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首页> 外文期刊>Materials Science and Engineering >Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects
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Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects

机译：Darcian多孔半导体熔体外壳中水肿玛龙龙对流流动的数值模拟，具有浮力和发热效应

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摘要

We present a mathematical and numerical study of the transient Marangoni thermo-convection flow of an electrically conducting Newtonian fluid in an isotropic Darcy porous rectangular semiconductor melt enclosure with buoyancy and internal heat generation effects, in an (x, y) coordinate system. The governing equations comprising the mass conservation, x-direction momentum, y-direction momentum and energy equation are formulated subject to a quartet of boundary conditions at the four walls of the enclosure. The upper enclosure wall is assumed to be "free" with an appropriate surface tension dynamic boundary condition. A series of transformations are implemented to render the mathematical model dimensionless and into a vorticity form. The governing thermophysical parameters are shown to be the Marangoni number for surface tension (thermo-capillary) effects {Ma), Prandtl number (Pr), Grashof number for buoyancy effects (Gr), enclosure aspect ratio (A), Hartmann hydromagnetic number (Ha), Darcy number for bulk porous resistance (Da), and the internal heat generation parameter (Γ) the latter being a function of the internal (Ra_I) and global Rayleigh numbers (Ra). An efficient finite difference numerical method is employed to solve the boundary value problem. Validations with earlier purely fluid solutions (Da →∞) are included. A mesh-independence test is included with further validation with other published studies. Isotherms and isovels (streamlines) are computed as are Nusselt numbers at selected boundaries. Solutions for the case of Pr - 0.054 (semiconductor melt) are also compared with earlier studies showing excellent correlation. The model finds applications in the bulk crystal growth of semiconductors, electromagnetic materials processing control and also hybrid fuel cells.
机译：我们在（X，Y）坐标系中，在各向同性达西矩形矩形半导体熔体外壳中的瞬态Marangoni热对流流体的瞬态Marangoni热对流流动的数学和数值研究。包括大规模保护，X方向动量，Y方向动量和能量方程的控制方程被制定为在外壳的四个壁的边界条件的四四方。上外壳壁被认为是“自由”，具有适当的表面张力动态边界条件。实现了一系列转换以使数学模型无量纲和涡旋形式。控制热物理参数被证明是表面张力（热毛细管）效应的Marangoni号码（热毛细管）{ma），prandtl编号（pr），浮力效应的Grashof编号（gr），外壳纵横比（a），hartmann水磁性数（ HA），散装多孔电阻（DA）和内部发热参数（γ）的达西数，后者是内部（RA_I）和全局瑞利数（RA）的函数。采用有效的有限差分数值方法来解决边界值问题。包括较早纯净的流体解决方案（DA→∞）的验证。与其他公布的研究进一步验证，包含网眼独立测试。在所选边界处计算等温线和Isovels（简化）是何种营销号码。与早期相关的早期研究相比，对PR-0.054（半导体​​熔体）的情况的解决方案也与显示出优异的相关性。该模型在半导体，电磁材料处理控制和混合燃料电池的散装晶体生长中找到了应用。

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  • 来源
    《Materials Science and Engineering》 |2020年第11期|114722.1-114722.23|共23页
  • 作者

    O. Anwar Beg; K. Venkatadri; V. Ramachandra Prasad; T.A. Beg; A. Kadir; Henry J. Leonard;

  • 作者单位

    Multi-Physical Engineering Sciences Group Aeronautical/Mechanical Engineering Salford University School of Science Engineering and Environment (SEE) Manchester M54WT UK;

    Dept Mathematics Sreenivasa Institute of Technology/Management Studies Chittoor Andhra Pradesh 517127 India;

    Dept Mathematics School of Advanced Sciences Vellore Institute of Technology Vellore 632014 India;

    Engineering Mechanics Research Israfil House Dickenson Rd Manchester M13 UK;

    Multi-Physical Engineering Sciences Group Aeronautical/Mechanical Engineering Salford University School of Science Engineering and Environment (SEE) Manchester M54WT UK;

    Multi-Physical Engineering Sciences Group Aeronautical/Mechanical Engineering Salford University School of Science Engineering and Environment (SEE) Manchester M54WT UK;

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  • 正文语种 eng
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  • 关键词

    Marangoni convection; Hydromagnetics; Porous media; Darcy model; MAC computation; Heat source; Semiconductor melt; Buoyancy; Materials processing;

    机译：Marangoni对流;水肿;多孔介质;达西模型;MAC计算;热源;半导体熔体;浮力;材料加工;

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