A Very Unique Heat Exchanger Problem - Heat Transfer Roller! 4

[grausch13]

Hi Everyone,

First post here, I lurk through the forums for help with certain design problems but I dare say I could not find one similar to this! Unfortunately, this problem has been a pain in my side from the moment I started dealing with it. I realize this is quite a long problem, however, I thought I'd throw it out here to see if anyone had any thoughts. Thanks to everyone who takes a look.

To Everyone Brave Enough To Tackle This Design Problem:

I am pretty deep into an R&D project in which I am trying to create an excel spreadsheet that would act as a quick means to calculate the answer to this problem based on the ability to quickly change the inputs. The problem and setup is always the same, however, the inputs change periodically.

The Problem: (please see the attached schematic for clarity)

To find the exiting temperature of a web substrate material after it comes in contact with, and leaves, a heat transfer roller. The roller itself acts as a heat exchanger of sorts. Water enters one end and leaves the other. The heat is transferred from the web material through the roller as it comes into contact with it. The temperature of the exiting water from the roller needs to be found as well.
This problem seems quite easy at first glance, however, I can assure you there is quite a lot involved. There is a certain process that needs to be taken in order to solve this problem, and I don’t believe I am there yet. Unfortunately, I cannot run any experiments either so a theoretical analysis is the only option. Obviously, the web material is only in contact with the roller for a brief period of time which I believe increases the degree of difficulty of this problem.

I would very much appreciate ANY help on this problem. Even bouncing ideas back and forth would be great. I will purposely leave out the steps I’ve taken so far as to not influence anyone else’s train of thought. I would be glad to share it with you though if you’d like.

Thanks,

Garrett

 

[IRstuff]

Wow! kudos for a great drawing and problem details. The only thing that you might want to consider, however briefly, is the air temperature, and whether that affects roller surface temperature before it gets to the web.

There is another thread: thread391-360043 that may have bearing on this, since it's also a transient analysis.

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[grausch13]

Thank you IRstuff. I am willing to disregard the cooling of the web to convection as well as the cooling of the outer shell to convection as well as I believe it will be negligible to the overall heat transfer. Thank you very much for your response!

Garrett

 

[MikeHalloran]

You might find some help by searching on analysis of paper machine dryer rolls.

They are normally quite a bit wider and somewhat larger in diameter than your drum. Their temperature can be assumed uniform because they are typically heated with steam, and the steam's pressure determines the temperature at which it condenses, on the inner wall of the roll. Steam goes in one end and condensate is siphoned out the other end.
They are normally used in banks of a dozen or more rolls, all set up so the web wraps at least 270 degrees over each roll. ... so there's a lot of contact area.

Your setup is giving up a lot of potential and easily utilized heat transfer area by using a small wrap angle. You're also running a damn fast web there.

I think one simplified analysis could look at a square unit of web, instantaneously brought into contact on one side with a surface at uniform temperature, and after a short time ( function of wrap angle and web speed), instantaneously removed. That time and the unit mass and specific heat of the web would give you a temperature rise for the web, and a heat flux out of the drum over the wrap area. You can probably take it from there.




Mike Halloran
Pembroke Pines, FL, USA

 

[MikeHalloran]

p.s.
For reasons I don't understand, your pdf appears blank in CentOS6's document viewer, but opens, after a puzzling long delay, in an app called Okular.
Is there anything atypical at your end?

The temperature rise in the cooling water should be fairly sensitive to how you 'stuff' the drum, e.g. to cause the water to flow only along the shell, or only along the part of the shell contacting the web. That's a fairly fancy problem by itself, possibly best shelved until/unless you can't get the process where you want it with adjustments external to the drum.




Mike Halloran
Pembroke Pines, FL, USA

 

[ione]

grausch13,

Maybe you can find some inputs at the link below:

https://minds.wisconsin.edu/handle/1793/7685

 

[racookpe1978]

Solve your roller (round transient arithmetic issues) after you find out the heat transfer transient issues (mass involved (thickness of web per area), pressures (heat transfer coefficient) and contact area and delta T's primarily))

Once you've resolved adequately for your assumptions "how long does this area of web have to touch a constant temperature metal surface to get hot enough all the way through the web material for my design?" then you can figure out the heat gain problem "how much do I have to heat the metal all the time so it can lose the previous amount of energy fast enough to heat the web fast enough?"

Then you can begin to solve the larger heat loss problem "how much energy is lost from this hot surface every second from ALL heat losses everywhere - whioch is actually the first time you need to worry about the size and diameter of the roller and all of the "not-in-contact-with-the-web heat losses of the roller.

