# Time for water to freeze in a pipe

## Main Question or Discussion Point

I need some help with a heat transfer issue.

I am trying to calculate if a exposed non flowing water filled pipe will freeze based on a varying temperature profile that varies from 26 deg to 45 deg in 24 hrs. This will depend on the size of the pipe but that is a variable that can be changed to determine the minimum size pipe to use.

For example if I have an ambient temp profile over 24 hrs in 1 hr increments what method would one use?

Would you need to just calculate the heat loss to get the pipe & water to 32Deg and then the heat loss to turn the water to ice? Is is just a convection problem, is there enough radiation involved to even inlcude that with the low temperature deltas?

I was thinking I would set up a spread sheet and calculate the heat loss for a finite number of steps to match the ambient temperature profile and see if the heat losses and gains result in the pipe freezing over a certain time.

Any ideas would be most helpful.

Kris

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AlephZero
Homework Helper
The biggest unknown you have is the heat transfer coefficient(s). These are usually based on experiment, so make sure the numbers or formulas you use correspond to the actual situation you have.

If the pipe is in the open air, wind speed will have a big effect on the HTC.

Heat transfer coeffs for boiler-tube situations (which are fairly easy to find on the web) may be assuming a higher temp difference, therefore more convection in the air, and therefore higher heat transfer rates than your situation. Sorry I can't give you a good reference to reliable data, my heat transfer calculation experience is all at conditions way different from this, But I know getting good quality HTC data can be hard!

Radiation will be irrelevant with such small temp differences. Remember the environment radiates heat back into the pipe, as well as the pipe radiating heat to the environment.

Another complication - when the pipe is partly frozen, presumably the ice will form an insulating layer on the inside of the pipe which will reduce the heat transfer. But as soon as the air temp goes above freezing, the ice will start to thaw from the outside and that will not restrict the heat flow in. Ignoring this seems like erring on the side of caution - but if the analysis is too far wrong, you may make the wrong design decisions.

A spreadsheet approach to doing the calcs should be OK. If would be a good idea to do it for different time intervals (e.g. 1 hour and 30 minutes) to check you get consistent results. Start off with a simple case (e.g. the pipe at 50 and the air at a constant 40) and check your spreadsheet agrees with the textbook solution to the equations for the pipe temperature.

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first of all it varies if u start from 45 or from 26..what i would do if it was a rotational repetitive cycle is to start from 45, and calculate heat loss according to the chosen increments. after each increment u can calculate the temperature the water has reached. then u start again. of course at every temperature you would need to recalculate the convection constants (h in W/m2 C, or other units since ur not using Celcius ur probably using BTU's). but this method should work, if u have a good book to get the thermal convection terms.