Originally posted by joe shmo
One of our process at the mill I currently work at is electro patenting. It is done in line ahead of a electro plating process. The wire comes in contact with a voltage source and ground as it is passing through the line causing it to heat up, which changes it microstructure etc.. I'd like to try to find the model for the temperature as a function of pos ...[text shortened]... T - T_∞ ) = I² * p / A
Is the term for axial conduction I derrived here in bold legitimate?
Pardon me for sticking in side issues but I have some experience with heat control and one thing for sure, the only time you can ignore heat loss through atmosphere is if there IS no atmosphere, like in a vacuum. In our sputtering and ion milling machines, the substrates gets hot and stays that way since radiation is a poor heat conductor compared to atmospheric heat loss.
We have a pallet coming out of the vacuum system heated to a couple hundred degrees C and sometime there is a delay before we extract the pallet and we find even hours later the pallet is still pretty hot. As compared to exchange to atmosphere and the temperature goes down to handling temps within 5 minutes or so.
Just saying, I think it will be wrong to ignore atmospheric heat loss.
BTW, that is exactly how a TC gauge works, Thermocouple gauge for vacuum. Atmospheric heat loss is so severe that the TC gauge is only accurate to about 1 torr, 1000 millitorr, after that the heat loss is so severe there is no more reading available to the TC. It is reasonably accurate from a few millitorr to 1 torr though because there is so much less air in that level of vacuum.
The TC gauge works like this: There are two very thin wires crossed like an X and one wire goes to a current source with a very well calibrated current source similar to your wire. That current is constant so there is a constant heat flow from the wire.
The other wire is a TC gauge, two wire device. It sits in the center of the heated wire.
It's job is simply to measure the temperature of the heated wire which will go up and down depending on the ambient vacuum in the system. The more air in the system, the lower the temperature reading and the opposite for less air, TC gauge reads hotter. So that is correlated with a vacuum reading, X current out of the TC gauge = Y vacuum reading.
This is a well known way to read vacuum pressures in the 1 to 1000 millitorr range and other techniques are available for ranges outside that level but the gist of this whole thing is the readings are totally unreliable for pressures even at 2 torr, a pretty good vacuum, about the level of the air on Mars.
So just trying to get across your expected temperatures will be pretty far off because of atmospheric heat loss.