A mathematical model to describe the heat transfer and fluid flow in the mu
tually 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 set
s of governing equations and auxiliary formulas, controlling the weld pool
and plasma are systems respectively, were solved by a finite difference met
hod. A boundary-fitted coordinate system was adopted because the free surfa
ce has a curved and unknown shape during welding. The results of this work
provide a fundamental basis for predicting the behavior of an integrated we
ld pool and are system from first principles.