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.
Development of the solid–liquid interface, distribution of the particle concentration field, as well as the development of thermosolutal convection during solidification of colloidal suspensions in a differentially heated cavity are investigated. The numerical model is based on the one-fluid mixture approach combined with the single-domain enthalpy porosity model for phase change, and it is implemented in fluent software package. The linear dependence of the liquidus and solidus temperatures with the concentration of the nanoparticles was assumed. A colloidal suspension consisting of water and copper or alumina nanoparticles were considered. In the current investigation, the nanoparticle size selected was 5 and 2 nm. The suspension was solidified unidirectionally inside a square differentially heated cavity that was cooled from the left side. It was found that the solid–liquid interface changed its morphology from a planar shape to a dendritic one as the solidification process proceeds in time, due to the constitutional supercooling that resulted from the increased concentration of particles at the solid–liquid interface rejected from the crystalline phase. Initially, the flow consisted of two vortices rotating in opposite directions. However, at later times, only one counter clockwise rotating cell survived. Changing the material of the particle to alumina resulted in crystallized phase with a higher concentration of particles. If it is compared to that of the solid phase resulted from freezing the copper–water colloidal suspension. Decreasing the segregation coefficient destabilizes the solid–liquid interface and increases the intensity of the convection cell with respect to that of the case of no particle rejection. At slow freezing rates, the resulting crystal phase consisted of lower particle content compared to the case of higher freezing rate.
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