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.

No abstract

No abstract

This paper presents the quasi-stationary Stefan problem in symmetric electrical contacts.The method of the solution can be obtained from the suggestion that the identity of equipotential and isothermal surfaces in contacts, which is correct for stationary fields in linear case, keeps safe for non-linear case as well. The idea is,transform the system of problem which is given in cylindrical coordinates into ellipsoidal coordinates.The analytical solution of stationary Stefan problem is found. Based on that decision was constructed the temperature profile to the approximate solution of heat problem with Joule heating in ellipsoidal coordinates. Keywords: quasi-stationary model, Stefan problem, integral method.