Modeling and simulating transient close-contact melting via space-time finite elements

Abstract

Close-contact melting phenomena occur when a heated body is in contact with a solid phase-change material. Deter-mining the velocity at which the heat source melts through the solid is fundamental to investigate the process and extrapolate it to operating conditions that cannot be replicated by experiments. Available results in the literature consider a thermo-mechanical equilibrium in the contact film and thus derive a constant melting velocity. In this work we relax this assumption and present a transient contact melting model for a planar heat source. After solving for the heat equation in the solid phase with a space-time finite element approach, the transient heat flux around the heated body is used to compute the time-dependent melting velocity. With the latter we can update the computational domain via a mesh-update method, so that the displacement of the heat source is represented over time. To demonstrate the potential of our approach, we introduce a numerical example with a 2D test case. Afterwards, we show the evolving position of the heat source and we compare the transient melting velocity against the equilibrium estimate. A more complex time-dependent input power is then considered in view of realistic applications.