Efficient aluminum foil heat transfer design

[Butters]

Aluminum foil reels have to be preheated for manufacturing but it's inefficient (the doors aren't sealed and the material isn't in close contact with heating elements at the sides). I'm considering an initiative of more efficient design.
How difficult would it be to evaluate heat transfer if each real is also in a plastic bag (so I have to consider different mediums)? Since it's aluminum foil I guess I should go with conduction and try to design heating elements tightly around each reel. The goal is to heat the the material fast to 50C thoroughly but never going over 60C.
I'll also have to consider rate of return, you think such custom design would be expensive?

 

[Baluncore]

Are you using foil from the roll as part of a fabrication process? Why does it need to be heated? How wide is the foil strip?

Depending on roll width, it might be quite difficult to heat a roll of foil because the multiple layers of metal, surface sapphire and air on the roll will each form an impedance mismatch that will reduce heat-flow. I know that trying to melt a tight wound roll of foil in a furnace is very difficult.

You might consider using induction heating to heat the foil as it comes from the roll. Temperature measurement could be by non-contact IR thermometer with feedback to regulate the induction heater.

Alternatively pass the foil between heated rollers like the fuser unit used to fix the toner in a photocopier or laser printer.

 

[Butters]

At the moment I can only provide approximate specs but here's the deal:
The foil is about 18cm in width, 30cm in diameter and inner core of about 10cm in diameter;
It is in a plastic bag that cannot be opened during heating because the menthol would evaporate;
It's the kind of foil that's tin one side and paper on the other;
After heating it has to be in the range of 35C to 60C throughout.

If I had all the conduction indexes maybe I could at least evaluate it theoretically. I'd have to somehow calculate heat flow to the bag, through the air in the bag, to the foil through all double sided layers of it considering the dimensions and everything. You think it's too complex?

 

[Butters]

Could you at least take me through calculations to evaluate heat flow in the reel? The model seems to be quite complicated:
a - width, b- inner core diameter, c - outer diameter;
th - thickness of one layer, l - length of unwrapped foil.

∆Q/∆t = -K×A×∆T/th -- (wikipedia)
∆Q/∆t is the rate of heat flow; -K - thermal conductivity factor; A - surface area; ∆T - change in temperature; th - thickness of the material

How do I transform this equation for multi-layered material transfer flow, i.e. foil wrapped around itself?
The goal is to find out how long would it take for the entire reel to reach above 35C degrees heating it in 60C degrees camera.

 

[Baluncore]

I guess heat will diffuse in from the long edge of the foil strip where it is exposed at the ends of the cylindrical spool. This is a diffusion problem. The question becomes; “How long must you place the spool in an oven at 60°C in order for all the foil to exceed 35°C”.

Maybe experiment by heating a known normal temperature roll in an oven at 60°C for a fixed time, say one hour. Then block the ends of the spool with thermal insulation and roll the spool in insulation. Let the spool sit for a while to equilibrate to a stable temperature, measure the equilibrated temperature inside the spool core to get an estimate of the rate of heat flow into the spool.

Maybe heat rolls in a 60°C oven, but for different durations. Then monitor the foil temperature as it is unrolled and record those profiles. If foil is used at a fixed rate, thermal equilibration deep in the spool can continue while the first part of the spool is being used. That will provide a data base of profiles from which the minimum pre-heat time can be selected.

 

[Butters]

I see, so no theoretical evaluation is possible?
Actually, I am intrigued by your earlier suggestion to use induction heating. The foil is cigarette inner liner like - would it respond to induction heating? Maybe having a coil around it in a certain way would be energy and time efficient. The temperatures aren't high and I've seen some heavy duty induction heating online.

P.S. Do you want to PM about this because it's just us in the Thread?

 

[Baluncore]

Induction heating would require little power. The inductor coils would be flat against the foil, there is no need to thread the foil through the coil. The coils could be on the paper side with the IR temperature measurement on the foil side. But what are you trying to regulate? The temperature of the oil in the paper or the metal foil.

Others are watching, they may join as the discussion continues. There are also those who may find the thread later through a search. So it is probably better to avoid PMs and stay in this thread.

 

[Butters]

Yes, the oil has to reach at least 35C to soak in (otherwise it crystallizes again and interferes with foil processing). It probably wouldn't work to heat up the whole bobbin due to penetration depth but heating the foil as it weaves out sounds good. Of course it raises the question whether the short amount of time between heat up and manufacturing would be enough for the oil to soak in.
Also, I was unfortunate to find an equation including temperature with induction heating, it just gets real messy with all those magnetic/electric properties. How to evaluate this without an experiment?

 

[256bits]

You can also consider infrared heaters to heat your unwrapped reel, and possibly during processing if necessary.
Wiki gives a brief,
http://en.wikipedia.org/wiki/Infrared_heater

For heating the reel this way, possibility of "hot spots" should be minimized, and the whole reel temperature more easily regulated, from the fact that the plate temperature can be made more even, if you use two plates as heating elements pressed against either side of the reel.

You have to match the infrared wavelength of the lamp with the absorption of the plates for most efficiency of capturing the radiation, so you would have to do some research on that.

 

[256bits]

View attachment 79550
Could you at least take me through calculations to evaluate heat flow in the reel? The model seems to be quite complicated:
a - width, b- inner core diameter, c - outer diameter;
th - thickness of one layer, l - length of unwrapped foil.

∆Q/∆t = -K×A×∆T/th -- (wikipedia)
∆Q/∆t is the rate of heat flow; -K - thermal conductivity factor; A - surface area; ∆T - change in temperature; th - thickness of the material

How do I transform this equation for multi-layered material transfer flow, i.e. foil wrapped around itself?
The goal is to find out how long would it take for the entire reel to reach above 35C degrees heating it in 60C degrees camera.

One thing you do not know is the thermal conductivity through the plastic covering from the heating element to the foil, ( including of course air gaps and whatnot between heating plate, plastic, and foil ) , so that is something you either have to guestimate or test.

You do know, though the mass of the reel, which includes the aluminium and the paper and the menthol, and the percentages of each in the foil.
Using the specific heat of each substance, you can calculate the total amount of heat that has to be transferred to the reel to raise its temperature from initial to final.
This figure you need regardless of how you heat the reel.

You can look at Newton's Law of Cooling, and work that into your problem.
Description,
http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html
http://amrita.vlab.co.in/?sub=1&brch=194&sim=354&cnt=1

The closer the object gets to its desired temperature, as time goes by the rate of heat transfer decreases and with that the rate of temperature change also decreases.

Not sure how close to Newton's Law of Cooling applies with induction heating.

 

[Butters]

I do realize that I'm drifting a bit off our topic now but I'd like you to take a different angle. Do you see any possibilities to improve already existing box shaped heating oven for those bobbins? As you can see, shelves can be adjusted to stack bobbins differently (parallel to the bottom, sides etc.). The problem is that the ones in the middle which are further from the heating elements take longer time. Maybe there's a better heat transfer medium than air which could be introduced?