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A mathematical model for fluid flow in a weld pool at high currents

In order to determine the heat transfer inside a TIG (tungsten/inert gas) weld pool, it is necessary to have a good understanding of the flow patterns of the liquid metal. The principal force driving the fluid motion is the electromagnetic j × B force due to the current from the welding arc and its self-magnetic field. In this paper we consider the flow of a viscous incompressible conducting fluid in a hemispherical container due to various distributions of the electric current. The problem is posed as a time-dependent problem and is solved numerically using the Du Fort–Frankel leap-frog method. Results are presented for currents of 100 A flowing through the weld pool. This is a typical current for TIG welding, and corresponds to a Reynolds number in the range 200 < Re < 600. Previous solutions of the problem were restricted to low Reynolds numbers, i.e. low currents.