Solving heat conduction problems in the start-up stage of direct chill casting processes via a temperature-enthalpy mixed formulation based on the improved element-free Galerkin method

•A temperature-enthalpy formulation based on element-free Galerkin methods is proposed.•The procedure is proven to be useful in solidification problems with moving boundaries.•Convergence under Newton-Raphson scheme is easy to achieve during phase change.•Smoothness and continuity features often unfeasible with mesh-based methods are achieved. A novel approach to solve the transient heat conduction problem with moving boundary and solid↔liquid phase change involved in the start-up stage of direct chill casting (DCC) processes is introduced in this work, which is based on the improved element-free Galerkin (IEFG) method. The procedure is developed under a temperature-enthalpy mixed formulation of the internal energy balance, but the construction of improved moving least squares (IMLS) is required only to approximate temperature. The reliability and suitability of this approach have been first proven in a 1-D alloy solidification benchmark problem with exact solution, and subsequently used to solve a more complex three-dimensional applied thermal problem concerning the start-up stage of the DCC process of an aluminium alloy slab. The domain growth conditioned by the bottom block (moving boundary) is modelled moving down the nodes used to represent the problem domain at each time step, and adding a new nodes plane at the domain upper boundary. Outcomes have revealed the usefulness of this technique to overcome the difficulties concerning solid↔liquid phase change marked non-linearities and moving boundaries involved in the transient analysis of DCC heat transfer problems, allowing the achievement of accurate and stable results in a remarkably simple manner.