# Edible Oils as Practical Phase Change Materials for Thermal Energy Storage
## 3 Results and Discussion
### Thermal Energy Storage with Coconut Oil in a Residential Greenhouse
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \(\Delta_{\text{fus}}H/\text{J g}^{-1}\) & \(T_{\text{mp}}\)\({}^{\text{a}}\)\({}^{\text{b}}\)C & **Comment** \\ \hline
**M1** & \(8\pm 1\) & \(35.5\pm 1.5\) & Small \(\Delta_{\text{fus}}H\) value. Thermally unstable after the first melt. \\  & & & Supercools by about 20 K in the DSC. \\ \hline
**M2** & \(7\pm 1\) & \(33.0\pm 1.5\)\({}^{\circ}\)C & Small \(\Delta_{\text{fus}}H\) value. Thermally unstable after the first melt. \\  & & & Supercools by about 20 K in the DSC. \\ \hline
**VS** & \(12\pm 1\) & \(44.8\pm 1.5\) & Small \(\Delta_{\text{fus}}H\) value. Better thermal stability than margarine. \\  & & & Supercools by about 15 K in the DSC. \\ \hline  & & & Large \(\Delta_{\text{fus}}H\). Thermally stable after 200 melt-freeze cycle. \\  & & & Supercooling decreases as the cooling rate decreases, and can be \\ R-CNO & \(105\pm 11\) & \(24.5\pm 1.5\) & negligible for a bulk sample. \(C_{p,\text{s}}\) = 1.6 \(\pm\) 0.2 J K\({}^{-1}\) mol\({}^{-1}\); \\  & & & \(C_{p,\text{l}}\) = 2.2 \(\pm\) 0.2 J K\({}^{-1}\) mol\({}^{-1}\); \(\kappa_{\text{s}}\) = 0.19 \(\pm\) 0.2 W m\({}^{-1}\) K\({}^{-1}\); \\  & & & \(\kappa_{\text{l}}\) = 0.17 \(\pm\) 0.2 W m\({}^{-1}\) K\({}^{-1}\). \\ V-CNO & \(106\pm 11\) & \(23.9\pm 1.5\) & Large \(\Delta_{\text{fus}}H\). Thermally stable after 200 melt-freeze cycle. \\  & & & Supercooling decreases as the cooling rate decreases. Thermal \\  & & & properties similar to those of R-NCO. \\ \hline \hline \end{tabular} \({}^{\text{a}}\) Based on peak temperature from DSC results.  
\end{table} 
Table 3: Summary of the thermal properties results obtained for the edible oils investigated in this study. inside temperature at 20 \({}^{\circ}\)C. The total heat load, \(Q_{\rm HL}\), calculated from the heat transfer equation in this simplified model is given by [51]:  
\[Q_{HL}=~{}A_{\rm c}~{}u~{}D~{}\Delta T, \tag{1}\]  
where \(A_{\rm c}\) is the total surface area of the greenhouse cover, \(u\) is the heat transfer coefficient, and \(D\) is the total duration of heating. For a greenhouse with a twin-wall polycarbonate panels [50], we take \(u\approx\) 3.3 W m\({}^{-2}\) K\({}^{-1}\)[51]. We also consider that the duration of heating is \(D=\) 10 h. The total surface area of the polycarbonate cover calculated from the dimensions of the greenhouse under consideration (Figure S8 in Supplementary Materials) is \(A_{\rm c}\cong\) 60 m\({}^{2}\). Therefore, for \(\Delta T=\) 10 K, the calculated total heat load is \(Q_{\rm HL}=\) 71.3 MJ. The total heat stored in 1 kg of R-CNO on melting, \(Q_{\rm R\text{-}CNO}\), is the sum of the sensible heat and latent heat of fusion \(\Delta_{\rm fus}H=\) 105 kJ/kg (Table 3). If the temperature inside the green house increases during the day from \(T_{1}=\) 20 \({}^{\circ}\)C to \(T_{2}=\) 30 \({}^{\circ}\)C, \(Q_{\rm R\text{-}CNO}\) is calculated from:  
\[Q_{R\text{-}CNO}=\int\limits_{T_{1}}^{T_{mpt}}mC_{p,\delta}\text{d}T+m\Delta_{ fus}H+\int\limits_{T_{mpt}}^{T_{2}}mC_{p,\delta}\text{d}T~{}, \tag{2}\]  
where \(T_{\rm mpt}=\) 24.5 \({}^{\circ}\)C, the heat capacity of solid R-CNO is C\({}_{\rm p,s}\) = 1.7 kJ K\({}^{-1}\) kg\({}^{-1}\) and that of the liquid is \(C_{\rm p,l}\) = 2.2 kJ K\({}^{-1}\) kg\({}^{-1}\), as determined above. (The actual temperature rise should be less, due to the mitigation of the PCM, but note that the dominant term in Equation (2) is due to the enthalpy of fusion.) Therefore, for 1 kg of R-CNO \(Q_{\rm R\text{-}CNO}\cong\) 125 kJ. Within the same temperature range, 20 to 30 \({}^{\circ}\)C, 1 kg of water stores sensible heat only (no phase transition in this range) with a value of \(Q_{\rm water}\cong\) 42 kJ [57]. Given the calculated value of \(Q_{\rm R\text{-}CNO}\), the total mass of R-CNO required to store thermal energy equivalent to \(Q_{\rm HL}\) (71.3 MJ) is 570 kg which is equivalent to a volume of 630 L (considering the density of coconut oil is 0.90 kg/L [58]).