Application of the heat-balance integral to an inverse Stefan problem |
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| Affiliation: | 1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;2. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19839, Iran;1. CEA/DEN Cadarache/SMTA/LPMA, 13108 St Paul lez Durance Cedex, France;2. CEA/DEN Grenoble/STCP/LTDA, 17 Rue des Martyrs, 38000 Grenoble, France;3. CEA/DEN Cadarache/STCP/LHC, 13108 St Paul lez Durance Cedex, France;1. Division of Casting of Metals, Department of Materials Science and Engineering, Royal Institute of Technology, Brinellvägen 23, 100 44 Stockholm, Sweden;2. Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland;1. Instituto de Matemática Pura e Aplicada – IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, RJ, 22460-320, Brazil;2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brazil |
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| Abstract: | Most phase change process controls are concerned with the inverse Stefan problem. In this paper, the heat-balance integral method is applied effectively to analyze the one-region and two-region inverse Stefan problems in Cartesian and spherical coordinates. It is shown that if the movement of the phase change boundary is specified arbitrarily the present technique to predict both the temperature and its gradient at the fixed boundary is simple and accurate. As numerical illustrations, the one-dimensional inward solidification problem in Cartesian and spherical coordinates are solved and discussed in detail when the movement of the phase change interface is specified as a power function. The accuracy of these approximate solutions, based on the heat-balance integral method, is demonstrated satisfyingly by comparison with the available exact and/or numerical solutions for the one-region and the two-region problems. |
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