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A mathematical model to describe the heat transfer and fluid flow in the mutually coupled weld pool and are by an interactive free surface of the pool for a stationary gas tungsten are welding (GTAW) is developed. The two sets of governing equations and auxiliary formulas, controlling the weld pool and plasma are systems respectively, were solved by a finite difference method. A boundary-fitted coordinate system was adopted because the free surface has a curved and unknown shape during welding. The results of this work provide a fundamental basis for predicting the behavior of an integrated weld pool and are system from first principles.

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