AbstractIn this work, a twin‐roll strip casting industrial process is analysed using a fixed‐mesh finite element formulation able to deal with unsteady incompressible thermally coupled flows including phase‐change and non‐Newtonian effects assumed to account for the flow behaviour during the whole cooling conditions. The weak form of the full Navier–Stokes equations is obtained using a generalized streamline operator in order to stabilize its numerical response while a temperature‐based algorithm is applied to describe the latent heat release. This proposed methodology is tested in a two‐dimensional analysis of a twin‐roll casting problem where an evaluation of different thermal and flow patterns is performed. Copyright © 2003 John Wiley & Sons, Ltd.