Heat transfer of a hot plastic thread in a cold water bath

[Rotzooi]

Hi,

I'll describe my problem more specific.
I have a continuous flow of this polymer thread (polystyrene) at 465 °K (190°C sorry I'm metric) that needs cooling down. It passes trough a water bath which is kept at 310°K (35°C). Now i try to calculate the heat exchange into the water, to determine the speed of the cooling, or to calculate how hot the thread still is after a time.

approach:
I was thinking using conduction from the thread's core to the exterior and then convection into the water. (water is not moving btw).

Now another look at this approach:
The core of the polymer will remain hot when the exterior is cold. Because there is a very low thermal conductivity (0,187 W/m.K). So maybe i ought to use another formula. Because my first approach doesn't cover this. But this is where my knowledge stops. And research doesn't seem to deliver results. (When a metal bar is put in water u can take a temperature that is uniform over the bar because the heat exchange in metal goes so fast, here it is not the case.)

Any ideas or remarks would be of great use!

 

[rumborak]

I'll leave better answers to others here, but it's probably also worth pointing out that the matter will be confounded by the convection effects of the water. The water will heat and thus rise up, causing turbulences and pulling cooler water from below. Calculating that on paper, not sure it can be done.

 

[Chestermiller]

This is a problem in man-made fiber spinning into a water bath. What is the diameter of the capillary at the spinneret, and what is the quenched diameter of the filament? I'm guessing that most of the filament deformation takes place within the air gap, although most of the cooling takes place below the water surface. As a first approximation, you can assume that the water is dragged along with the filament velocity, so that, at each cross section of filament, you are dealing with transient 1D conductive heat transfer into an infinite medium.

I'm also guessing that you have multiple filaments in an array, and not just one filament. If that is the case, the thermal boundary layers from the filaments can interfere with one another, and inhibit the heat transfer. The drag flow from outer rows of filaments can also prevent cooler water from reaching the inner rows. This then becomes a pretty complicated problem. Because of the high speed involved, natural convection is going to be negligible, but the main flow effect will be filaments dragging fluid downward and inward towards and through the array.

You need to hit the literature on fiber spinning.

Chet

 

[Rotzooi]

I'll leave better answers to others here, but it's probably also worth pointing out that the matter will be confounded by the convection effects of the water. The water will heat and thus rise up, causing turbulences and pulling cooler water from below. Calculating that on paper, not sure it can be done.

Hi, thanks for the response.
Ok, i get what u want to say but this is thinking a little too far. I will never be able to clalculate this indeed.
What is your opinion on the effect that i describe in approach two?

 

[Rotzooi]

This is a problem in man-made fiber spinning into a water bath. What is the diameter of the capillary at the spinneret, and what is the quenched diameter of the filament? I'm guessing that most of the filament deformation takes place within the air gap, although most of the cooling takes place below the water surface. As a first approximation, you can assume that the water is dragged along with the filament velocity, so that, at each cross section of filament, you are dealing with transient 1D conductive heat transfer into an infinite medium.

I'm also guessing that you have multiple filaments in an array, and not just one filament. If that is the case, the thermal boundary layers from the filaments can interfere with one another, and inhibit the heat transfer. The drag flow from outer rows of filaments can also prevent cooler water from reaching the inner rows. This then becomes a pretty complicated problem. Because of the high speed involved, natural convection is going to be negligible, but the main flow effect will be filaments dragging fluid downward and inward towards and through the array.

You need to hit the literature on fiber spinning.

Chet

Hi, thanks, fiber spinning is indeed a bit similar! Will search the term for more!

My problem however has nothing to do with fiber spinning, its just for cooling so cutting it to a granulate form goes easier.
The diameter of the thread is 3milimeter. (no quenched diameter of filament available) And there is only one filament at a time in the water bath.

 

[Chestermiller]

Hi, thanks, fiber spinning is indeed a bit similar! Will search the term for more!

My problem however has nothing to do with fiber spinning, its just for cooling so cutting it to a granulate form goes easier.
The diameter of the thread is 3milimeter. (no quenched diameter of filament available) And there is only one filament at a time in the water bath.

OK. You're making pellets. That's a pretty big diameter thread. If there's any kind of circulation in the water bath, that's going to enhance the heat transfer.

If it were I working on this, I would solve the problem using the 1D transient heat transfer approximation I mentioned in post #3. This would probably require numerical analysis. You probably would have to take into account the heat of fusion, although, if you want to do it crudely, that could be lumped in with the heat capacity, particularly since the phase change is going to occur over a range of temperatures (in the case of a polymer).

So basically, you have a cylinder with one set of thermal properties embedded within semi-infinite medium with a different set of thermal properties, where, at time zero the cylinder is uniformly hot and the medium is uniformly cold. You then solve this transient heat conduction problem.

Chet

 

[Rotzooi]

It is indeed an interesting approach. However, difficult to calculate.
Anyway you pushed me in the right direction. So thank u Chet!

This summed it up pretty good! Thanks alot!

So basically, you have a cylinder with one set of thermal properties embedded within semi-infinite medium with a different set of thermal properties, where, at time zero the cylinder is uniformly hot and the medium is uniformly cold. You then solve this transient heat conduction problem.

Still a little unclear what u meant by this

I'm guessing that most of the filament deformation takes place within the air gap

 

[Chestermiller]

It is indeed an interesting approach. However, difficult to calculate.
Anyway you pushed me in the right direction. So thank u Chet!

This summed it up pretty good! Thanks alot!
Still a little unclear what u meant by this

That's when I still thought we were dealing with spinning.

Check out Carslaw and Jaeger.

Chet