modeling heat transfer/heat loss of solenoid

heyo!

working on a magnetic bearing project, and would like to find change in temperature a chosen distance outside solenoid due to current flow. also would like to find magnetic field and energy lost to heating.

have been working to use "multi-turn coil domain" for solenoid and joule heating for heating part. haven't convinced myself that these are correct/most efficient physics to use for the purpose

any advice or suggestions would be greatly appreciated!
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