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

LIAO Fucheng; ZU Cuie; ZHENG Liancun; WANG Zidong; LI Weidong

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

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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

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

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

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

Received Date: 2003-03-28

Abstract

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