# Demonstration of Phase Change Thermal Energy Storage in Zinc Oxide Microencapsulated Sodium Nitrate
## 2 Materials and Methods
A stainless-steel envelope covers the insulation to a final cylinder length of 0.95 m and diameter of 0.6 m. Material loading gates (three 20 mm diameter holes) are placed at the top of the storage tank and accessible from outside by cap closed tubes that span the thermal insulation. The heat exchanger is made of a SS 316 tube (12 mm outer diameter, 10 mminner diameter, 5.04 m length), shaped as a helical-coil wrapped around the longitudinal axis in 15 loops (120 mm diameter). Mineral oil is used as a heat transfer fluid (HTF) at a temperature that is maintained by an external recirculating pump with heating/cooling capability. Temperatures were continuously monitored (digital recording) by eight type J thermocouples (T1-T8) placed as indicated in Figure 1. For the 50 to 400 \({}^{\circ}\)C measurement interval, the thermocouples were linearly calibrated to work within a \(\pm\)1.5 \({}^{\circ}\)C reading error. T3, T4, and T5 measured temperatures inside the tank, at the central longitudinal axis, and they protruded to their measurement spot through tank-fixed one-end-closed tubular sheets (5 mm outer diameter, 3 mm inner diameter, 0.5 m long). The relative positions of the protruding thermocouple sheets and heating coil loops were designed to maximize the separation space and avoid contact. Temperatures were monitored across the energy storage material for two sections that are transversal to the tank cylinder, by placing T1 and T2 directly on the outer surface of the tank cylinder, at the same longitudinal positions as their corresponding T4-T3 (respectively) pair. T7 and T8 were in direct contact with the heating coil at the tank-envelope entry and exit points. The installation is pictured in a previous publication ([PERSON] et al., 2019) ([PERSON] et al., 2019). Tank heating-cooling cycles. Precise amounts of microcapsules were successively loaded into the storage tank (as powder) to total 15.75, 19.232, and 22.067 kg. After each load, the tank was subjected to several charge-self-discharge cycles. A cycle consists of a heating phase, when HTF (360-375 \({}^{\circ}\)C) circulates inside the heat exchanger until T1 to T5 readings are all above the melting temperature of sodium nitrate, then it follows the self-discharging phase when the HTF pump is off and the tank is left to cool by itself downward to room temperature. **Adapted calorimetric method**. To assess the amount of thermal energy available as latent heat in the storage tank, a heat flow calorimetry method was developed. It is based on temperature monitoring in key points inside and outside the tank, thus estimating the heat loss through the thermal insulation of the tank. The method considers a quasi-static approximation to [PERSON]'s law:  
\[\text{Q}/\text{dt}=-\text{K}\text{\Delta}\text{T}_{\text{in-out}},\]  
with dt as the time interval for measurements, short enough to approximate a constant \(\text{\Delta}\text{T}_{\text{in-out}}\). The approximation is intended to simplify the calculation, as it was determined that the use of differential form to account for \(\text{\Delta}\text{T}_{\text{in-out}}\) changes does not significantly improve the precision for a narrow temperature interval around 300 \({}^{\circ}\)C. In the tank setup, at the time-point t, \(\text{\Delta}\text{T}_{\text{in-out}}=\text{t}\text{T}1-\text{t}\text{T}6\), where tT1 and tT6 are the temperatures indicated by T1 and T6, respectively. Figure 1: Schematic drawing of the prototype tank (median longitudinal section—viewed from the top): light blue—microapsules, green—T1 to T8 thermocouples, yellow—insulation, red—heat exchanger. T6 is the room temperature thermocouple. For two different material loads of the tank with masses m\({}_{1}\) and m\({}_{2}\), it may be written:  
\[\mathrm{Q_{m1}}/\,\mathrm{dt_{1}}=-\mathrm{K}\;\mathrm{\Delta T_{in\text{-out}}} \tag{1}\]  
\[\mathrm{Q_{m2}}/\,\mathrm{dt_{2}}=-\mathrm{K}\;\mathrm{\Delta T_{in\text{-out}}} \tag{2}\]  
where K is a proportionality coefficient for heat transfer from the storage tank to the environment.