The combined effect of natural and thermocapillary convection on the melting of phase change materials in rectangular containers

Abstract

The results of numerical simulations investigating the influence of natural and thermocapillary convection on the solid/liquid phase transition of n-octadecane in rectangular containers are presented. The melting process is modelled using an enthalpy-porosity formulation of the Navier–Stokes equations. A systematic analysis is performed by varying key dimensionless parameters including the container aspect ratio (Γ), the Rayleigh (Ra) and Marangoni (Ma) numbers, which quantify the strength of natural and thermocapillary convection, and the dynamic Bond number (Bodyn), which measures their relative importance. In large containers with Γ≫1 and Bodyn≪1, thermocapillary convection is shown to significantly accelerate the melting process, enhancing the heat transfer rate of the system by as much as a factor of 20 at large applied Ma. For Γ≲8, this enhancement factor takes reduced values of 1–3 and exhibits relatively weak dependence on Ma. In short containers with Γ≲3 and Bodyn∼O(1), the thermocapillary effect is detrimental on average and increases the total melting time. The presence of normal vertical gravity is seen to stabilise the dynamics of the flow, delaying the appearance of oscillatory convection beyond the range of parameters considered here. By reducing Bodyn, we examine the transition to microgravity and determine the critical value Bodyncr for oscillatory flow at large Ma for the representative aspect ratios 1.5 and 12.