Abstract
ABSTRACT This study presents a mathematical model for the thermal dynamics of arc erosion in closed electrical contacts, incorporating a heat source and nonlinear thermal coefficients within a Stefan‐type model. The model describes temperature distribution during metal vaporization, utilizing a spherical heat equation with Joule heating and free boundary determination. A similarity transformation technique is applied to reduce the problem to an ordinary differential equation, enabling rigorous mathematical analysis. The existence and uniqueness of solutions are established using fixed‐point theorems in Banach spaces. Additionally, an explicit solution is derived for the case of constant and linear thermal coefficients, providing valuable insights into phase transition dynamics. The novelty of this study lies in its integration of nonlinear thermal behavior within a spherical heat conduction model, leading to an exact solution under constant thermal coefficients. This work provides new theoretical insights into phase transition processes in electrical contacts and has practical implications for enhancing the reliability and efficiency of electrical devices.