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The mathematical model describing the dynamics of closed contact heatingwhich involves vaporization of the metal when instantaneous explosion ofmicro-asperity occurs is presented through a Stefan type problem. Thetemperature field for metallic vaporization zone is introduced as heatresistance that decreases linearity. Temperature fields for liquid and solidphases of the metal described by spherical heat equations with nonlinearthermal coefficients and Joule heat source have to be determined as well as thefree boundaries. Joule heating component depends on space and time variablewhen alternating current is considered. Solution method of the problem based onsimilarity variable transformation is applied which enables us to reduce theproblem to an ordinary differential equations and nonlinear integral equations.Existence and uniqueness of the integral equations are proved by using fixedpoint theorem in Banach space.

Mathematical model of thermal phenomena of closure electrical contact with Joule heat source and nonlinear thermal coefficients