Calculate Cooling Time of Steel Rope in Water Trough

In summary, the cooling time of an extrduded steel wire running thru a water trough at a certain feet per minute speed can be calculated using either an analytical solution with bessel functions or charts if the Biot number >0.1.
  • #1
ProEng28
1
0
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.
 
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  • #2
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 [Broken]

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.
 
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  • #3
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.
 

1. How do you calculate the cooling time of steel rope in a water trough?

To calculate the cooling time of steel rope in a water trough, you need to use the formula t = (m x c x ΔT) / h, where t is the cooling time, m is the mass of the steel rope, c is the specific heat capacity of steel, ΔT is the difference in temperature between the steel rope and the water, and h is the heat transfer coefficient. This formula takes into account the physical properties of the steel rope and the heat transfer rate between the steel rope and the water.

2. What is the specific heat capacity of steel?

The specific heat capacity of steel is approximately 0.49 J/g°C. This value may vary slightly depending on the type of steel and its composition.

3. How does the heat transfer coefficient affect the cooling time of steel rope in a water trough?

The heat transfer coefficient is a measure of how easily heat can be transferred between two objects. A higher heat transfer coefficient means that heat can be transferred more easily, resulting in a shorter cooling time for the steel rope in the water trough. A lower heat transfer coefficient means that heat transfer is slower, resulting in a longer cooling time.

4. Can the cooling time of steel rope in a water trough be affected by other factors?

Yes, the cooling time of steel rope in a water trough can be affected by other factors such as the initial temperature of the steel rope, the temperature of the water, and the environmental conditions (e.g. air temperature, wind speed). These factors can impact the heat transfer rate and therefore affect the cooling time of the steel rope.

5. How accurate is the calculated cooling time of steel rope in a water trough?

The calculated cooling time of steel rope in a water trough is an estimation and may not be completely accurate due to variations in physical properties and environmental factors. It is important to keep in mind that this calculation provides a general idea of the cooling time and may not reflect the exact time it takes for the steel rope to cool in a specific scenario.

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