Mathematical models of heat and mass transfer in electrical contacts

Mathematical models describing phenomena of heat and mass transfer in electrical contacts are based on systems of partial differential equations for temperature and electromagnetic fields. The influence of Joule, Kohler and Thomson heat sources on the temperature field in closed contacts is discussed. The mathematical model of the ring-shaped welding in closed contacts is presented. Dynamics of contact opening is considered as consecutive stages including the initial stage of heating up to the melting point, the stage of a liquid bridge, metallic and gaseous arc stages. The dimensionless criteria of Thomson and Kohler are introduced which may be responsible for the displacement of the hottest isotherms of a bridge from its middle and corresponding bridge material transfer. The conditions for self-restrained bridge transfer are discussed. Phenomenon of contact floating due to metallic vapour pressure produced by a vacuum micro-arc is investigated experimentally and then described by a mathematical model. A mathematical model is presented describing transient phenomena accompanied a vacuum short arc at the initial stage of contact opening. It enables to describe the evolution of transient short anode dominated arc, which appears just after the rupture of molten bridge, into diffusive cathode dominated arc. The mechanisms of arc erosion are described by several models due to evaporation, droplets ejection, Marangoni effect, ejection of solid particles at thermo-elastic stresses. The hybrid mathematical model is elaborated to describe dynamics of the arc and forces acting in contact gap. It includes experimental oscillograms of current, voltage and contact displacement and nonlinear equations for arc, anode and cathode temperature fields and contact motion. It is shown theoretically and confirmed experimentally that in the range of high current the force of metallic vapour pressure at arcing in vacuum is comparable with magnetic repulsion force and should be taken into consideration.The mathematical model describing transition from arc to glow at contact opening in circuits with a high inductance and small current is elaborated and identified experimentally. The mechanism of thermionic emission from the cathode surface based on Richardson-Dushman equation is corrected by addition of another emission mechanism due to electrochemical phenomena in melted pool on the cathode. The influence of current frequency on the rate of the arc erosion at contact opening is investigated using the model of transition of the metallic arc phase into gaseous phase.