Mathematical modeling of the thermal process of arc erosion with current carrying heating effect in a temperature gradient

• Published in: Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2024-09, Vol.11, p.100888, Article 100888
• Main Author: T.A., Nauryz
• Format: Article
• Language: English
• Subjects: Fixed point theorem; Generalized heat equation; Nonlinear thermal coefficient; Similarity transformation; Stefan problem; Thomson effect; Vaporization
• ISSN: 2666-8181; 2666-8181
• DOI: 10.1016/j.padiff.2024.100888

This paper presents a mathematical model aimed at comprehensively understanding the thermal processes associated with arc erosion of closed electrical contacts triggered by the instantaneous explosion of micro-asperities including Thomson effect and Joule heat source. The phenomenon involves vaporization and liquid zones, and the temperature distribution is governed by a generalized heat equation, accounting for the heating effect due to current flow in temperature gradients and effect of heat source. The proposed model allows for a nuanced analysis of the thermal dynamics, shedding light on the complex phenomena involved in arc erosion. The proposed method in this paper employs similarity transformation techniques to effectively reduce the complexity of the problem, transforming it into a set of manageable ordinary differential equations. The study establishes the existence and uniqueness of the solution through rigorous analysis. The behavior of the solution of the problem is successfully considered for special cases of Thomson and thermal coefficients. By leveraging similarity transformations, the paper offers a powerful approach for unraveling the intricacies of the thermal processes in arc erosion of closed electrical contacts, providing valuable insights into the phenomena associated with current-carrying heating in the presence of temperature gradients.