A mathematical formulation is presented for the transient development of the fluid-flow field and the temperature field in a liquid pool, generated by a spatially variable heat flux falling on an initially solid metal block. This physical situation is an idealized representation of a TIG (tungsten-inert-gas) welding process. In the formulation allowance is made for electromagnetic, buoyancy and surface forces and the resultant equations are solved numerically.

It is found that both the convective flow field and the temperature field are markedly affected by the nature of the heat flux and the flux of electric current falling on the free surface.

In the absence of surface-tension effects a broadly distributed heat flux and corresponding current distribution cause a situation where both electromagnetic and buoyancy forces are important in determining the fluid-flow field; however, in these systems the fluid-flow field does not play a significant role in defining the heat-transfer process. In contrast, a sharply focused heat flux and current density on the free surface give rise to strong electromagnetically driven flows, which play an important role in determining the shape of the weld pool.

Calculations are also done exploring the effect of surface-tension-driven flows. It is found that surface-tension gradients may produce quite high surface velocities and can have a profound effect on determining the weld-pool shape.