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

TL;DR

This paper develops a mathematical model for heat transfer and electromagnetic field behavior in closed electrical contacts, incorporating Thomson effects and nonlinear thermal properties, solved via similarity transformation and fixed point theory.

Contribution

It introduces a novel mathematical framework for modeling heat and electromagnetic dynamics in electrical contacts, including Thomson effects and nonlinear material properties.

Findings

Model successfully describes temperature and electromagnetic fields in contacts.

Reduction of complex Stefan-type problem to nonlinear integral equations.

Existence of solutions proved using fixed point theory.

Abstract

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.