In this paper a two‐dimensional model of fluid and heat flow in weld pools is considered and a solution methodology is presented that is based on a perturbation expansion with the Prandtl number as a small parameter. This allowed us to determine the temperature field efficiently and by using it to determine the location of the phase front to map the molten region into a semicircular region in which the Boussinesq form of the Navier–Stokes equations were solved. Doing so allows the domain to be represented with a much smoother phase boundary than is usual in phase change problems. The flow in the weld pool made with a moving laser shows vigorous convection on the solidification side of the weld pool and crowding of the isotherms on the melting side.