The mathematical model describing the dynamics of heating in opening electrical contacts is presented. It takes into account the imperfect thermal contact between anode and cathode due to tunnel effect. The model is based on the system of spherical heat equations in a domain with moving boundary. The analytical solution is found in the form of series containing the integral error functions.

Exact solution of inverse one phase Stefan problem is represented in the form of linear combination of integral error functions. Heat flux function is reconstructed and coefficients of solution function are found exactly. Test problem was considered for engineering purposes and it was shown that by collocation method the error for three points does not exceed 0.01%. Error estimate was calculated by maximum principle.