# THeat1: Heating and Cooling of a Slot of an Electric Machine

Problem Type:
The plane-parallel problem of heat transfer with convection.

Geometry:

All dimensions are in millimeters. Stator outer diameter is 690 mm. Domain is a 10-degree segment of stator transverse section. Two armature bars laying in the slot release ohmic loss. Cooling is provided by convection to the axial cooling duct and both surfaces of the core.

Given:

1. Working cycle
We assume the uniformly distributed temperature 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 –cooling 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.

2. Material Properties
The thermal conductivity values are the same as in the Heat1 example. For transient analysis the values of specific heat C and volume density are also required:

 Heat Conductivity (W/K·m) Specific Heat (J/kg·K) Mass Density (kg/m3) Steel Core 25 465 7833 Copper Bar 380 380 8950 Bar Insulation 0.15 1800 1300 Wedge 0.25 1500 1400

3. Heat sources and cooling conditions
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 are zero. We suppose the temperature of contacting air to be the same fro 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·m2) Temperature of contacting air (°C) Convection coefficient (W/K·m2) Temperature of contacting air (°C) Inner stator surface 250 20 20 20 Outer stator surface 70 20 70 20 Cooling duct 150 20 20 20

Solution:
Each phase of the loading cycle is modeled by a separate QuickField problem. For the loading phase the initial temperature is set to 20°C, for the cooling phase the initial thermal distribution is imported from the final time moment of the previous solution.

Moreover, we decide to break the cooling phase into two separate phases. For the first phase we choose time step as small as 100 s, because the rate of temperature change is relatively high. This allows us to see that the temperature at the slot bottom first increases by approximately 1 grad for 300 seconds, and then begins decreasing. The second stage of cooling, after 1200 s, is characterized by relatively low rate of temperature changing. So, we choose for this phase the time step to be 600 s.

For heating process the time step of 300 s is chosen.

Results:

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

Please see following problems in the Examples folder: