a = 2b: 4.11 (3.39)
a = 4b: 5.35 (4.44)

Ref:
J. Sucec, "Heat Transfer", Wm. C. Brown, 1985.
ISBN: 0-697-00257-8

 

[vic chan]

First thanks for the quick response and the help!

What I neglected to point out is that I'm searching for correlations based on a developing flow (thermally and hydrodynamically developing) Also the De (Deans) number ranges from 10 to 200 based on different dimensions and inlet Re (Reynolds) numbers. I have already found correlations for straight rectangular ducts. And have averaged the friction factor over the entrance region (as it increases from inlet until it reaches a steady value in the fully developed region). I have also found correction factors for the friction factor for curved duct flows which incorporate the fully developed friction factor for straight rectangular ducts. The friction factor for curved rectangular ducts is about 20 percent greater than the friction factor for straight rect. ducts. However, there don't appear to be any studies on the developing hydrodynamic entrance region and the friction factor in the inlet region of these ducts. I'm assuming it may also be more than 20 percent greater than for straight ducts. As for using the moody diagram, the moody diagram friction factors are strictly for fully developed flow and even when the Diameter of a circular pipe is replaced by the Hydraulic Diameter of the rectangular duct, the error is usually stated to be above 20 percent. It is a good estimate in the field, however I am seeking something a little better than a quick estimate. I wish to achieve more accurate results with either known experimental data, or numerical data. The same is true for the Nusselt number as it varies with x and is a decreasing function of x (duct/pipe lenght) in the thermally developing region. So far I have only seen infinitely parallel plates with a constant temperature boundary condition. Handbook of Heat Transfer by Rohsenow, Warren M., Hartnett, James P., and Cho, Young I., seem to only point out that the Hydrodynamic entrance length of curved duct flow is 20 to 50 percent less than that for straight duct flow, but don't mention specific studies.