Friction stir welding (FSW) has many promising industrial applications due to its solid-state nature and the associated benefits it can offer, such as low cost and small distortion and residual stress, etc. However, challenges exist like serious tool wear and lack of welding depth and slow welding speed when FSW is used, especially, to join materials like steels and titanium alloys. Electricity-assisted FSW (EAFSW) has been proposed to improve this technique in this aspect. In a typical EAFSW process, transport phenomena like the generation and transfer of the frictional heat between tool shoulder (and pin) and the work-piece, the electrical resistance heat, the dissipation heat due to the plastic deformation, the stirred material flow due to the spinning of the tool, and the cooling process are critical in determining the weld quality. In this study, mathematical models for a typical EAFSW process are developed to study the aforementioned transport phenomena and the entire welding process. The validated models can be further used to optimize the friction welding process to achieve quality welds.