控制熔體濃度三維穩定態方程的精確解

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控制熔體濃度三維穩定態方程的精確解

廖福成, 祖翠娥, 鄭連存, 王自東, 李為東

文章導航 > 工程科學學報 > 2004 > 26(1): 53-55

廖福成, 祖翠娥, 鄭連存, 王自東, 李為東. 控制熔體濃度三維穩定態方程的精確解[J]. 工程科學學報, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

引用本文:

廖福成, 祖翠娥, 鄭連存, 王自東, 李為東. 控制熔體濃度三維穩定態方程的精確解[J]. 工程科學學報, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

LIAO Fucheng, ZU Cuie, ZHENG Liancun, WANG Zidong, LI Weidong. Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth[J]. Chinese Journal of Engineering, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

Citation:

LIAO Fucheng, ZU Cuie, ZHENG Liancun, WANG Zidong, LI Weidong. Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth[J]. Chinese Journal of Engineering, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

廖福成, 祖翠娥, 鄭連存, 王自東, 李為東. 控制熔體濃度三維穩定態方程的精確解[J]. 工程科學學報, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

引用本文:

廖福成, 祖翠娥, 鄭連存, 王自東, 李為東. 控制熔體濃度三維穩定態方程的精確解[J]. 工程科學學報, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

LIAO Fucheng, ZU Cuie, ZHENG Liancun, WANG Zidong, LI Weidong. Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth[J]. Chinese Journal of Engineering, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

Citation:

LIAO Fucheng, ZU Cuie, ZHENG Liancun, WANG Zidong, LI Weidong. Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth[J]. Chinese Journal of Engineering, 2004, 26(1): 53-55. doi: 10.13374/j.issn1001-053x.2004.01.015

控制熔體濃度三維穩定態方程的精確解

doi: 10.13374/j.issn1001-053x.2004.01.015

1. 北京科技大學應用科學學院, 北京 100083;
2. 北京科技大學材料學院, 北京 100083

基金項目:

國家重點基礎研究規劃項目(No.G2000067206-1)和北京市科技新星計劃資助課題(No.954811800)

作者簡介:
廖福成男,48歲,教授

中圖分類號: TG111.4
計量
- 文章訪問數: 156
- HTML全文瀏覽量: 43
- PDF下載量: 7
- 被引次數: 0
出版歷程
- 收稿日期: 2003-03-28

Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth

1. Applied Science School, University of Science and Technology Beijing, Beijing 100083, China;
2. Materials Science and Engineering School, University of Science and Technology Beijing, Beijing 100083, China

摘要: 研究了一類關于濃度的三維穩態晶體生長控制方程.這類問題由于帶有遠場條件,無法按常規方法給出其解析解或數值解.在復數域內利用分離變量法,得到了這類方程的級數形式的解析解,而最后的解是實數形式.結果表明,固液界面前沿濃度是指數震蕩衰減的.
- 晶體生長 /
- 分離變量法 /
- 偏微分方程 /
- Fourier級數
Abstract: A class of partial differential equations (PDE) which describe three-dimension steady state crystal growth for concentration were studied. Because there exists far-field condition, their exact solution or numerical solution can not be derived based on known results about PDE. By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained. The result shows that the concentration in the solid-liquid interface is exponentially damped oscillation.
- crystal growth /
- detached variable method /
- partial differential equation /
- Fourier series

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文章訪問數: 156
HTML全文瀏覽量: 43
PDF下載量: 7
被引次數: 0

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