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Main >> Applications >> Sample problems >> Heating and cooling of a slot of an electric machine

Heating and cooling of a slot of an electric machine

Two armature bars laying in the slot produce ohmic loss. Cooling is provided by convection to the axial cooling duct and surfaces of the core.

Problem Type:

Plane-parallel multiphysics problem of the Steady-state heat transfer coupled to Transient heat transfer.

Slot of an electric machine During the loading phase the slot is heated by the power losses in copper bars Wedge Insulation Copper Copper Steel Cooling duct 69 mm 29 mm 20 mm 105 mm Ø 15 mm Ø 690 mm Ø 480 mm T = +20°C T = +40°C

All dimensions are in millimeters. Stator outer diameter is 690 mm. Domain is a 10-degree segment of stator transverse section.

Outer stator surface convection boundary condition: 20 W/K·m2, 20°C.

Heat Conductivity

Specific Heat

Mass Density

Steel core




Copper bar




Bar insulation








During the loading phase the slot is heated by the power losses in copper bars. The specific power loss is 360000 W/m3. When unloaded, the power loss is zero.
We suppose the temperature of contacting air to be the same for both phases of working cycle. In turn, the convection coefficients are different, because the cooling fan is supposed to be stopped when the motor is unloaded.

Convection coefficient (W/K·m2),
temperature of contacting air (°C)



Cooling duct

150 W/K·m2, 40°C


Inner stator surface

250 W/K·m2, 40°C


We assume the uniformly distributed temperature of 20°C before the motor was suddenly loaded. The cooling conditions supposed to be constant during the heating process. We keep track of the temperature distribution until it gets almost steady state. Then we start to solve the second problem - getting cold of the suddenly stopped motor. The initial temperature field is imported from the previous solution. The cooling condition supposed constant, but different from those while the motor was being loaded.

Each phase of the loading cycle is modeled by a separate QuickField problem. For the cooling phase the initial thermal distribution is imported from the final time moment of the previous solution.

Temperature vs. time dependence at the bottom of the slot (where a temperature sensor usually is placed).

electric machine operation cycle temperature

  • Video:
  • View simulation report in PDF
  • Download simulation files (files may be viewed using any QuickField Edition).
    See problems THeat1Ld.pbm for loading, THeat1S2.pbm for the stopped state.

    QuickField 6.4