Numerical Solutions of Moving Boundary Problem with Thermal Convection in the Melt and Magnetic Field During Directional Solidification

1999 ◽  
pp. 295-309
Author(s):  
M. El Ganaoui ◽  
P. Bontoux ◽  
D. Morvan
Keyword(s):  
Magnetic Field ◽  
Boundary Problem ◽  
Directional Solidification ◽  
Thermal Convection ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Moving Boundary Problem

The Method of Fundamental Solutions for the Moving Boundary Problem of the One-Dimension Heat Conduction Equation

2014 ◽  
Vol 1039 ◽  
pp. 59-64 ◽  
Author(s):  
Xin Jiang ◽  
Xiao Gang Wang ◽  
Yue Wei Bai ◽  
Chang Tao Pang
Keyword(s):  
Heat Conduction ◽  
Boundary Problem ◽  
Heat Conduction Equation ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Fundamental Solutions ◽  
Metal Wire ◽  
Moving Boundary Problem ◽  
Conduction Equation ◽  
Temperature Function

The melting of the material is regarded as the moving boundary problem of the heat conduction equation. In this paper, the method of fundamental solution is extended into this kind of problem. The temperature function was expressed as a linear combination of fundamental solutions which satisfied the governing equation and the initial condition. The coefficients were gained by use of boundary condition. When the metal wire was melting, process of the moving boundary was gained through the conversation of energy and the Prediction-Correlation Method. A example was given. The numerical solutions agree well with the exact solutions. In another example, numerical solutions of the temperature distribution of the metal wire were obtained while one end was heated and melting.

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