Free convection IN a slender vertical cylinder

[weschrist]

Hi,

I have run into a problem and can't find an answer. I am trying to estimate the heat transfer coefficient for water INSIDE a vertical cylinder exposed to uneven heating.

The cylinder is 1m high with a diameter of 0.035m. D/L is then 0.035.

I have calculated the Grashof number 417200 and the Rayleigh number 3950887. There is a correlation equation for D/L>=35/Gr^(1/4). But I have D/L=0.035 and 35/Gr^(1/4)=1.38, so the equation is not valid. Apparently the curvature of the cylinder walls affects the fluid flow, but how? Would a Nusselt number (hence the heat transfer coefficient) calculated with the invalid correlation equation be a minimum, assuming flow is more inhibited with increased curvature?

I have searched high and low but can't find anything for flow INSIDE a vertical pipe for this geometry. A paper by LeFevre and Ede (1956) got me excited, but it is for flow OUTSIDE the slender vertical pipe.Any suggestions or help would be greatly appreciated.LeFevre, E. J., and Ede, A. J. (1956). Laminar Free Convection from the Outer Surface of a Vertical Circular Cylinder, Proc. 9th International Congress on Applied Mechanics, Brussels,
Vol. 4, pp. 175–183.

 

[AndyW]

Hi there,

Thank you for reaching out with your problem. It sounds like you have already done some thorough calculations and research. I am a scientist who specializes in fluid mechanics and heat transfer, and I may be able to offer some suggestions and help.

First of all, you are correct in your assumption that the curvature of the cylinder walls affects the fluid flow. This is known as the "entrance effect" and it is common in flow through pipes with small diameters. In your case, the curvature of the walls may create a boundary layer that affects the heat transfer coefficient.

One approach you could take is to use a numerical simulation software, such as Computational Fluid Dynamics (CFD), to model the flow and heat transfer inside the cylinder. This would allow you to account for the curvature of the walls and potentially give you a more accurate estimation of the heat transfer coefficient.

Another option is to look for experimental data or correlations for flow inside a curved pipe. While your geometry may not be exactly the same as what has been studied before, it could still provide some insight into the behavior of the flow and heat transfer.

Additionally, you could consider simplifying your problem by assuming a constant heat transfer coefficient throughout the cylinder and using the Nusselt number correlation for a straight pipe. This may not be as accurate, but it could give you a rough estimate to work with.

I hope these suggestions are helpful. If you have any further questions or need more guidance, please feel free to follow up with me. Best of luck with your research!