For the thermal modelling of electrical machines, three main methods exist and are used by EOMYS [1]: the lumped method, the finite element modelling and CFD simulation. EOMYS has an expertise in the three methods as each method is complementary with the others. They all have different levels of accuracy and different computational times. Moreover, each method can be used in 2D or 3D.

### Lumped Method

The lumped method (also called Nodal Method or Thermal Network Method) is based on electrical resistances analogy to simulate the thermal behavior of the machine. The model is macroscopic: results will be obtained for elements of the machines (stator teeth, windings, yoke, etc.) instead of having local results. This method can be used in steady or unsteady states with variable external loads (for example, a driving cycle for a car motor). The main advantage of the method is its low computational time: itâ€™s the ideal method for optimization. However, it requires the convective boundary conditions inside the machine. They can be determined using correlations from scientific literature, experimental results or more complex CFD simulations.

### Conductive simulation using Finite Elements Method

Finite Elements Method (FEM) can solve directly the heat equation inside the solid parts of an electric machine. With this type of modelling, the local temperature field can be evaluated: it allows a detailed analysis of hot spots. The mesh of an electromagnetic simulation can be directly used for the thermal modelling and the two resolutions can easily be coupled. The computational time is higher than the lumped method. However, the convective boundary conditions must be imposed like the lumped method: correlations or CFD results must be used.

### CFD Modelling

Computational Fluid Dynamics (CFD) allows a resolution of the flow inside the machine coupled with heat transfer. The required mesh are generally very fine and may depend on the fluid velocity. Computational time is very high. With CFD, there is no need to use correlations from literature the coupled velocity and thermal fields are directly solved. The level of uncertainties is, however, relatively important and the convergence of the calculations is not necessarily guaranteed especially for very unstable flows (high turbulence level, high rotating speed, etc.). A good practice for CFD in electrical machines is to focus on certain elements of the machine and use the results (flow rates, heat transfer coefficients, etc.) in a FEM or lumped model of the full machine. For the cooling of electric machines, CFD is usually done in steady state: the time to reach the steady state of the flow is much lower than the thermal characteristic time, which can reach a few hours.