Calculate the temperature of a wire as an electrical current flows through it

[Mr.somebody]

Hey, so I'm just wondering what are the formulas needed to calculate the temperature of a wire after x amount of time as an electrical current is passed through it. I know how to solve for it... I just forgot the formulas.
Thanks

 

[berkeman]

Hey, so I'm just wondering what are the formulas needed to calculate the temperature of a wire after x amount of time as an electrical current is passed through it. I know how to solve for it... I just forgot the formulas.
Thanks

Start with the power being dissipated by the wire, P = R * I^2 where R is the resistance of the wire, and I is the current flowing.

Then things get more complicated. You need the "thermal resistance" from the wire to the surrounding air or other medium. This number is published in the datasheets of heat sinks and for integrated circuits mounted on PC boards, but I don't know offhand where you can find the numbers for wire. It will depend on the wire gauge and insulation thickness mainly. The thermal resistance is in units of degrees C per Watt, so once you have that thermal resistance number, calculating the temperature rise from the power is straightforward...