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inductor air solenoid heating

rf_engineer_5

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Are there some formulas for how one can calculate the steady state temperature (or temp rise) of a wound air solenoid at a given high frequency and applied current through it?
This would be for frequencies around 10MHz for example.
The solenoid would have physical dimensions but just looking for a way to incorporate those dimensions into a calculation.
As an example problem:
freq is 10MHz
applied current is 4Arms
inductance is 400nH (about 25ohms reactance)
the Q of the solenoid is 300 (then the calculated resistance is 0.084 ohms, which is R =|25|/300)
the power dissipated is I^2 * R, which is 4*4 * 0.084 = *16 = 1.34W
How do I get a temperature from this point?
 
You can get a clue from ampacity tables which list a safe Ampere level for a single wire or wound wires. Somewhere is a formula telling what level makes a given gauge 'too hot'.

Some links:


https://technifest.com/technical-documents/wire-guage/




Here's a link to another wire gauge table. Its ampacity values are much different than the other tables.


Possible reason for the disparity: One source may base ampacity on a higher temperature which makes the wire get too hot to hold, while the other source may use a lower temperature where copper's electrical characteristics start to change even though it is only warm.


--------------


 
Last edited:
You need an estimation of thermal resistance Rth, dimension K/W. It's a function of surface area, form, convection or forced air cooling. Tables should be available in literature.

I am not sure what literature to look in. Are you talking about a book? IEEE papers? This is not something I have done in the past so I don't know what I don't know.
 
You can get a clue from ampacity tables which list a safe Ampere level for a single wire or wound wires. Somewhere is a formula telling what level makes a given gauge 'too hot'.

Some links:


https://technifest.com/technical-documents/wire-guage/




Here's a link to another wire gauge table. Its ampacity values are much different than the other tables.


Possible reason for the disparity: One source may base ampacity on a higher temperature which makes the wire get too hot to hold, while the other source may use a lower temperature where copper's electrical characteristics start to change even though it is only warm.


--------------



Going the ampacity tables is not bad but the values listed are usually DC or 50/60Hz. As frequency goes up this all goes out of the window. I do have access to a 3D solver but there must have been a way to hand calculate before 3D solvers came about.
 

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