# Layer of Ice in water pipe (affect on heat transfer)

sam...wise
Hi

I am curious to know if anyone can provide a formula/answer to the affect of a thin layer of ice may have on heat loss in water flowing in a pipe.

Example.
I have a smooth plastic pipe approx 20mm diameter, 5m length. 400ml of water travels down the pipe, approximately 0.5m/s. in -10C external temperature (assuming no wind chill), the temperature of liquid drops from a start temp of 30C to an exit temp of 20C.

But by how much would a thin layer of ice inside the length of the pipe say 2mm have on the exit temp of the water? Is there a calculation I can use to work out by how much the temperature will reduce?

Thanks in advance for any assistance.

Sam...wise

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Gold Member
The thermal conductivity of ice is somewhat low at 2.22 W/mK, but you would have to calculate the convective coefficient of the water in the pipe to know for certain what effect it would have.

Gold Member
It is actually a fairly simple heat transfer problem assuming you know the pipe thickness and the ice thickness. Ice would help insulate the pipe, but you also have to keep in mind that it is sitting there at 0 C itself.

Homework Helper
It is actually a fairly simple heat transfer problem assuming you know the pipe thickness and the ice thickness. Ice would help insulate the pipe, but you also have to keep in mind that it is sitting there at 0 C itself.

The only simple calculation is whether there will be any ice at all. From the volume flow rate, and the inlet and outlet temperatures, you know the rate of heat loss from the water. If you assume the outside of the pipe wall is at -10C (which is pessimistic) then you can estimate the temperature of the inside wall to conduct away that quantity of heat, given the pipe diameter and wall thickness and the thermal conductivity of the material.

If the answer to that is below 0C, then doing a detailed calculation is actually very complicated, because the ice thickness will vary along the length of the pipe and the thickness profile will have to be calculated, probably by a computer simulation of the ice build-up in the pipe.

The assumption the ice would all be at 0 C is obviously wrong, because that would mean there was no temperature gradient in the ice and therefore no heat flow through it.

My gut instinct would be that the mean outlet temperature is 20C, there will be no ice in the pipe. Of course if the flow stops, that situation will soon change!

Gold Member
Even with all of that, it isn't a terribly difficult problem if you just make some simple assumptions that don't introduce any meaningful error into the calculations. I doubt this guy needs it to be accurate to 0.1% or anything so crazy. Assuming lengthwise uniform ice thickness wouldn't be a bad approximation. Even without that assumption, it isn't terrible with various other valid simplifications.

Homework Helper
Even with all of that, it isn't a terribly difficult problem if you just make some simple assumptions that don't introduce any meaningful error into the calculations. I doubt this guy needs it to be accurate to 0.1% or anything so crazy. Assuming lengthwise uniform ice thickness wouldn't be a bad approximation. Even without that assumption, it isn't terrible with various other valid simplifications.

Anybody can get the wrong answer by making a pile of unjustified (and unjustifiable) assumptions. Garbage in, garbage out and all that.

Anyway, I already made my simplifying assumption:water outlet temp 20C = zero ice.

Gold Member
That is true, but none of those assumptions I mentioned are necessarily garbage. You can toot your own horn all you want, but the problem doesn't have to be overly complicated to get a good engineering estimate. It all depends on what the final application is. There are very few that require the kind of accuracy you propose.

sam...wise
Firstly, thanks for the replys. I was thinking, to simplify the situation I would be able to assume an average ice thickness. Once I have the calculation, I could vary this and see what affect it has.

AlephZero, you are right, with water of outlet temp 20C ice shouldnt be present, but flow is not constant and small volumes of water do remain in the pipe, which quickly freeze. This builds up in layers to create a problem.

Instead of making this too complicated, is there any way I can work out how much quicker ice would cool the water vs air? My present calculation is for water flowing through a pipe with ambient air temp of -10. Pipe temp is same as ambient and thickness is ignored. Could I make it into a flat plate example of convection with ice as the surface and water flowing over it?

I know from practical tests that 400ml water flowing in a pipe with ice in it is not exiting at 20C but nearer to 5C.

Sorry, I hope that makes sense...

sam...wise
I have realised this question is somewhat irrelevant to my problem.

If the exit temperature of the water is above zero at the exit point, ice will not have a great affect on this, as it too is the temperature of ambient surroundings.

What this question is really asking is how much liquid would freeze at the boundary layer between the ice and water as the water flows over it? A tricky and in this case probably irrelevant question.