Controlling Phase Interface Motion in Inverse Heat Transfer Problems with Solidification

Abstract

In this paper, an inverse numerical model is presented for solidification problems. It is used to predict the transient boundary conditions, which produce a prescribed interfacial surface motion and heat transfer. The formulation calculates the required boundary temperature to provide a specified velocity of the phase interface during solid-liquid phase transition. A control-volume-based finite element method is employed for the numerical solution of the energy conservation equation. The finite element framework provides a novel alternative to other inverse techniques based on structured grids. The effects of Stefan number and interface velocity on the solidification processes will be investigated. Numerical examples are presented and discussed for one-dimensional and two-dimensional solidification problems. The accuracy and performance of the formulation are assessed by comparisons with analytical solutions. Based on the model's capability of efficiently providing stable and accurate results, it is viewed to be a worthy design tool in practical engineering applications such as thermal energy storage and materials processing, such as casting and extrusion processes.