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Heating and cooling of a slot of an electric machine
THeat1: 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 problem of heat transfer.
Geometry:
All dimensions are in millimeters. Stator outer diameter is 690 mm. Domain is a 10degree segment of stator transverse section.
Given:

Heat Conductivity (W/K·m) 
Specific Heat (J/Kg·K) 
Mass Density (kg/m^{3}) 
Steel core 
25 
465 
7833 
Copper bar 
380 
380 
8950 
Bar insulation 
0.15 
1800 
1300 
Wedge 
0.25 
1500 
1400 
During the loading phase the slot is heated by the power losses in copper bars. The specific power loss is 360000 W/m^{3}. 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.

Loading 
Stopped 
Convection coefficient (W/K·m^{2}) 
Temperature of contacting air (°C) 
Convection coefficient (W/K·m^{2}) 
Temperature of contacting air (°C) 
Inner stator surface 
250 
40 
 
 
Outer stator surface 
20 
20 
20 
20 
Cooling duct 
150 
40 
 
 
Solution
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.
Results
Temperature vs. time dependence at the bottom of the slot (where a temperature sensor usually is placed).
Download simulation files (THeat1Ld.pbm for loading phase, THeat1S2.pbm for the stopped phase)
Video.