Mathematical modeling of heat process in a cylindrical domain with nonlinear thermal coefficients and a heat source on the axis

Abstract

A mathematical model of the heat process in one-dimensional domain which consists of a Stefan problem governed by a cylindrical heat equation with a heat source on the axis z=0 and nonlinear thermal coefficients is studied. The developed model is particularly applicable for analyzing temperature variations on electrical contact surfaces, where precise thermal management is crucial for ensuring optimal performance and preventing overheating. The use of similarity transformation allows us to obtain an equivalent system of nonlinear integral equations that is solved by applying a fixed point theorem, providing a rigorous mathematical foundation for our analysis.