Effect of surface heat exchange on phase change materials melting with thermocapillary flow in microgravity

Abstract

A numerical analysis of the melting of n-octadecane in microgravity is presented for a small aspect ratio rectangular container. The container is bounded above by an air layer that exchanges heat with the phase change material (PCM) and supports thermocapillary convection in the liquid phase. The air temperature is assumed to match the applied temperatures at the lateral walls and to change linearly between them. The effect of key dimensionless parameters is investigated including the Marangoni number (Ma), which quantifies the heat transport due to the thermocapillary flow, and the Biot (Bi) number, which characterizes the heat exchanged across the PCM/air interface. Several different dynamic regimes are distinguished according to whether the flow is quasi-steady or oscillatory; the latter may be characterized by an oscillatory standing wave (OSW), a hydrothermal traveling wave, or a novel type of thermal traveling wave (TTW). The results are summarized with a stability map in terms of Bi and Ma. Notably, there are parameters where the flow undergoes transitions between distinct regimes during melting, including a transition between the TTW and OSW modes and other regions where the oscillatory flow undergoes a homoclinic bifurcation. The effect of Bi on heat transport is also investigated and shown to be particularly relevant for small Ma.