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An analytical method for solving the two-phase inverse Stefan problem

Hetmaniok E., Słota D., Wituła R., Zielonka A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 3

583--590

In the paper we present an application of the homotopy analysis method for solving the two-phase inverse Stefan problem. In the proposed approach a series is created, having elements which satisfy some differential equation following from the investigated problem. We reveal, in the paper, that if this series is convergent then its sum determines the solution of the original equation. A sufficient condition for this convergence is formulated. Moreover, the estimation of the error of the approximate solution, obtained by taking the partial sum of the considered series, is given. Additionally, we present an example illustrating an application of the described method.

Identification of the heat transfer coefficient in phase change problems

Słota D.

Archives of Thermodynamics

2010

Vol. 31, no. 1

61-78

In this paper, an algorithm will be presented that enables solving the two-phase inverse Stefan problem, where the additional information consists of temperature measurements in selected points of the solid phase. The problem consists in the reconstruction of the function describing the heat transfer coefficient, so that the temperature in the given points of the solid phase would differ as little as possible from the predefined values. The featured examples of calculations show a very good approximation of the exact solution and stability of the algorithm.