The topic of this Master Thesis is the multi-physics modelling of a magneto-rheological braking system developed by IEHV- Innovative Electric and Hybrid Vehicles - Research Group. This component is a part of ZEDS, the Zero-Emissions Driving System which can be used in electric vehicle to reduce the emissions generated by brakes. Such a component integrates an In-Wheel Electric Motor and a braking system. The functioning of this last one is based on the magneto-rheological properties of the fluid (MRF) placed between a rotor and a stator. Consequently, the emissions of the electric vehicles are drastically reduced because friction-based braking technology is no more used, as a consequence, no particulate matters emitted by such a component.