Element-Free Galerkin Formulation by Moving Least Squares for Internal Energy Balance in a Continuous Casting Process

Abstract

The present work has been conducted in order to develop an alternative solution to the heat transfer problem in a conventional continuous casting (CC) process using an Element-Free Galerkin (EFG) technique with shape functions formulated by a moving least squares approximation. The Internal Energy Balance Equation (Eulerian Description) has been developed with this weak formulation in order to solve the heat transfer problem. The EFG features and the shape functions construction have also been described. The resulting equation system has been adapted to a 2-D steady-state temperature distribution over the longitudinal thickness of a solidifying wide slab into the mold region. The transport laws, the nonlinear aspects, and the boundary conditions have been specified. Finally, the model has been solved in order to estimate the thermal distribution and the solidified shell evolution. The results have revealed that this technique could be used successfully in the modeling of CC heat transfer problems.