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

In the framework of the #nite element method, a temperature-based thermally coupled 3ow formulation including phase-change e;ects 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 #xed #nite element mesh is used to avoid the di?culties 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 di;erentially heated recipient using distinct geometric aspect ratios