Abstract We study the melting dynamics of a phase change material by the action of thermocapillary driving. The geometry corresponds to squares and rectangles with a top free flat surface. We simulate a phase change material with Prandtl number Pr ~ 60 in the liquid phase and two Stefan numbers S t e = 0.67 and S t e = 0.33 . The interplay between conduction and convection dominated regions within the liquid phase of the PCM determines the melting dynamics. We find that some magnitudes follow simple power laws; such as the position of the melting front, the time to full melting, and the input of energy into the system. In addition, we find that the dynamic Marangoni number scales with the Nusselt number as a power-law Nu ~ Maα, where the exponent α depends on the aspect ratio of the geometry and position of the melting fronts at the surface and bottom. These scalings prevail in a wide range of Marangoni numbers and are only slightly affected by the Stefan number.

中文翻译：

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由热毛细作用驱动的熔化过程中的缩放定律

摘要 我们通过热毛细管驱动的作用研究相变材料的熔化动力学。几何图形对应于具有顶部自由平面的正方形和矩形。我们模拟液相中 Prandtl 数 Pr ~ 60 和两个 Stefan 数 S te = 0.67 和 S te = 0.33 的相变材料。PCM 液相内传导和对流主导区域之间的相互作用决定了熔化动力学。我们发现一些量级遵循简单的幂律；例如熔化前沿的位置，完全熔化的时间，以及输入系统的能量。此外，我们发现动态马兰戈尼数与作为幂律 Nu ~ Maα 的 Nusselt 数成比例，其中指数 α 取决于几何形状的纵横比以及表面和底部熔化前沿的位置。这些标度在广泛的 Marangoni 数中普遍存在，并且仅受 Stefan 数的轻微影响。