Mathematical modelling of heat transfer in closed electrical contacts and electrical potential field dynamics with Thomson effect

In this study we develop a mathematical model that describe the behavior of electromagnetic fields and heat transfer in closed electrical contacts that arises when instantaneous explosion of the micro-asperity which involves vaporization zone and liquid, solid zones where temperature is defined by a generalized heat equation with Thomson effect. This model account for the nonlinear nature of the thermal coefficients and electrical conductivity depended on temperature. Our proposed solutions are based on similarity transformation which allows us to reduce a Stefan-type problem to a system of nonlinear integral equations whose existence of solution is proved by the fixed point theory in Banach spaces.