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Exact solution for a Stefan problem with latent heat a power function of position

机译：潜热的Stefan问题的精确解是位置的幂函数

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摘要

A one-phase Stefan problem with latent heat a power function of position is investigated. The second kind of boundary condition is involved, and the surface heat flux is considered as a corresponding power function of time. The problem can be viewed as a special case of the shoreline movement problem under the conditions of nonlinear variation of ocean depth and a surface flux that varies as a power of time. An exact solution is constructed using the similarity transformation technique. Theoretical proof for the existence and the uniqueness of the exact solution is conducted. Solutions for some special cases presented in the literature are recovered. In the end, computational examples of the exact solution are presented, and the results can be used to verify the accuracy of general numerical phase change algorithms.
机译：研究了潜热与位置幂函数的一相Stefan问题。涉及第二种边界条件，并且表面热通量被视为时间的相应幂函数。在海洋深度和表面通量随时间变化的非线性变化条件下，该问题可以看作是海岸线运动问题的特例。使用相似变换技术构造精确的解决方案。对精确解的存在性和唯一性进行了理论证明。文献中提出的一些特殊情况的解决方案得到了恢复。最后，给出了精确解的计算示例，其结果可用于验证通用数值相变算法的准确性。

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  • 来源
  • 作者

    Yang Zhou; Yi-jiang Wang; Wan-kui Bu;

  • 作者单位

    State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, Jiangsu, PR China,School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, Jiangsu, PR China,State Key Laboratory for Ceomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, Jiangsu, PR China;

    State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, Jiangsu, PR China,School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, Jiangsu, PR China;

    State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, Jiangsu, PR China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Stefan problem; Variable latent heat; Exact solution; Similarity transformation;

    机译：斯蒂芬问题;可变潜热;确切的解决方案;相似度转换;

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