Dynamics of melting in a slab under harmonic heating and convective cooling boundary conditions

Abstract

The dynamics of steady periodic melting-solidification in finite thickness slabs are relevant for numerous natural and engineered systems, including for the thermal management of pulsed power devices. Despite this, the characteristic thermal response and temperature rise at the heated surface of a slab resulting from a simple harmonic heating under convective cooling boundary conditions on the opposing side has not been investigated in detail. This configuration is critical for understanding the frequency regime under which a reversible endothermic transformation (e.g., melting/solidification) in a slab serves to effectively buffer temperature rise at a device surface. This study presents a numerical investigation of steady periodic melting-solidification in a slab due to conductive heat transfer, focusing on the resulting temperature rise and phase lag at the heated surface. The internal temperature distribution within the slab closely follows the transient thermal response of a single-phase material, with the exception of a perturbation within a localized region of frequency and amplitude of the harmonic heating. Within this regime, the melt front exhibits antiresonance with the harmonic heating, resulting in a phase lag and a depression in the peak observed temperature on the heated surface. The peak frequency and amplitude at which this antiresonance occurs decrease as the heat transfer coefficient on the cooling side of the slab decreases. This analysis reveals the interaction between material parameters, the system geometry, and the nature of the boundary conditions and is critical for designing systems that are appropriately tuned to particular heating profiles.