Applying Newton's cooling equation to a pipe cooling

In summary, the person is trying to apply Newton's cooling equation to a system where plastic piping is being cooled via water sprays. They are looking for help in calculating how fast the pipe can be run through the sprays and predicting the final temperature for any size and thickness. This requires solving the heat conduction equation and determining the heat transfer coefficient between the pipe and the cooling water.
  • #1
scootaash
2
0
Hi. I'm trying to apply Newton's cooling equation (if relevent) to the following system. We produce plastic piping, extruded at about 200 'C and cooled via water sprays to 35 'C. We are trying to calculate how fast we can run the pipe through the cooling sprays. It's been a very long time since I did any of this so any help would be appreciated! I'm not even sure if the equation is useful in this instance.


Newton's cooling equation is :

dT/dt = k(T-M) where T is the object temp, t time and M the outside temperature.

So

T = C(e^kt) + M
Where C is the difference between the start and ambient temperature.

I can measure this for certain thicknesses and sizes of pipe, but the point is to be able to predict the final temperature for any size and thickness of pipe, given the same cooling. I have no idea how I would extend to do this!

The main problem is that only the external surface is cooled, so upon leaving the cooling tank the surface heats up again as heat is conducted to the surface.

Any suggestions for how to proceed would be greatly appreciated!
 
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  • #2
This requires solution to the heat conduction equation $$\rho C_p V\frac{\partial T}{\partial z}=k\frac{\partial ^2T}{\partial r^2}$$neglecting the curvature of the cylinder wall, with v representing the axial velocity of the pipe moving through the spray. The boundary condition is $$-k\frac{\partial T}{\partial r}=h(T-T_w)$$ at r = R. Here, h is the heat transfer coefficient between the outside of the pipe and the cooling water. This would have to be determined from some scouting experiments. The distance z of the water spray region would be that required for the calculated average temperature of the pipe to reach the desired level.
 

1. How do you apply Newton's cooling equation to a pipe cooling?

To apply Newton's cooling equation to a pipe cooling, you first need to determine the surface area of the pipe and the temperature difference between the pipe and the surrounding environment. Then, you can plug these values into the equation: Q/t = hA(Ts - T0), where Q/t is the rate of heat transfer, h is the heat transfer coefficient, A is the surface area, Ts is the temperature of the pipe, and T0 is the ambient temperature.

2. What is the significance of Newton's cooling equation in pipe cooling?

Newton's cooling equation is significant in pipe cooling because it allows us to calculate the rate of heat transfer from a pipe to its surroundings. This is important in industries such as manufacturing and engineering, where precise temperature control is necessary for the proper functioning of machinery and equipment.

3. Can Newton's cooling equation be used for all types of pipes?

Yes, Newton's cooling equation can be used for all types of pipes as long as the necessary parameters are known, such as the surface area and temperature difference between the pipe and its surroundings. However, the accuracy of the equation may vary depending on the specific characteristics of the pipe, such as its material and thickness.

4. What are the limitations of Newton's cooling equation in pipe cooling?

One limitation of Newton's cooling equation in pipe cooling is that it assumes a constant heat transfer coefficient, which may not always be the case in real-world scenarios. The equation also does not take into account other factors that can affect heat transfer, such as wind speed and humidity.

5. How can Newton's cooling equation be applied in practical situations?

Newton's cooling equation can be applied in practical situations by using it to determine the heat transfer rate from a pipe to its surroundings. This information can then be used to design and optimize cooling systems for various applications, such as in industrial processes or HVAC systems. It can also be used to troubleshoot issues with pipe cooling and make necessary adjustments to improve efficiency.

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