Solving heat conduction problems with phase-change under the heat source term approach and the element-free Galerkin formulation

Abstract

The present work has been conducted in order to introduce an alternative solution for heat transfer problems with phase-change and moving boundaries, via the element-free Galerkin (EFG) method. In this novel approach, the phase-change non-linearity is addressed under the heat source term methodology. For this purpose, the global weak-form of the internal energy balance for such a non-linear transient heat transfer problem has been developed by including the latent heat as a source vector. In order to prove the reliability of this approach, the EFG formulation has been adapted to the solution of a 1-D alloy solidification benchmark problem. The suitability and potentialities of this novel approach have also been depicted in the solution of a variable domain (moving boundary) solidification problem, by considering the start-up stage of a round billet steel continuous casting process as an applied example. Results have revealed that this technique can be successfully used to deal appropriately with the marked non-linearity related to the fusion latent heat release in heat transfer problems with phase change, and its straightforward implementation leads to both accurate and stable numerical results.