Anyway I need a place to start with heating and controlling the temperature of aluminum flat stock. Is it as simple as a current controlled supply feeding power through the bar with a temp sensor feedback? Also how do I make sure the entire element maintains an even temperature? I'm assuming power needed is calculated by the current and the resistance properties of the aluminum but how do you determine thermal conductivity and efficiency?
Nah, if it was that easy it wouldn't be any fun
Trying anyway, you'd quickly get into trouble where they were terminated - aluminum oxide manifests faster than you can remove it (literally, scrape with a knife on a piece of alu and right at the back of the edge, oxide will have formed).
Add to that, the fact that aluminum expands and contracts a lot in such app. (Just listen to an "iron" when it's heating up or cooling down).
Haven't you ever opened an iron? On the aluminum plate is a conventional heating element, similar to what's in a cooker and that's what you need to replicate - along the entire length of the bar.
Using a single heating element and a bar of a certain thickness, it will have the same temperature along its length. Just make sure you don't loose heat where it's fastened, or you may get lower temps there.
Use some kind of spring loading to hold the heating element, as it will have a different expansion than the alu and will have to be able to keep different rates, dor the bar will bend.
I think a much better way to do this would be a couple of heated (motorized) rollers where the hem is run through. This would take some arrangement like a couple of light gates to ensure the fabric is going straight and stays far enough in between the rollers and perhaps some means to brake either "side" of the hem to steer it straight.
At least, it would be cheaper and would work with any
length of fabric.