inductor air solenoid heating

[rf_engineer_5]

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?

 

[BradtheRad]

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:

Wire Gauge: Nikola Tesla Page

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

American Wire Gauge Chart and AWG Electrical Current Load Limits table with ampacities, wire sizes, skin depth frequencies and wire breaking strength

AWG Wire size chart and ampacity table for design engineers including skin depth frequencies and tensile strength data; electrical cable size

www.powerstream.com

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

http://www3.telus.net/chemelec/Projects/Wire/Wire-1.png

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.


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http://www.helukabel.de/pdf/english/technik/X_081_Current_ratings_for_UL-CSA_cables.pdf

Wire Current Calculator

AWG: In the American Wire Gauge (AWG), diameters is generally computed by utilizing the formula D(AWG)=.005·92((36-AWG)/39) inch. For the 00, 000, 0000 etc. gauges you choose -1, -2, -3, helping […]

www.homemade-circuits.com

 

[FvM]

How do I get a temperature from this point?

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.

 

[rf_engineer_5]

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.

 

[rf_engineer_5]

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:

Wire Gauge: Nikola Tesla Page

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

American Wire Gauge Chart and AWG Electrical Current Load Limits table with ampacities, wire sizes, skin depth frequencies and wire breaking strength

AWG Wire size chart and ampacity table for design engineers including skin depth frequencies and tensile strength data; electrical cable size

www.powerstream.com

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

http://www3.telus.net/chemelec/Projects/Wire/Wire-1.png

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.


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

http://www.helukabel.de/pdf/english/technik/X_081_Current_ratings_for_UL-CSA_cables.pdf

Wire Current Calculator

AWG: In the American Wire Gauge (AWG), diameters is generally computed by utilizing the formula D(AWG)=.005·92((36-AWG)/39) inch. For the 00, 000, 0000 etc. gauges you choose -1, -2, -3, helping […]

www.homemade-circuits.com

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.

 

[FvM]

I am not sure what literature to look in.

Technical thermodynamics text books.