How Can I Estimate Heat Transfer in a Rotating Cylinder with Flow on Both Sides?

[minger]

This should be a fairly easy problem, although my Heat Transfer is quite rusty. I'm trying to get a ballpark estimate for a rotating cylinder that has flow on both the inside and outside.

I know the temperature of the air at the inlet and outlet and am trying to get a decent estimation for the wall temp. I would be happy assuming that I'm doing a 1D problem at both inlet and outlet and then letting the numerical program converge the answer (more complex geometry than just cylinder).

I was treating this as basically a 1D wall problem with moving flow on both sides. I have velocities on both sides and am struggling with how to proceed. I'm looking through my textbook but can't seem to find a decent Nusselt number or anything. Maybe I'm looking in the wrong place though.

On second though, perhaps I can treat it as two separate "Flow over a Flat plate" problems and then just use each solution separately for heat transfer coefficients. From that point, I can just do a simple wall problem. Would this get my in the ballpark?

Thanks

 

[Bob S]

I understand you are designing a heat exchanger. Be sure to use a counterflow design to get maximum benefit of the heat transfer.

 

[Topher925]

Where exactly is your heat source? Is it from one of the fluids or from the cylinder itself? I would first try the problem assuming the cylinder is stationary, then assume its rotating. The only difference between the two should be that your velocities slightly change direction and magnitude.

Are you trying to solve this problem with FEA or by hand?

 

[minger]

The heat is coming from the fluid itself. I was thinking the same thing regarding the rotation. The problem is structural in nature. We were assuming constant temperature profile to being, but getting some less-than-optimum answers, so we figured we'd delve in a little further.

I was able to find a journal article that gives a Nusselt number approximation for a rotating cylinder as
$$Nu = 0.6366\left[\frac{D^2 \Omega}{2\nu}Pr\right]^{1/2}$$
Which I can believe for the outside. The inside however I'm not entirely sure how to get. Flat plate? Not sure.

The CFD has been ran and the film coefficient (what CFX calls it) is orders of magnitude smaller than the analytical solution. So this leads me thinking that something is screwy with the CFD run (reference temperature, etc).

Ideally there would be something like a heat exchanger relationship. I guess I can assume the cylinder non-rotating and adjust the velocities. Then I just have a cylinder with both inner and outer flow. Sounds like a single-tube heat exchanger.

edit: What the deuce is wrong with tex right now?