Mathematical modeling of the heat process in closure electrical contacts with a heat source

This study presents a mathematical model that describes the heat process during the vaporization of metal at electrical contacts. The arc erosion model for the micro-asperity in the liquid state is established using a one-phase Stefan problem. Two problems involving Joule heating effects on the generalized heat equation are considered. The solution of these two problems is based on the similarity principle, which allows for the reduction of the problem to ordinary differential equations. The existence and uniqueness of the solutions are proven using fixed point theory in a Banach space. Additionally, a solution for the particular case of constant thermal coefficients is provided.