A fixed‐mesh finite element thermally coupled flow formulation for the numerical analysis of melting processes

In the framework of the finite element method, a temperature‐based thermally coupled flow formulation including phase‐change effects is proposed to study melting processes. The governing equations of the problem, written in terms of its primitive variables, are solved using a generalized streamline operator technique that enables the use of equal interpolation functions for the unknowns: velocity, pressure and temperature. Moreover, a unique fixed finite element mesh is used to avoid the difficulties related to moving meshes. This methodology is applied and assessed in the numerical analysis of a benchmark problem known as the melting process of gallium in a differentially heated recipient using distinct geometric aspect ratios.