Exact solution to a Stefan-type problem for a generalized heat equation with the Thomson effect

Abstract

We study a one-dimensional Stefan type problem which models the behavior of electromagneticelds and heat transfer in closed electrical contacts that arises, when an instantaneousexplosion of the micro-asperity occurs. This model involves vaporization, liquid and solid zones, inwhich the temperature satises a generalized heat equation with the Thomson eect. Accountingfor the nonlinear thermal coecient, the model also incorporates temperature-dependent electricalconductivity. By employing a similarity transformation, the Stefan-type problem is reduced to asystem of coupled nonlinear integral equations. The existence of a solution is established using thexed point theory in Banach spaces.