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Determination of the heat-transfer coefficient during solidification of alloys

机译：合金凝固过程中传热系数的确定

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摘要

We consider a three-phase inverse Stefan problem. Such a problem consists in a reconstruction of the function describing the coefficient of heat-transfer, when the positions of the moving solid and liquid interfaces are well-known. We introduce three partial problems for each phase (liquid, solid and mushy) separately. The solutions of these problems are used for the determination of the unknown heat-transfer coefficient. The missing data for a mushy (solid) phase are computed from over-determined data at the moving liquid (solid) interface taking into account the transmission condition. At the end we present numerical calculations in one dimension using piecewise linear continuous finite elements in order to demonstrate the efficiency of the designed numerical algorithm.
机译：我们考虑三相反斯蒂芬反问题。当移动的固体和液体界面的位置是众所周知的时，这样的问题在于重构描述热传递系数的函数。我们分别为每个阶段（液体，固体和糊状）引入三个部分问题。这些问题的解决方案用于确定未知的传热系数。糊状（固相）相的缺失数据是根据流动条件（在流动的液体（固相）界面）的超额确定数据计算得出的。最后，我们提出了使用分段线性连续有限元的一维数值计算，以证明所设计数值算法的效率。

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