Effective convection coefficient for porous interface and solute segregation

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• 作者：A.G. Ostrogorsky ; ^{AOstrogo@iit.edu}
• 关键词：A1. Convection ; A1. Diffusion ; A1. Directional solidification ; A1. Segregation ; A2. Czochralski method ; A2. Growth from melt
• 刊名：Journal of Crystal Growth
• 出版年：2012
• 期刊代码：49_00220248
• 类别：ch
• 出版时间：1 June, 2012
• 卷：348
• 期：1
• 页码：97-105
• 文件大小：1030 K

摘要

Convective heat and mass transfer coefficients are used to calculate the rate at which convection sweeps heat and mass away from the interface. Convection in melt growth is driven by various forces, and the resulting convoluted flows are laminar or turbulent. Furthermore, cross-flow through the 鈥減orous鈥?interface has a profound effect on convection. Thus, a general effective coefficient (h_eff ), which accounts for: (i) uniform flow 鈥渟uction鈥?through the porous interface, (ii) forced and/or natural convection, (iii) laminar or turbulent flow, and (iv) finite Schmidt numbers, is derived. Focusing next on solute segregation, mass conservation is used to derive a simple equation for k_eff (effective segregation coefficient) as a function of h_eff. Here, h_eff is an input, which provides the rate at which convection sweeps the rejected solute away from the interface.

From the general expression, even simpler expressions are developed for restricted range of conditions, e.g., Czochralski growth under forced laminar convection (no natural convection or turbulence). h_eff utilizes numerous established correlations, all developed for impermeable solids.