Once that is solved, you only need to figure out how to get that much energy into the roller.

Then you can start thinking about the dynamics of how fast the roller goes and the web goes.

You're worried (properly !) about too much too soon. To repeat: start with the basics. How much heat energy per area is needed to "cure" your web (get one side of the web hot enough to get the far side hot enough for the chemical reaction to work) is the start. Then you need to "transfer that much energy for hot (flat!) plate to the web surface: pressure, heat transfer coef at that pressure, delta T, etc.

 

[grausch13]

Everyone,

Your inputs are so much appreciated. I have a bunch of great insight to digest here and a weekends worth of work on my hands I think!

I will keep you all posted with the process. Thanks again,

Garrett

 

[chicopee]

The surface temperature of the roller where contact is made with the web should not change that much, therefore, you can think of that temperature to be constant along the area of contact. You can estimate how long it will take to cool down the web as long as you know the thermal conductivity, density and specific heat of the web, and the convective heat transfer coefficient on the air side of the web. As stated above, you can compare that time with the time of contact.

 

[dvd]

I recommend that you build a tester and use in conjunction with calculations. One aspect that you will have a hard time modeling is the contact pressure and conduction from an uneven chilled roll surface (microfinish) and surface irregularities on the web. I like cyphering answers with equations quite a bit, but to witness the cooling process in person is invaluable.

There is a boundary layer of air traveling with the web and the roll, when you bring the web into contact with the chilled roll there will be a layer of air separating the web from the roll surface and preventing good surface contact along with unwanted cooling of hitch-hiking entrained air.

A few rhetorical questions:

What happens when the dewpoint in the plant is higher than 60F? Is your sweaty roll going to ruin product? Is the cooling capacity going to go toward creating condensate? How thick is the web? Is it a good conductor? Are you just going to cool the lower surface? Why aren't you considering forced convection? What is your source for the chilled water? (I assume that it is recirculating water, otherwise 50 gpm starts to add up) Would a similar amount of cooling applied via cooled air deserve a look? Is there any chance for buildup of the web material on the chilled roll surface, which would limit the heat transfer capability of the roll?

 

[Dougt115]

You can design your spreadsheet into an array.
Across the top is the temperature aligned with the axis of the roller.
Down is the temperature of the sheet running over the roller.

Start with the initial conditions.
Solve the first row and first columns of the array as a 2D model for the temperatures, a simple heat exchanger.
Then use these rows for your new initial conditions to progressively fill in the array.

You can plot the results on a 3D graph to see the temperature variations from intake to output.

Assumptions:
The leading edge of the roller is 60 degrees F all the time.
No convection
The temperature in the roller has a constant gradient from the leading edge to the following edge, intake to output.

 

[grausch13]

Hi Guys,

I've taken much of your advice and have made nice progress:

I've assembled an equation to predict the temperature of the outer surface of the roller needed to cool down the substrate for a given amount of time (which coincides with how long the web is in contact with the roller). Basically, it amounts to the transient temperature profile of a plane wall (the substrate or web) given a constant wall temperature and an initial temperature. The equation I used was (T(x,t)-Ts)/(Ti-Ts) = erf (x/(2*sqrt(alpha *t))), where T(x,t) is the temperature at location x (the thickness of the web), Ts is the temperature of the surface, and Ti is the initial temp of the web/substrate. t is the time in contact with the roller. Any thoughts on the validity of using this equation for this instance?

Knowing the temperature of the outer surface of the roller and the amount of energy needing removal from the web (function of line speed, web thickness, web width, density, and specific heat, think q=mc delta T) I can calculate the temperature of the inside wall of the roller shell (Q = kA(delta T)/L, where L is the thickness of the wall) and thus can calculate the temperature the fluid needs to be on the inside of the roller (Q = hA(delta T), where h is the film coefficient)So, In theory (and I could be way off here, but I'm hoping one of you gentlemen, or ladies, can steer me clear) I have all the pieces to the puzzle.

I do recognize a few issues with this. member "DVD" pointed out that air entrapment comes into play. This is especially true at fast speeds. I need to address this somehow. The other main issue is accounting for the contact resistance between the roller and substrate. Any thoughts on the best way to tack that one - I believe this contact resistance could possibly be a big design factor along with the air entrapment.

dougt115, I like the sound of the spreadsheet idea, but I don't quite think I follow...

Thanks again guys, I've gotten quite a lot of insight and I really appreciate it.

Garrett