Electrical machines can be classified into two categories - radial and axial flux machines. Radial flux machines are more common and are in use for long time. Though axial flux machines are not that new, their use has been increased only during the past two decades. The difference as their names imply is that in axial flux the magnetic flux direction is parallel to the machine rotation axis whereas in radial flux machines, the magnetic flux direction is radial.
Figure 1 - Main components of radial and axial flux machines  Figure 2 - Axial flux motor devepoled by Magnax 
Why Axial flux machine is considered superior to Radial flux machine?
In the radial machine, the flux path is much longer than axial machine because it goes from one rotor pole to the first tooth in stator, Then through the stator back iron to the second tooth until it reaches the another rotor pole again. Opposite to the radial machine, the axial flux machine has shorter and direct flux path. It goes directly from one to another pole through the airgap. The magnetic field remains strong along the shorter path which help to increase the efficiency and the power density of the machine.
In figure 4, 2D simulations created by EMWorks2D show the magnetic flux path and direction in both machines.
Figure 3 - Direction of magnetic field in both radial and axial flux machines  Figure 4 - Flux lines generated by EMWorks2D 
In the radial machine, the flux has a 2-dimensional path. Thus, grain-oriented steel cannot be used in these machine types. While in the axial machine, the magnetic flux path is unidirectional which allows the use of grain-oriented steel. Due to the higher permeability of this steel type, the iron losses in an axial flux machine can be decreased, and the efficiency can be increased up by 2%.
Figure 5 - Difference between grain oriented and non-oriented steel  Figure 6 - The magnetic field vector direction
Axial flux machine has an important advantage compared to radial machine in term of winding. It has a higher active winding copper and less overhang which means more ability to increase the number of turns and less heat caused by end effect. Moreover, winding can be in contact with aluminum which is good heat conductor. This means an easier cooling system. The heat in a radial machine should be evacuated through the stator core made of steel that has a low thermal conductivity.
Figure 7 - Comparison between winding of a radial flux concept and Magnax axial flux
Figure 8 - Example of an axial flux motor with aluminium housing 
Comparison between two examples of radial and axial flux generator simulated with EMS
To help us in understanding this difference between radial and axial flux machines, EMS for SOLIDWORKS was used to study the two machines. The first machine is the radial interior PM synchronous machine (Figure 9) used in the 2004 model of Toyota Prius (hybrid car) and the second one is 24 poles double sided rotor axial flux generator (Figure 10).
Both generator models are seamlessly built inside SOLIDWORKS and the simulations are performed using EMS coupled to SOLIDWORKS motion. The no-load voltage results of both machines are shown in Figure 11. The radial PM machine generates an output voltage of 80V while the axial flux machine provides an output voltage of 86V. The axial flux machine provides higher output power with less material and more compact structure.
Figure 9 - Radial interior permanent magnet synchronous machine
Figure 10 - Axial flux permanent magnet machine
Figure 11 - Data comparison between radial and axial flux machines