# Thermal Energy Storage Performance of Tetrabutylammonium Acrylate Hydrate as Phase Change Materials
## 3 Results and Discussion
### In the System with Mechanical Agitation  
As written in 3.1., the surface of the heat exchanger coil was covered by hydrate. This hydrate adhesion increased thermal resistance. To solve this problem, mechanical agitation was used. In addition, to investigate the effect of the rotation rate, we changed the rate to 100 rpm, 300 rpm and 600 rpm. Figure 6a-c shows the time evolution of T\({}_{\text{in}}\), T\({}_{\text{out}}\) and T\({}_{\text{PCM}}\) in each rotation rate. Time zero was defined as the time at which the circulating water is started to be flown. In every rotation rate, T\({}_{\text{PCM}}\) decreased twice after the experiment started and temporarily increased. In the agitated system, T\({}_{\text{PCM}}\) increased earlier than the static system. As the rotation rate became quicker, T\({}_{\text{PCM}}\) increased earlier. When T\({}_{\text{PCM}}\) increased, the temperature was around 282 K, which is the same as the static system. This result indicates that the forced convection generated by the agitation increased the convective heat transfer coefficient, which resulted in faster cooling of the heat storage medium and thus faster nucleation. T\({}_{\text{PCM}}\) increased rapidly more than the static system, which was almost vertically to around 288 K. This would be due to the increase in heat and mass transfer rates caused by the forced convection generated by the agitation, which led to the increase in the hydrate growth rate. T\({}_{\text{PCM}}\) changed from a rise to a fall around 288 K and then descended slowly. As the hydrate grew, the viscosity of the heat storage medium increased and the forced convection was weakened, which lowered the hydrate formation rate. T\({}_{\text{PCM}}\) decreased because the hydrate growth rate became smaller, and the heat absorption by the heat exchanger exceeded the heat generated from hydrate formation. Figure 7a-c shows the pictures of crystal growth in the system when the mechanical agitation rate was 300 rpm. At t = 0.6 h, numerous small crystals began to float in the aqueous solution. After t = 0.7 h, hydrate was formed in the entire aqueous solution. The hydrate nucleation occurred in the entire aqueous solution. This was because of the forced convection generated by the agitation, which stripped the hydrate from the heat exchange coil and suspended it in the aqueous solution. This convection increased the hydrate growth rate as well. Within a few minutes, the heat exchange coil was only faintly visible  
Figure 5: Time evolution of thermal energy storage rate and density in static system. (**a,b**) depict the thermal energy storage rate and density, respectively. by the hydrate, as shown in Figure 7b. The hydrate formation has progressed and the viscosity increased as shown in Figure 7c, after which little change was observed. Figure 6: Time evolutions of the temperature at inlet of the chiller (T\({}_{\text{in}}\)), outlet (T\({}_{\text{out}}\)) of the chiller and thermal energy storage medium (T\({}_{\text{PCM}}\)) in the system with the mechanical agitation. (**a–c**) depict each curve at the agitation rate of 100 rpm, 300 rpm and 600 rpm, respectively. Figure 7: Optical observation changing in the container with mechanical agitation of 300 rpm. (**a–c**) are the pictures at 0.6 h, 0.7 h and 1 h after cooling water started to be circulated, re-spectively. We visually observed that TBAAc hydrate formed and grew to the bulk of the solution. The gap between the heat transfer surface and the corner of the container was about 5 cm. In other words, when the cooling temperature was 10 K lower than the equilibrium temperature, TBAAc hydrate formed and grew at a distance of more than 5 cm from the heat transfer surface in the agitated system. The same tendency was observed at the rotation rate of 100 rpm and 600 rpm. Figure 8a shows the time evolution of thermal energy storage density. To make a comparison with the static system, the time evolution of the static system is also shown in Figure 8a.