Numerical Simulation of the Effect of the Size of Suspensions on the Solidification Process of Nanoparticle-Enhanced Phase Change Materials

Nanostructure-enhanced phase change materials (NePCM) have been widely studied in recent years due to their enhanced thermal conductivity and improved charge/discharge in thermal energy storage applications. In this study, the effect of the size of the nanoparticles on the morphology of the solid–liquid interface and the evolving concentration field during solidification is reported. Combining a one-fluid-mixture approach with the single-domain enthalpy-porosity model for phase change and assuming a linear dependence of the liquidus and solidus temperatures of the mushy zone on the local concentration of the nanoparticles subject to a constant value of the segregation coefficient, thermal-solutal convection as well as the Brownian and thermophoretic effects are taken into account. A square cavity containing a suspension of copper nanoparticles (diameter of 5 and 2 nm) in water was the model NePCM considered. Subject to a 5 °C temperature difference between the hot (top) and cold (bottom) sides and with an initial loading of the nanoparticles equal to 10 wt. % (1.22 vol. %), the colloid was solidified from the bottom. The solid–liquid interface for the case of NePCM with 5 nm particle size was almost planar throughout the solidification process. However, for the case of the NePCM with particle size of 2 nm, the solid–liquid interface evolved from a stable planar shape to an unstable dendritic structure. This transition was attributed to the constitutional supercooling effect, whereby the rejected particles that are pushed away from the interface into the liquid zone form regions of high concentration thus leading to a lower solidus temperature. Moreover, for the smaller particle size of 2 nm, the ensuing solutal convection at the liquid–solid interface due to the concentration gradient is affected by the increased Brownian diffusivity. Due to size-dependent rejection of nanoparticles, the frozen layer that resulted from a dendritic growth contains regions of depleted concentration. Despite the higher thermal conductivity of the colloids, the amount of frozen phase during a fixed time period diminished as the particle size decreased.