Abstract In this study, a two dimensional enthalpy-based lattice Boltzmann method was developed to simulate the non-Newtonian melting process inside an enclosure. To examine the effect of power-law indexes in the phase change process, Nusselt number and the position of melting front for flow exposed to different flow behavior indexes ( 0.8 − 1.8 ) and Rayleigh number (50000, 170000, 840000) were investigated. Results show that as flow behavior index increases for a flow with a given Rayleigh number, average Nusselt number at hot wall and the rate of melting decrease. In order to verify the accuracy of proposed numerical scheme, step-by-step verification of sub-models is explained in detail.

中文翻译：

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使用格子 Boltzmann 方法对对流非牛顿幂律固液相变的数值模拟

摘要 在这项研究中，开发了一种基于二维焓的晶格玻尔兹曼方法来模拟外壳内的非牛顿熔化过程。为了检查幂律指数在相变过程中的影响，研究了暴露于不同流动行为指数 (0.8 - 1.8) 和瑞利数 (50000, 170000, 840000) 的流动的努塞尔数和熔锋位置。结果表明，对于给定瑞利数的流动而言，随着流动行为指数的增加，热壁处的平均努塞尔数和熔化速率会降低。为了验证所提出的数值方案的准确性，详细解释了子模型的逐步验证。