Element-free Galerkin formulation for solving transient heat transfer problems of direct chill casting processes

Abstract

ABSTRACTThe present work has been conducted in order to develop a novel solution for the transient heat transfer problem during the startup phase of a direct-chill casting (DCC) process by using the element-free Galerkin method (EFGM). The material domain evolution is conditioned by a bottom block, which represents the material moving boundary. The governing equations have been solved on the basis of this global weak formulation under a Lagrangian description during the startup phase, and coupled with an Eulerian description once the block has reached the lower boundary of the computational domain along the casting direction. Finally, the EFG formulation has been adapted to an axisymmetric temperature transient problem over an aluminum alloy round billet. The feasibility and suitability of this novel approach has been verified by comparison with the numerical techniques proposed and the results reported by other researchers. The results have revealed that this technique could be used successfully in the solution of the DCC heat transfer problem during the startup phase.