  In this paper we elaborate a hybrid classical-quantum framework which allows
one to model and solve heat and mass transfer problems occurring in electric
contacts. We utilize special functions and Harrow-Hassidim-Lloyd (HHL) quantum
algorithm for finding temperature and arc flux functions exactly and
approximately for the Stefan type problems. The Stefan type problems we are
considering are based on the Generalized Heat Equation with free boundaries. As
examples we consider exact and approximate solutions of inverse one-phase and
two-phase Stefan problems. An Inverse Generalized One-Phase Stefan Problem is
considered as a model problem. Computational experiments were conducted and
demonstrated on IBM Quantum Machine.
