# average thermal conductivity (?)

by KyoYeoon
Tags: electric motor, thermal conductivity, thermal resistance, thermodynamics
 P: 5 Hey all, i'm trying to set up a thermal model of a permanent magnet synchronous electric motor. This by doing a lumped system analysis of the motor. In the thermal network that I've set up, I'm trying to introduce an equivalent thermal conductivity value (W/mK) for the copper conductors plus their insulation. This way I can introduce one thermal resistance in the network for the conductors in the stator. The thermal conductivity of the insulation is 0.22 W/mK and the typical thermal conductivity of copper is 390 W/mK. Is there a way to get an average thermal conductivity value from these? Can I simply add them up and devide by 2? please help, regards, Kyo.
 Sci Advisor PF Gold P: 11,383 I don't understand the basis for your model. There is no thermal equivalent to Reactance, and this is quite relevant to the behaviour of a motor. The only valid analog between thermal and electrical systems would, afaik, involve thermal and electrical resistances.
 P: 5 I do believe I mentioned the term Thermal Resistance..... But yeah, I'm building a thermal resistance network to model the electric motor. The thermal resistance of a cylinder is given as: R_th= LN(R/r)/k*2∏*L i'm considering 1/18 of the stator, and therefore i have to introduce a correction value, which is known to me, the only thing i miss right now is a thermal conductivity that can be plugged in. So again my question is, can I determine a equivalent thermal conductivity value from the given two....
PF Gold
P: 11,383

## average thermal conductivity (?)

Sorry - I may have got the wrong end of the stick here. You want to calculate how hot the motor will get. It's an electric model of a thermal system - not specifically an electric motor.
It looks like you have a power source (hot wires) and a number of series thermal resistive elements with a radiative element, finally.
Thinking aloud, as it were . . . .That, at its simplest, would be a current source in series with two series electrical resistances. This would represent the thermal power dissipated internally (a fixed amount, hence the current source), a resistor for the conduction path and a resistor representing the radiative path - assuming a sink at 300K. At equilibrium, the coil temperature and the motor surface temperature would correspond to the voltages at the current source terminal and the junction of the two resistors. The 'radiation' resistor would be non-linear and would follow the Stefan Boltzman law (4th power of the temperature difference).
 P: 5 We're almost on common ground now! I want to determine the thermal "bottlenecks" within the electric motor. This by doing a lumped system analysis of the motor, e.g. determining all the different thermal resistances of the different parts of the motor. I choose the copper winding cores as the primary heat source, so that the motor heats up from the windings. The heat flow is equivalent with the copper loss term. So that would mean P=I^2 * R, which is the current source in the model ( one of many, every loss term is equal to a current injection within the thermal resistance network). So yes i do agree with your story. BUT, back to the question, to determine the thermal (equivalent) resistance of the windings, including their insulation within the stator slots, I'd like to introduce only ONE thermal resistance. This means I want to bypass the fact that there are 780 different conductors running through 1/18 th of the motor, with each of those 780 conductors/wires their own insulation. To bypass this, I need to know if I can determine a thermal conductivity term (k) which is a "educated guess" of the complete thermal conductivity value of copper+insulation. I just want to simplify the winding part of the thermal model, so all the other resistances, e.g. radiation and convection, plus conduction to the rotor part of the motor are all evaluated.