Resistance Heating moving conductor

[osmax67]

I have a 400 amp 0-40 volt dc supply, I need to heat a wire by wrapping it around two bronze/nickel pulleys 12" diameter , with one connected to the positive terminal of the supply and one to the negative. The wire being mild steel .148" diameter moving at a rate of 50' per second with the desired temperature being 400°f , 240" after coming off the second pulley in an controlled environment 80°f .How would you calculate the spacing between the positive and negative pulleys for varying speeds and diameter? Assuming the wires ambient temperature to be 80°f before it is heated and the pulleys have a controlled temperature of 120 °f..

 

[mfb]

Do you have a sketch of the setup? At least for me, it is hard to imagine how it looks like.

 

[osmax67]

Thank you for your interest .

Yes I can send you a cad drawing if you would like.

Its a single continuous strand wrapped a couple times around a pulley at the entry point that would have brushes to provide the voltage and current to the pulley transferred to the wire and then would repeat the wrap around another pulley spaced 20' or so away to increase the resistance, The second pulley would have the opposite polarity . -------o----------------o----------- I have already set this up and it works I would really like to understand more than just the Ohms law part of the equation. The heating of the wire is not from the outside in, or between the two conductors as I had thought originally , but takes time to come to the outer surface after it has passed the pulley contacts.
Again Thanks for you thoughts.

 

[mfb]

Please don't write PMs, I see your replies here.

Okay, so current goes in at one pulley, goes through the wire to the opposite pulley and out there.

The resistance of the contacts to the pulleys would be interesting.
Assuming we can neglect this and the resistance of the pulleys itself: P=UI=U²/R (where the second = is Ohm's law), R will be linear with the length of the wire segment between the pulleys. A shorter wire leads to smaller R and a larger power - until the resistance in the remaining circuit becomes important.
The resistance is the resistivity of your material multiplied by the length and divided by the cross-section of the wire. The resistivity is temperature-dependent, but you can probably use the average temperature to get a reasonable approximation.

Heat losses to the environment are another issue.

 

[256bits]

And the specific heat of the wire is needed to determine the rise in temperature as the current is fed through the wire.