How long to freeze standing water in steel pipe

In summary, the conversation is about determining the approximate time it would take for standing water in an 18-inch steel pipe to freeze. The parameters and assumptions for the calculation are discussed, as well as two different methods that were used to calculate the time. The first method uses the lumped capacitance method, while the second method uses the overall heat transfer coefficient. A concern is raised about the accuracy of the calculations due to the roughness of the pipe not being taken into account. The individual posting the conversation is a mechanical engineer working on a design project and is seeking help to determine the freezing time.
  • #1
jt316
32
0
I posted this in another section and haven't receive any feedback so I thought I might have it in the wrong section. Thanks in advance for any help.

I'm at little rusty on my heat transfer and could use some help.

I'm trying to calculate the approximate time to freeze standing water in a 18inch steel pipe. I have some parameters and made some assumptions and they are:

The pipe is 18inch carbon steel
The standing water is initially around 68oF
The outside temp is around 0oF
There is a constant breeze around 5mph
No insulation around pipe
The pipe is exsposed to the air and not buried
The pipe is completely filled with water


I've calculated this two different ways and came up with two completely different time values. One was around 8.7hrs and the other was around 4.8hrs.

For the first method, I calculated the surface heat transfer coefficient (h) at the wind/pipe interface by:

First calculating the Reynolds number (Re) of the wind/pipe interface from Re=VD/v(kinematic viscosity of air)
Then I found the Prandtl number (Pr) for air at 0oF
Then I calculated the Nusselt number (Nu) by Nu=0.023 x (Re)4/3 x (Pr)1/3
Then I found the thermal conductivity of the air kf
Then I calculated the surface heat transfer coefficient(h) by h=(Nu x kf)/Dpipe

I came up with h~11 W/(m2 K)

Once I found the surface heat transfer coefficient, I calculated the Biot number (Bi) by Bi=hD/ks , where ks is the thermal conductivity of the carbon steel pipe.

I found Bi=0.003364666 , and with Bi<0.1 I figured could use the lumped capacitance method.

Note: density=rho=p
ps=density of steel
pw=density of water
cs=heat capacitance of steel
cw=heat capacitance of water
Ti=initial water temp
Tinf=air temp
T=water at 32oF or 273.15 K

Using the lumped capacitance method, time (t) in secs can be found from t=[(pVc)tot/(hAs)]*ln[(Ti-Tinf)/(T-Tinf)]

Where (pVc)tot=[((pscs(Do-Di))/4)s+((pwcw(Di))/4)w]

and so ((pVc)tot)*(1/h)*ln[(Ti-Tinf)/(T-Tinf)]=t

This method is how I came up with 8.7hrs. I came up with 4.8hrs using a method out of an ASHRAE handbook.

Is the method okay for a good approximation? Is 8.7hrs a good approximation? If there's something I'm doing wrong or a better approach, please let me know.

Thanks for the help.
 
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  • #2
I don't think that can use the lumped capacitance method when dealing with a phase change so I've tried another approach... Is this the correct method?

I calculated the surface heat transfer coefficient (h) by [tex]h=\frac{N_u * k_f}{D_o}[/tex], where [tex]k_f[/tex]= thermal conductivity of air

Then I calculated the overall heat transfer coefficient (U) by [tex]U=\frac{1}{\frac{1}{h*2*PI*r_o}+{\frac{ln\frac{r_i}{r_o}}{2*PI*k_s}}}[/tex], where [tex]k_s[/tex]=thermal conductivity of the steel pipe.

Then I calculated the heat loss per length of pipe by [tex]q = U*A_s*(T_i-T_\infty )[/tex], where [tex]A_s[/tex]=suface area of pipe per length of pipe, [tex]T_i[/tex]= initial water temp and [tex]T_\infty[/tex]=outside air temp.

The I calculated the time for the water to reach the freezing temperature by:

[tex]t_c = \frac{C_{pw} * M_{lw} *(T_i - T_f )}{q}[/tex] , where [tex]C_{pw}[/tex]= specific heat of water, [tex]M_{lw}[/tex]= mass of water per length of pipe, and [tex]T_i[/tex]=intial temp of water, [tex]T_f[/tex]=freezing temp of water and [tex]t_c[/tex] is in seconds.

I calculated [tex]t_c=14485.17 s [/tex] or 4.02 hrs

Then I calculated the time for the water to actually freeze once it reaches the freezing temp by:

[tex]t_f = \frac{h_{fs} * M_{li} }{q}[/tex], where [tex]h_{fs}[/tex]=latent heat of fusion for water, [tex]M_{li}[/tex]=mass of ice per length of pipe.

I calculated [tex]t_f= 58098.86 s [/tex] or 16.14 hrs

So the total time to freeze would be [tex]t_{tot}= t_c + t_f = 20.16 hrs[/tex]

I've attached a pdf of my entire calculation if you would like to check my numbers..

Thanks for the help
 

Attachments

  • Pipe Freezing Problem.pdf
    47.9 KB · Views: 636
  • #3
Boy, I hated my heat transfer class: it's a lot of work for something that in real life is never actually done and isn't all that accurate anyway. Yeah, it's good to learn the theory, but I don't know that the theory is really all that useful to actual engineers. Anway, that's why I didn't respond before...

I think the flaw may be in the calculation of the pip-air heat transfer coefficient. I don't see anything about the roughness of the pipe in there. I can't remember if the calculation assumes it is smooth, but in any case, if it isn't smooth, you get much more turbulent flow and much more convection. I'm not certain of this, so consider it just food for thought.
 
  • #4
Ah... so you think this is a homework problem? I was wondering why no one was responding to the problem...

I am a mechanical engineer and this is actually a design related problem. We are in the design phase of a project that requires the installation of a cooling tower and 18 inch water lines. We are trying to determine that if there was ever failure of the pump, how long we would have before the water in the pipe would freeze. We have a contractor working for us who thinks this pipe will never freeze and we have another mechanical engineer that think it might, under these conditions.

I've been given the task to determine when it would actually freeze. Well, at least a good approximation.

It's been several years since I've had heat transfer as well.

Any and all help is greatly appreciated.

Thanks
 

1. How long does it take to freeze standing water in a steel pipe?

The exact time it takes for standing water in a steel pipe to freeze will depend on various factors such as the temperature, the thickness of the pipe, and the volume of water. However, on average, it can take anywhere from a few hours to a full day for the water to completely freeze.

2. Can standing water in a steel pipe freeze instantly?

No, it is not possible for standing water in a steel pipe to freeze instantly. While the metal pipe may quickly cool down, the water inside will still take some time to freeze completely. Additionally, the freezing process is also affected by the surrounding temperature and other factors.

3. How does the thickness of the steel pipe affect the freezing time of standing water?

The thicker the steel pipe, the longer it will take for standing water to freeze inside. This is because thicker pipes have more insulation and can retain heat better, which slows down the freezing process.

4. Will the freezing time of standing water in a steel pipe be affected by the shape of the pipe?

Yes, the shape of the steel pipe can affect the freezing time of standing water. For example, a pipe with a larger diameter will take longer to freeze compared to a pipe with a smaller diameter. This is because the larger surface area of the water in a wider pipe allows for more heat exchange with the surrounding environment.

5. Can the freezing time of standing water in a steel pipe be affected by the type of water used?

Yes, the type of water used can affect the freezing time in a steel pipe. For instance, saltwater has a lower freezing point compared to freshwater, so it may take longer for saltwater to freeze inside a steel pipe. Additionally, impurities in the water can also affect the freezing time.

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