Unsteady, axisymmetric transport of mass, momentum, energy, species, and magnetic field intensity with a mushy-zone phase change in workpieces and temperature, and magnetic fields in electrodes during resistance spot welding, are systematically investigated. Electromagnetic force, joule heat, heat generation at the electrode–workpiece interface and faying surface between workpieces, different properties between phases, and geometries of electrodes are taken into account. The computed results show consistencies with observed nugget growth, electrical current, and temperature fields. The effects of the face radius and cone angle of the electrode, parameters governing welding current, electrical contact resistance, magnetic Prandtl number, electrical conductivity ratio, and workpiece thickness on transport phenomena are clearly provided.