Enthalpic lattice Boltzmann formulation for heat conduction during melting of PCMs with embedded solid blocks with different thermophysical properties

Abstract

In this paper, we extend the enthalpic formulation introduced in previous work of Hamila et al. [1], to solve transient conduction heat transfer during melting of phase change material. The volume fraction of liquid phase is described by a Heaviside step function smoothly approximated by a logistic curve having a common "S" shape, also called sigmoid curve. Several conduction test problems during melting of some specific phase change material are simulated and comparisons are made with the control volume solutions. The simulation of conduction heat transfer during melting of commercial PCM filling the cavity, in which one or more circular solid blocks (with enhanced thermophysical properties) are embedded, is performed. The proposed formulation can handle accurately conduction heat transfer problem with phase change including interface evolving over time. Special attention is given to distinction between thermophysical properties of solid and liquid phase which are not equal.