Calculate Cooling Time of Steel Rope in Water Trough

[ProEng28]

I have been tasked with calculating the cooling time of an extrduded steel rope running thru a water trough at a certain feet per minute speed. I've been researching conduction heat transfer equations and can't seem to find what I am looking for. I was oping someone could help me with the equation I am looking for.

 

[256bits]

How good at you with math:
http://www.cdeep.iitb.ac.in/nptel/Mechanical/Heat%20and%20Mass%20Transfer/Conduction/Module%204/main/4.4.html

There is the analytical solution with bessel functions.
Or you can use charts if the Biot number >0.1.
The charts did not show up for me, probably because I am using an ancient browser - hopefully they will for you.

here is another site with description,
http://www.ewp.rpi.edu/hartford/~ernesto/S2006/CHT/Notes/ch03.pdf

I found those by searching " heat conduction long cylinder."

I do not know if there is a simplied method.
Good luck.

 

[Chestermiller]

Hi ProEng28l. Welcome to Physics Forums.

I presume the water is circulated to the trough. How is the water temperature maintained? What type of mixing or counterflow is provided? Is the flow mainly parallel to the wire or perpendicular?

You might be able to bound the answer. When the wire enters the tank, it begins to drag water along with it. The water at the surface of the wire travels along with the wire. If you assume that a large amount of water is traveling along with the wire, you might be able to look at the situation is a transient conduction problem between a cylinder in an infinite ocean of water. At time zero, the temperature of the cylinder would be equal to the temperature of the steel extrudate. This analysis would lead to an upper bound on the amount of residence time to cool the wire. As a lower bound to the amount of residence time, you could assume that the temperature at the surface of the cylinder is maintained at the bulk temperature of the cooling water during the process. This would be transient cooling of a cylinder with constant surface temperature. See what answers these two bounds give you an how far apart they are. Or, for design purposes, you might conservatively employ the upper bound solution, saying that, in actual practice, the cooling time would be less than this.