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On the problem of heat transfer in phase-change materials for small Stefan numbers |
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| Affiliation: | 1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China, 200092;2. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China, 200092;3. Department of Civil Engineering, Tianjin University, Tianjin, China, 300072;1. Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, No. 3-11, Wenhua Road, Shenyang 110004, PR China;2. Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMAP, Grenoble F-38000, France;3. School of Metallurgy, Northeastern University, Shenyang 110004, PR China;4. Laboratoire de physique des matériaux, Université Amar Telidji-Laghouat, Route de Ghardaia - BP 37G, Laghouat, Algeria;5. College of Material Science and Opto-electronic Technology, University of Chinese Academic Sciences, Beijing 100049, China |
| Abstract: | The problem of solidification of an infinite liquid slab by linear convection cooling from the adjacent air is considered. It is assumed that at the initial moment the slab has a critical temperature and that on one side the air temperature has diurnal fluctuations of relatively small amplitude. The solution is found in the form of power series of small parameters. The first three terms of each series are obtained. This permits construction of a simple formula for the total solidification time. Evaluation of the accuracy of the solution based on the integral heat balance equation is suggested. Some particular cases of the problem are considered on the assumption that one side of the slab is insulated. One of these cases is the simplest Stefan problem which has an exact solution. Comparison with this solution is made. |
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